ملزمة-Hydraulics-Lab-2

8/22/2019 Hydraulics-Lab-2-

1/111

The Islamic University of GazaEngineering FacultyCivil Engineering Department

Hydraulics LabECIV 3122

This course involves conducting a number of lab

experiments to support and verify the principles

taught in fluid mechanics and hydraulics

courses.

2012-2013
http://www.google.com/imgres?imgurl=http://www.michiganboardups.com/images/WATER%20BACKGROUND.jpg&imgrefurl=http://www.michiganboardups.com/&usg=__En9VGFaIY8CZ9WQMdXsQZUNAY44=&h=155&w=155&sz=8&hl=en&start=6&zoom=1&tbnid=D4sm_ZwCGFGsJM:&tbnh=97&tbnw=97&ei=CEYkTrSuH4K2hAfk5Z2aAw&prev=/search?q=water+background&um=1&hl=en&biw=1280&bih=568&tbm=isch&um=1&itbs=1


2/111

Hydraulics Lab - ECIV 3122 Table of contents

I

Contents

Experiment (1): Hydrostatic Force on a Plane Surface 1

Experiment (2): Buoyancy & FlotationMetacentric Height 8

Experiment (3): Impact Jets 24

Experiment (4): Flow Measurement 32

Experiment (5): Flow through orifice 43

Experiment (6): Flow Over Weirs 48

Experiment (7): Investigation of Bernoulli Theorem 56

Experiment (8): Minor Losses 61

Experiment (10): Centrifugal Pump 73

Exercise B 74

Exercise C 79

Exercise D 85

Exercise E 86

Experiment (11): Series and Parallel Pumps 88

Exercise F 90

Exercise G 93

Experiment (12): Open Channel Flow 95

REFERENCES 96

APPENDIX A: Report Cover Page 97

APPANDIX B: FINAL EXAM 2nd Semester 2010-2011 98


3/111

Hydraulics Lab - ECIV 3122 Experiment (1): Hydrostatic Force

1

Exp. (1): Hydrostatic Force on a Plane Surface

Purpose: To verify the theoretical prediction of the resultant hydrostatic force and its

point of action on both (a) partially submerged and (b) fully submerged plane surface

in a liquid.

Apparatus: Armfield Hydrostatic Force Demonstration Unit (Fig1).

Theory:

Review the derivation of the resultant magnitude and point of action of hydrostatic

force on a submerged plane surface. List these expressions for a vertical surface that

is (a) partially submerged, and (b) fully submerged.

(a) When the surface is fully submerged (Fig2):

)2d-(ydbgF (Theoretical)

H12

d

2

da

LgMF

2(Practical)

)2

d-(y

H12

dH

2

P (Centre of pressure)


4/111


2

Figure 2 - Surface is fully submerged

(b) When the surface is partially submerged (Fig3):

ybg0.5F 2 (Theoretical)

3

yda

LgMF (Practical)

y3

2HP (Centre of pressure)

Figure 3 - surface is partially submerged


5/111


3

Procedure:

1. Measure the dimensions a, b and d of the quadrant, and the distance between thepivot and the weight hanger L.

2. Insert the quadrant into the tank locating the balance arm on the knife edges.

Adjust the counter-balance weight until the balance arm is horizontal, as indicatedon the datum level indicator.

3. Add all the weights supplied to the weight. Fill the tank with water until thebalance beam tips lifting the weights then drain out a small quantity of water to

bring the balance arm horizontal, don't level the balance arm by adjustment of the

counter balance weight or the datum setting of the balance arm will be lost.

Record the water level shown on the scale. Fine adjustment of the water level may

be achieved by over-filling and slowly draining, using the drain cock.

4. Remove one or more weights from the weight carrier and level the balance arm bydraining out more of the water. When the arm is level record the depth of

immersion shown on the scale on the quadrant.

5. Repeat reading for reducing masses on the weight carrier.

Data & Results:

L= mm , a= mm , d= mm , b= mm

1) Complete Immersion

Trials 1 2 3

Total weight on arm (M grams)

Depth of Water (y mm)

F=

H12

2d(2)d(aMgL (N)

Force on End Surface

(Theoretical) F = gbd(y - 2d ) (N)

Depth of Centre of Pressure Hp

(mm)

2) Partial Immersion

Trials 1 2 3

Total weight on arm (M grams)

Depth of Water (y mm)

F= 3ydaMgL (N)

Force on End Surface

(Theoretical) F = 0.5gby2 (N)

Depth of Centre of Pressure Hp

(mm)


6/111


4

Exp 1: Hydrostatic Force

SI US

mass kg Slug

Force N (kg.m/s2) lb (Slug.ft/s2)

1 lb = 4.4482 N

1 slug = 14.5938 kg

1 ft = 0.3048 m

g = 9.81 m/s2 = 32.2 ft/s2

(21Times New Roman).

.

:

F+Center of pressure

:quadrant( ) (pivot.)

Hp

PivotCounterWeight


7/111


5

:

(Plane)

centroid

:

Quadrantplane surface.

Scaleyquadrant.

(pole( )pivot).

Counterweightpolequadrant.

05.

3.

D0

R

PC

G

S

A

A


8/111


6

Complete Immersion:Area, A = bd

, (Theoritical)

(Practical)

Partial Immersion:Area, A = by

, (Theoritical)

(Practical):

2)a, b, d and L(a=10 cm, b=7.5 cm, d=10 cm, L=27.5 cm)

1)3)counterweight.

):counterweight)4):05((quadrant.

+0)Complete Immersion.6)poley>100mm.

(pole)7)y(mm)m(kg)8)F.9)678complete Immersion.

25)Partial Immersion(0


9/111


7


10/111

Hydraulics Lab - ECIV 3122 Experiment (2): Buoyancy

8

Exp. (2): BUOYANCY & FLOTATIONMETACENTRIC HEIGHT

Purpose: To determine the metacentric height of a flat bottomed vessel.

Introduction:

A floating body is stable if it tends to return to its original equilibrium position

after it had been tilted through a small angle.

For a floating body to be stable it is essential that the metacenter (M) is above the

center of gravity; metacentric height (MG) should be positive.

Fig. (1) Stable & unstable equilibrium

The greater the metacentric height, the greater is the stability, however, very large

metacentric heights causes undesirable oscillations in the ships and are avoided.

Theory:

If a body is tilted through an angle ,B1 will be the position of the center of buoyancy

after tilting. A vertical line through B1 will intersect the center line of the body at (M)

(Metacenter of the body), MG is the metacentric height. The force due to buoyancy

acts vertically up through B1 and is equal to W, the weight of the body acts

downwards through G. The resulting couple is of magnitudePx


11/111


9

Px = W. GG1

= W. GM. sin

W

PxGM (1)

in radian

Fig.(2) Metacentric height

* The metacentric height can be calculated as followed:

MG = BM + OBOG..........(2)

Where:

-

V

IBM -BMis the metacentric radius ,

- 3

12

1LDI - I : Moment of inertia of pontoon

- V: Total volume of displaced liquid.

- OB = 0.5 (LxD

V)

Experimental Set-up:

The set up consists of a small water tank having transparent side walls in which a

small ship model is floated, the weight of the model can be changed by adding or

removing weights. Adjustable mass is used for tilting the ship, plump line is attached

to the mast to measure the tilting angle.


12/111


10

Fig.(3) Experimental set-up Fig.(4) Cross section

Pontoon measurement:

- Pontoon dimension : Depth (H) = 170 mm

Length (L) = 380 mm, Width (D) = 250 mm.

- The height of the center of gravity of the pontoon is OGvm = 125 mm from outer

surface of vessel base.

- The balance weight is placed at x = 123 mm from pontoon center line.

- The weight of the pontoon and the mast Wvm = 3000 gm.

PART (1) : Determination of floatation characteristic for unloaded and for

loaded pontoon

Procedure:

1. Assemble the pontoon by positioning the bridge piece and mast.

2. Weigh the pontoon and determine the height of its center of gravity up the line of

the mast.

3. Fill the hydraulic bench measuring tank with water and float the pontoon in it, then

ensure that the plumb line on the zero mark.

4. Apply a weight of 50 g on the bridge piece loading pin then measure and record

the angle of tilting and the value of applied weight.

5. Repeat step 4 for different weights; 100, 150, & 200 g, and take the corresponding

angle of tilting.

6. Repeat the above procedure with increasing the bottom loading by 2000 gm and

4000 gm.


13/111


11

7. Record the results in the table ( Table " 1" ),

8. Calculate GM practically wheresin

)123(

W

PGM , W has three cases.

9. Draw a relationship between (x-axis) and GM (y-axis), then obtain GM when

equals zero.

10. Calculate GM theoretically according to equation (2),

whereWbWvm

xWbOGWvm

WbWvm

OGWbOGWvmOG vmbvm

)1()()()(

OGvm = 125 mm, OGb= x1: from table "1".

PART (2) : Determination of floatation characteristic when changing the center

of gravity of the pontoon.

1.Replace the bilge weights by 4x 50 gm weights.

2. Apply a weight of 300gm on a height of 190 mm from the pontoon surface.

3. Apply weights of 40, 80 &120 gms on the bridge piece loading pin, then record the

corresponding tilting angle.

4. Move 50 gm bilge weight to the mast ahead, then repeat step 3.

5. Repeat step 3 moving 100, 150 & 200 gm bilge weight to the mast.

6. Calculate GM practically where sin3500

)123(PGM .

7. Determine the height of the center of gravity for each loading condition.

8. Calculate GM theoretically according to equation (2),

whereW

LWmWbWbWvm

OG

)2

790()190(1)35()125(

Where : In case of 50 gm, L = 10 mm.

In case of 100 gm, L = 20 mm.



Fig.(5) Weights & Dimensions


14/111


12

Tables of results:

Table "1": Part(1)

Bilge Weight Off balance wt.Mean

Def.

Exp.

GM

GM at

=0BM OB

Theo.

GM

Wb (gm) P (gm)

(degree)(mm)

from

graph(mm) (mm) (mm)

0.00 50 2.13

100 4.45

150 6.90

200 9.23

2000.00 50 1.95

x1 = 30 100 3.98

150 6.10

200 8.25

4000.00 100 3.35

x1 = 37.5 150 5.10

200 6.90

250 8.75


15/111


13

Table "2": Part(2)

Off balance wt.

Mean

Def. Exp. GM BM OG

Theo.

GM M above

P (gm)

(degree) (mm) (mm) (mm) (mm)

water

level

Mast Weight = 0.0

40 2.40

80 4.88

120 7.50

Mast Weight = 50.0

40 3.45

80 7.23

120 10.50

Mast weight = 100.0

20 3.28

40 6.35

80 12.00

Mast Weight = 150.0

10 3.70

20 10.23

40 14.78

Mast weight = 200.0

Unstable


16/111


14

Experiment 2: Buoyancy

When a body is submerged or floating in a static fluid, the resultant force exerted on it

.Buoyancy Forceby the fluid is called the

* = =* Upthrust force on the body = weight of the fluid displaced by the body

.vertically upward center of volume

Center of Buoyancy: centroid of the volume of fluid displaced.

Archimedes Principle: :.

The equilibrium of a body may be:

Stable: if when displaced returns to equilibrium position.

Unstable:

Neutral:

Stability ofsubmerged Bodies: ()

Center of gravity , Center of Buoyancy .

Center of gravity (G)Center of Buoyancy(B).

I) Stable:

(G( )B)Center of gravity below Center of Buoyancy

restoring moment

II)Unstable:

G is above , B is below

III)Neutral:

B,G

BG

BG

R

W W

R

BG G

R

W

R

W

B


17/111


15

Stability ofF loating Bodies: ()

Center of gravity , Center of Buoyancy .

Center of gravity (G)Metacenter (M).

I) Stable:

Center of gravity below MetacenterGM

BM:Metacentric Height ( ): M G II)Unstable:

G is above , M is below

III)Neutral: M GIf M coincides with G, the body is in neutral equiblrium

:just stableneutral

F loating BodiesSubmerged Bodies

MGBG Center of gravity (G):

Center of Buoyancy (B):

The shape of submerged part is

altered when the body is tilted

Center of gravity (G):

Center of Buoyancy (B):

The shape of displaced fluid is not

altered when the body is tilted

BG

BG

M

W=mg

W=mgR=WR=W

x

B

G

B

G

W=mg

W=mgR=W

R=Wx

M


18/111


16

If M lies above G arighting moment is produced, equilibrium is stableand GM is

regarded as +ve. ( is small)

(

)

Determination of the Metacentric Height ( : , P W: weight of the vessel including P Determination of the position of the Metacenter relative to the center of Buoyancy: BM: metacentric radius

V:

I: moment of inertia

longitudinal

Water line planeaa

:Bcenter of volume

G

W=mgR=W

B1B

O

M

Water line plane


19/111


17

:(flat bottomed vessel)

:

2)

1)Center of gravity

Part 1: Determination of floatation characteristics for unloaded and for loaded

pontoon:

Wvm (i.e. vessel + mast) = 3000 gm

:Depth H = 170 mm

Length L = 380 mm

Width D = 250 mm

part134

:[ Wb (i.e. bilge weight) = 0.0 ]

(P)50gm,100gm150gm200gm) (.

OG = OGvm = 125mm

:Wb (bilge) = 2000g2555

205255205155) (.

OGOGvmOGb

:15552555(Wb = 4000

gm)

(213)

255205155105

OG


20/111


18

(Wb)(P). ) (

x1OGb(center of gravitybilge weightO)

:

x = 123 mm

P: off balance weight ) (W: W total = Wb + Wvm (355505557555) :

:

Draw a relationship between (x-axis) & Exp. GM (y-axis)(

x( )Exp GMy).

Exp. GM=0(y-intercept. )

:

, L = 380 mm, D = 250 mm, V = ?

:OB or EB

OC:

:


21/111


19

GM

GM practical=0GM theoretical=0.

Part 2: Determination of effect on floatation characteristics of altering the center of

gravity of the pontoon, with given total loading:

G

:2-1-4x05(bilge.)

Wb = 200 gmOGb = 35 mm3-(300gm:)150gm

Wb1 = 300 gmOGb1 = 190 mm

Wvm = 3000 gmOGvm = 125 mmWtotal = 3500 gm

4-P(off balance weight):43:Wb = 200 gmWm = 0

:P4585215.:PWtot.

:Wb = 150 gmWm = 50 gm05155(mast)

L is given in by the following table:Wb(gm)

200

Wm

(gm)

0

L(mm)

-

150 50 10

100 100 20

50 150 30

0 200 40

790 mm.

150 gm150 gm

35

OGm=

790+L/2

Wm

Wb

OGvm=

125mm

OGb1=190mm

Wb1

total=??

Wvm

P

X = 123 mm


22/111


20

:center of gravity

:Wb = 100 gmWm = 100 gm

05

:P154585.:Wb = 50 gmWm = 150 gm

05

:P251545.:Wb = 0 gmWm = 200 gm

Unstable

:

:.

:

P: ,

x = 123 mm

W = 3500 gm

:

tan

sin

:

xGMy.

:


23/111


21

:

:

:

Homework:

Write the momentum equation on a paper with explanation of the symbols.


24/111


22


25/111


23


26/111

Hydraulics Lab - ECIV 3122 Experiment (3): Impact of Jet

24

Exp. (3): Impact Jets

Purpose: To investigate the reaction force produced by the impact of a jet of water

on various target vanes.

Apparatus: Impact Jet Apparatus (Fig. 1), Targets (Fig. 2).

Figure 1: Impact jet apparatus

Figure 2: Interchangeable Target Vanes


27/111


25

Theory:

Figure 3 : Impact of a Jet

-

Q V

R

i

cos1

A

QVn

g hVV ni 2-22

Where:

R : Impulse force.

iV : incident velocity.

Q : Volumetric flow rate.

nV : jet velocity.

h : height of target above nozzle.

Procedure:

1. Position the weight carrier on the weight platform and add weights until the top of

the target is clear of the stop and the weight platform is floating in mid position.

Move the pointer so that it is aligned with the weight platform.

2. Start the pump and establish the water flow by steadily opening the bench

regulating valve until it is fully open.3. The vane will now be deflected by the impact of the jet. Place additional weights

onto the weight carrier until the weight platform is again floating in mid position.

Measure the flow rate (volume collected in certain time) and record the result on

the test sheet, together with the corresponding value of additional weight on the

tray. Observe the form of the deflected jet and note its shape.

4. Reduce the weight on the weight carrier in steps and maintain balance of the

weight platform by regulating the flow rate in about eight or ten even steps (In the

lab we made 3 steps only), each time recording the value of the flow rate and

weights on the weight carrier.5. Close the control valve and switch off the pump. Allow the apparatus to drain.


28/111


26

6. Replace the 5mm nozzle with the 8mm diameter nozzle and repeat the tests.

7. Replace the normal vane with the 45 conical vane and repeat the test with both

the 5mm and 8mm nozzles.

8. Replace the 45 conical vane with the hemispherical vane and repeat the test with

both the 5mm and 8mm nozzles.

Data & Results:

1. Record the results on a copy of the result sheet provided.

2. Calculate for each result the flow rate and the nozzle exit velocity. Correct the

nozzle velocity for the height of the target above the nozzle to obtain the

impact velocity.

3. Calculate the impact momentum, and plot graphs of the impact force R against

impact momentum and determine the slope of the graphs for each target.

Compare with the theoretical values.

Target Vanes

(degrees)

Nozzle

Dia -- d --

(mm)

Additional

Weights -- m --

(gm)

Volume of water

Collected - V - (Liter)

Time to

collect -- t --

(sec)

590

=

Flat

8

320 20 48

250 20 58

160 20 71

545

=

Conical

8

110 20 48

80 20 52

60 20 82

5135

=

Semi-

spherica

8

450 20 55

300 20 66

150 20 88

Comment:


29/111


27

Experiment 3: Impact of jet

Rate of flow

Mass rate of flow () Volume rate of flow (Q)

Momentum Equation: m

: :

[vector equation]x-direction y-direction resultant force acting on the fluid 1- F1 = FR: by any solid body touching the control volume

2- F2 = FB: body force such as gravity

3- F3 = FP: fluid Pressure

R = - FR

FR+ FP + FB = . Vector equationApplication of the momentum equation:

Impact of a jet on a plane surface

Force due to flow round a curved vane

Force due to the flow of fluid round a pipe bend

Reaction of a jet

:Pelton Wheel

momentum equation

, R: Impact Force, : Incident Momentum

V1 V1

A1

V2

V2


30/111


28

3 Target Vanes:

Flat Conical Hemispherical 1-cos

=1 = 0.293 = 1.707

Nozzle diameter:

5 mm or 8 mm

:

:Flat Vane (

)(nozzle 5 mm)

) (platform.

(pointer)platform.

flow5.

platformimpact of the jet.

) (.

volume.

jet.

platformflow.

..

flownozzle(0( )8)3.

:target 5mm8mm.: hemispherical.

PointerWeights

Weight Carrier

Weight Platform


31/111


29

:

(Target)(Nozzle Dia.)(Additional Weights)(VolumeCollected)(Time to collect. :)

:Volumetric Flow Rate (Q) t = 1 : 41.25 = 1*60+41.25

:Nozzle Velocity ()

:Height above Nozzle ()Height of the target above the nozzle (h) 2 mm

:Impact Velocity () ,

:Impact Force (

)

( ) : Incident Momentum

, :

:R(N)yx

(5 5)

y=ax=a.


32/111


30


33/111


31


34/111

Hydraulics Lab - ECIV 3122 Experiment (4): Flow Measurement

32

Exp. (4) : FLOW MEASUREMENT

Purpose: To study some of the famous instruments used in flow measurements.

Theory:

There are many instruments used in flow measurements such as Venturi meter, orifice

plate and the Rotameter.

Fig.(1) Flow measurement instruments

Fig.(2) Flow measurement instruments


35/111


33

1. Sudden Enlargement

The head loss through the sudden enlargement he

g

Vkehe

2

2

1 . (1)

Where 222

2

1 11

A

Ake

2

1

D

D ,

2

12

A

A

Fig.(3) Sudden enlargement

2. Venturi Meter

The flow through venturi meter can calculated from the following equation

42 1

2

gHACQ dact (2)

Where Cd is the coefficient of discharge.

Fig.(4) Venturi Meter

3. Orifices plate

The flow through venturi meter can calculated from the following equation

42 1

2

gHACQ dact . (3)

Where Cd is the coefficient of discharge.

Fig.(5) Orifices plate

4. Elbows

The head loss through the elbow hb

g

Vkh bb

2

2

1 (4)

Where kb is the coefficient of the elbow

5. Rotameter

The Rotameter reads the flow directly.

21

2

12

2

1

)12(2

A

A

A

A

hhgV


36/111


34

Procedure:

1. Prepare the instruments such that the water passes Sudden Enlargement, then

Venturi meter, Orifice plate , Elbow , and finally Rotameter .

2. Switch the pump on , allow the water to enter the flow measurement instruments ,

which are connected to Manometers tubes.

3. Control the flow valve to obtain different readings of the heads in manometers and

the corresponding flow from the volume tank .

4. Record the results.

5. Calculate the head losses from the manometer readings and the flow and Cd

for Venturi and orifice plate .

Data & Results

Volume flow (Liters)

Time (min)

Head at tapping 1 (cm)



Head at tapping 4(cm)





Rotameter flow rate


37/111


35

Experiment 4: Flow Measurement

From Bernoulli:

(1)* * from Continuity equation

(2)

From (1) and (2) we get

FromMechanics of fluids byB.S. Massey, Sixth Edition

The net force acting towards right

the mean pressure of eddying fluid over the annular face GDAssume

Net force:

From steady-flow momentum equation this force equals the rate of increase of

momentum in the same direction:


38/111


36

From energy equation for a constant :-

represents the loss of total head between 1 & 2

FromJ.C. Borda and L.M. M Carnot

H.G.L is below E.G.L by

Step up occur in pressure

line at Enlargement.

{ } Since negative, exceeds

ExitLoss

(E.G.L)

Pressure Line

(H.G.L)


39/111


37

For sudden enlargement ( ) :

Continuity equation:

12

Using Bernoulli equation - Head Loss equations:

, or

Substitute continuity equation, we get:

[ ] [ ]

[ ]

[ ]

12


40/111


38

Purpose: To study some of the famous instruments used in flow measurement.

Q

There are many instruments used in flow measurements such as Venturimeter,

orifice plate and rotameter (Variable area meter).

Description of apparatus:

Water Flow Measuring Apparatus is designed as a free-standing apparatus for

use on the Hydraulics Bench, although it could be used in conjunction with a low

pressure water supply controlled by a valve and a discharge to drain. Water enters the

apparatus through the lower left-hand end and flows horizontally through a sudden

enlargement into a transparent venturi meter, and into an orifice plate, a 90 elbow

changes the flow direction to vertical and connects to a variable area flow meter, a

second bend passes the flow into a discharge pipe which incorporates an atmospheric

break.

The static head at various points in the flow path may be measured on a

manometer panel. The water flow through the apparatus is controlled by the delivery

valve of the Hydraulics Bench and the flow rate may be confirmed by using the

volumetric measuring tank of the Hydraulics Bench. Calculations:

I. Sudden Enlargement:

Cdxy. Cd


41/111


39

II. Venturi:

-:

-:

xy. (0,0)(Excel)

. Calculate Cd & check in the range (0.9750.995)III. Orifice:

ventureh3, h4h6, h7

IV. Rotameter:

flowL/min. xyKK=Slope:-(Units).

-.


42/111


40


43/111


41


44/111


42


45/111

Hydraulics Lab - ECIV 3122 Experiment (5): Flow through Orifice

43

Experiment 5: Flow through orifice

Purpose:

- Studying the flow through small orifice discharging to atmosphere.

- Calculating the coefficient of discharge (Cd).

- Calculating the coefficient of velocity (Cv).

- Calculating the coefficient of contraction (Cc).

-

-

Theory:Orifice: H ) (

3:308.

H is constant

: Cd in the range [0.6-0.65] , where is the coefficient of velocity , where is the coefficient of contraction


46/111


44

xytrajectory: In x-direction:

In y-direction: , assuing positive is downward +

Calculations:

o Part 1 (Cd):

Head 50cm and 25 cm H.


47/111


45

xy(0,0)

o Part 2 (Cv):

(H)05(d)8

xy.(0,0)

trajectory:

x

y

y (-ve)

or

y

Homework:

+flow in open channel (Notches and Weirs):

{Rectangular, Triangular (Vee) and Trapezoidal}


48/111


46

:

-ypoint gauge:

-.

Extension Pipe

head225.

.) (

.

point

gauge

.

Pipe

.


49/111


47


50/111

Hydraulics Lab - ECIV 3122 Experiment (6): Flow over Weirs

48

Exp. (6): Flow Over Weirs

Purpose:

o To demonstrate the characteristics of flow over weirs.o To determine the 'Coefficient of Discharge' for each type of weir.

Introduction:

In open channel hydraulics, weirs are commonly used to either regulate or to

measure the volumetric flow rate. They are of particular use in large scale situations

such as irrigation schemes, canals and rivers. For small scale applications, weirs are

often referred to as notches and invariably are sharp edged and manufactured from

thin plate material.

Apparatus:

Hydraulics Bench incorporates a weir channel. The rectangular notch weir or

(V) vee notch weir to be tested is clamped to the weir carrier in the channel by thumb

nuts.

Figure 1:Flow over Weirs - Figure 2:Flow over Weirs -

vee notch weir rectangular notch weir

Hydraulics Bench Basket of glass spheres

Weir channel Volumetric measuring tank

(V) Vee notch weir Rectangular weir

Hook & point gauge Hook Gauge and Scale

There are different shapes of weirs that can be used to measure the volumetricflow rate. These shapes with their dimension are shown in fig 3 below.

4

3

5 8

7

1

2

5

6

7

1

3

2

6

84


51/111


49

Figure 3: Details of weirs

Theory:

Rectangular Weir:

A rectangular notch is a thin square edged weir plate installed in a weir channel as

shown in figure 4.

Figure 4: Rectangular Notch

Consider the flow in an element of height at a depth h below the surface.Assuming that the flow is everywhere normal to the plane of the weir and that thefree surface remains horizontal up to the plane of the weir, then

velocity through element Theoretical discharge through element Integrating between h = 0 and h = H

Total theoretical discharge


52/111


50

So, In practice the flow through the notch will not be parallel and therefore will not be

normal to the plane of the weir. The free surface is not horizontal and viscosity

and surface tension will have an effect. There will be a considerable change in theshape of the nappe as it passes through the notch with curvature of the stream

lines in both vertical and horizontal planes as indicated in Figure 5, in particular

the width of the nappe is reduced by the contractions at each end.

Figure 5: Shape of a Nappe

The discharge from a rectangular notch will be considerably less.

time

VolumeHgBCQCQ dthdact

2

3

23

2

In British Code:2

3

)001.0](2716.05461.0[ HHQact Important Note: This Equation is special forCussonsHydraulic Bench

(Rectangular Notch B = 10 cm ),For other notches (like Armfield Hydraulic

Bench) refer to original equation in British code.

Vee (Triangular) Notch:

A sharp edged triangular notch with an included angle of is shown in Figure 6

Figure 6: Triangular or V Notch


53/111


51

Operation:

1. FLOW

MEASUREMENT

The discharge from the weir may be measured using either the

Rotameter (if fitted) or by using the volumetric measuring tank

and taking the time required to collect a quantity of water. The

time to collect the water is at least 120 seconds to obtain a

sufficiently accurate result.

2. Measuring the

Weir Datum

head-gauge datum or gauge zero, which is defined as the gaugereading corresponding to the level of the weir crest (rectangular weirs) or

the level of the vertex of the notch (triangular-notch weirs)..BS ISO

1438:2008

3. Measuring the

Head

The surface of the water as it approaches the weir will fall, this is

particularly noticeable at high rates of discharge caused by high

heads. To obtain an accurate measure of the undisturbed water

level above the crest of the weir it is necessary to place the hook

gauge at a distance at least three times the head.

Experimental Procedure:

1. Place the flow stilling basket of glass spheres into the left end of the weir channeland attach the hose from the bench regulating valve to the inlet connection into the

stilling basket.

2. Place the specific weir plate which is to be tested first and hold it using the fivethumb nuts. Ensure that the square edge of the weir faces upstream.

3. Start the pump and slowly open the bench regulating valve until the water levelreaches the crest of the weir and measure the water level to determine the datum

level Hzero.4. Adjust the bench regulating valve to give the first required head level of

approximately 10mm. Measure the flow rate using the volumetric tank or the

rotameter. Observe the shape of the nappe.

5. Increase the flow by opening the bench regulating valve to set up heads above thedatum level in steps of approximately 10mm until the regulating valve is fully

open. At each condition measure the flow rate and observe the shape of the nappe.

6. Close the regulating valve, stop the pump and then replace the weir with the nextweir to be tested. Repeat the test procedure.

Results and Analysis:

1. Record the results on a copy of the results sheet. Record any observations of theshape and type of nappe paying particular attention to whether the nappe was

clinging or sprung clear, and of the end contraction and general change in shape.

2. Plot a graph of loge (Q) against loge (H) for each weir. Measure the slopes and theintercepts.

From the intercept calculate the coefficients of discharge and from the slopes of

the graphs confirm that the index is approximately 1.5 for the rectangular weir

and 2.5 for the triangular weirs.

3. Compare the results with those predicted using the empirical formula for

rectangular weirin British Standard BS3680.


54/111


52

Experiment 6: F low Over Weir s

Purpose:

To investigate the discharge-head characteristics of weirs Determination of the coefficient of discharge for different shapes of weirs

Introduction:

In open channel weirs are used to either regulate or to measure the volumetric

flow rate.

flowQ

weirnotch:weirnotch.Vee:rectangularHVee Notch

Types:o Rectangular:

o Triangular or Vee Notch:

Angle 60o or 90 o.

o Trapezoidal or Cippoletti:

o Linear:

Produce linear head flow characteristics

(general equation)

Rectangular

[ ]

Triangular (Vee)

b=


55/111


53

For Rectangular Notch:

,

cussonsweir=25 For Vee Notch:

Cd:

y-axis y-intercept x-axis

:

oRectangular weir.o(Basket of glass spheres)) (Armfield.o.o.oH.oMeasuring head: place the hook guage at a distance at least three times the head

o.olnHxlnQyyCd.


56/111


54

oVee Notch.o.olnHxlnQyyCd.

:

Qact = V/t

ln Qact

ln H

Qth

Intercept and Cd

::the shape of the Nappe

H


57/111


55


58/111

Hydraulics Lab - ECIV 3122 Experiment (7): Bernoulli Theorem

56

Exp. (7): Investigation of Bernoulli Theorem

Purpose: To investigate Bernoulli Theorem Experimentally.

Apparatus: Bernoullis Apparatus (Fig. 1, Fig. 2)

Figure 2:


59/111


57

Table (1): Area of each section:

Tapping

Number1 2 3 4 5 6 7 8 9 10 11

Flow

Area(mm

2)

102.56 90.11 77.66 65.22 52.77 40.32 52.77 65.22 77.66 90.11 102.56

Theory:

Bernoullis Theorem

tconszg

v

g

ptan

2

2

Where:

g

p

: pressure head

g

v

2

2

: kinetic head

z : potential head

Losses

fHzg

v

g

pz

g

v

g

p 2

2

221

2

11

22

Where:

fHHH 111

pressure Recovery

Recovery pressure =611hh

Loss pressure =61hh

61

611

hh

hhR degree of pressure recovery


60/111


58

Procedure:

1. Open the pump and let the water go through the apparatus until all the air

bubbles leave.

2. Set the difference between the tanks to 10 cm by using the arm beside theshorter tank.

3. When the height of water in the piezometers not change put a white paper (

A3 ) behind the piezometers and mark on it the height of water.

4. Close the valve of the basin and begin the stop watch to calculate Q.

5. Repeat the previous steps with different differences between the two tanks (

15 then 20 cm )

6. Take the paper and connect every set of points with lines.

Data & Results:

1. Record the results on a copy of the result sheet provided.

2. Calculate the flow rate for each set of results.

3. For each set of results calculate at the cross-section adjacent to each

manometer tube, the flow velocity.

4. Plot a graph of head (H) against distance (S) and also (H+V2/2g) against

distance (S).


61/111


59


62/111


60


63/111

Hydraulics Lab - ECIV 3122 Experiment (8): Minor Losses

61

Experiment 8: Minor Losses

Purpose:

To determine the loss factors for flow through a range of pipe fittings

including bends, a contraction, an enlargement and a gate-valve.

Introduction:

Energy losses in pipe flows are the result of friction between the fluid and the

pipe walls and internal friction between fluid particles. Minor (secondary) head

losses occur at any location in a pipe system where streamlines are not straight, such

as at pipe junctions, bends, valves, contractions, expansions, and reservoir inlets and

outlets. In this experiment, minor head losses through a pipe section that has several

bends, transitions, and fittings will be measured.

Apparatus:

Energy Losses in Bends and Fittings Apparatus.

It consists of:

- Sudden Enlargement

- Sudden Contraction

- Long Bend

- Short Bend

- Elbow Bend

- Mitre Bend figure 1:minor losses apparatus

Figure 2: Schematic drawing of the energy-loss apparatus


64/111


62

Figure 3: Minor Losses Apparatus with hydraulic bench

- Flow rate through the circuit is controlled by a flow control valve.

- Pressure tappings in the circuit are connected to a twelve bank manometer, which

incorporates an air inlet/outlet valve in the top manifold. An air bleed screw

facilitates connection to a hand pump. This enables the levels in the manometer

bank to be adjusted to a convenient level to suit the system static pressure.

- A clamp which closes off the tappings to the mitre bend is introduced when

experiments on the valve fitting are required. A differential pressure gauge gives a

direct reading of losses through the gate valve.

Theory:

The energy balance between two points in a pipe can be described by the

Bernoulli equation, given by

where pi is static pressure (in Pa) at point i, g is specific weight of the fluid (in

N/m3), zi is the elevation (in meters) of point i, Vi is the fluid velocity (in m/s) at

point i, g is the gravitational constant (in m/s2), and hL is head loss (in meters).

The term pi/ is referred to as the static head; z i is the elevation head; and Vi2/2g is the

dynamic (or velocity) head. The summation of the static head and the elevation head, pi/ +zi, is referred to as the piezometric head. The piezometric head is what is measured with the

piezometer (manometer) board on the apparatus for this experiment.

Head loss, hL, includes the sum of pipe friction losses, hf, and all minor losses,

where hi is the minor head loss (in meters) for the ith component and n is the number

of components (fittings, bends, etc.).

Lhg

Vz

p

g

Vz

p

22

2

22

2

2

11

1

ni

ifL hhh1


65/111


63

Pipe friction losses are expressed as the Darcy-Weisbach equation given by

where f is a friction factor, L is the pipe length, and D is the pipe diameter. Pipe

friction losses are assumed to be negligible in this experiment

The energy loss which occurs in a pipe fitting (so-called secondary loss) is

commonly expressed in terms of a head loss (h, meters) in the form:

Where K = the loss coefficient and

v = mean velocity of flow into the fitting, For the expansion and contraction,

the V used is the velocity of the fluid in the smaller-diameter pipe.

Because of the complexity of flow in many fittings, K is usually determined

by experiment. For the pipe fitting experiment, the head loss is calculated from two

manometer readings, taken before and after each fitting, and K is then determined as

Due to the change in pipe cross-sectional area through the enlargement and

contraction, the system experiences an additional change in static pressure. This

change can be calculated as

To eliminate the effect of this area change on the measured head losses, this

value should be added to the head loss readings for the enlargement and the

contraction. Note that (h1 - h2) will be negative for the enlargement and

will be negative for the contraction.

For the gate valve experiment, pressure difference before and after gate is measured

directly using a pressure gauge. This can then be converted to an equivalent head loss

using the equation

1 bar = 10.2 m water

Procedure:

It is not possible to make measurements on all fittings simultaneously and,

therefore, it is necessary to run two separate tests.

o Part A :

1) Set up the losses apparatus on the hydraulic bench so that its base is horizontal

by adjusting the feet on the base plate if necessary. (this is necessary for accurateheight measurements from the manometers). Connect the test rig inlet to the bench

g

V

D

Lfhf

2

2

g

VKh

2

2

g

VhK

2/

2

gvgv 2/2/2

2

2

1

gvgv 2/2/2

2

2

1


66/111


64

flow supply and run the outlet extension tube to the volumetric tank and secure it

in place.

2) Fully open the gate valve and the outlet flow control valve at the right hand end of the

apparatus.

3) Close the bench flow control valve then start the service pump.

4) Gradually open the bench flow control valve and allow the pipework to fill with

water until all air has been expelled from the pipework.

5) In order to bleed air from pressure tapping points and the manometers close

both the bench valve and the test rig flow control valve and open the air bleed

screw and remove the cap from the adjacent air valve. Connect a length of small

bore tubing from the air valve to the volumetric tank. Now, open the bench valve

and allow flow through the manometers to purge all air from them; then, tightenthe air bleed screw and partly open both the bench valve and the test rig flow

control valve.

Next, open the air bleed screw slightly to allow air to enter the top of the

manometers, re-tighten the screw when the manometer levels reach a convenient

height.

6) Check that all manometer levels are on scale at the maximum volume flow rate

required (approximately 17 liters/ minute). These levels can be adjusted further by

using the air bleed screw and the hand pump supplies. The air bleed screw

controls the air flow through the air valve, so when using the hand pump, the

bleed screw must be open. To retain the hand pump pressure in the system, the

screw must be closed after pumping.

7) If the levels in the manometer are too high then the hand pump can be used to

pressurise the top manifold. All levels will decrease simultaneously but retain the

appropriate differentials.

If the levels are too low then the hand pump should be disconnected and the

air bleed screw opened briefly to reduce the pressure in the top manifold.

Alternatively the outlet flow control valve can be closed to raise the static pressure

in the system which will raise all levels simultaneously.

If the level in any manometer tube is allowed to drop too low then air will

enter the bottom manifold. If the level in any manometer tube is too high then

water will enter the top manifold and flow into adjacent tubes.

8) Adjust the flow from the bench control valve and, at a given flow rate, take

height readings from all of the manometers after the levels have steadied. In order

to determine the volume flow rate, you should carry out a timed volume collection

using the volumetric tank. This is achieved by closing the ball valve and


67/111


65

measuring (with a stopwatch) time taken to accumulate a known volume of fluid

in the tank, which is read from the sight glass. You should collect fluid for at least

one minute to minimize timing errors. ( note: valve should be kept fully open.)

9) Repeat this procedure to give a total of at least five sets of measurements over a

flow range from approximately 8 - 17 liters per minute.

o Part B :

10) Clamp off the connecting tubes to the mitre bend pressure tappings (to prevent

air being drawn into the system).

11) Start with the gate valve closed and open fully both the bench valve and the

lest rig flow control valve.

12) open the gate valve by approximately 50% of one turn (after taking up any

backlash).

13) For each of at least 5 flow rates, measure pressure drop across the valve from

the pressure gauge; adjust the flow rate by use of the test rig flow control valve.

Once measurements have started, do not adjust the gale valve. Determine the

volume flow rate by timed collection.

14) Repeat this procedure for the gate valve opened by approximately 70% of one

turn and then approximately 80% of one turn.

Data & Resul ts:

The following dimensions from the equipment are used in the appropriate

calculations.

Internal diameter of pipework d = 0.0183 m

Internal diameter of pipework at enlargement outlet and contraction inlet

d = 0.0240 m


68/111


66

Table 1. Raw Data for All Fittings Except Gate Valve

Case No. I II III IV V

Volume (L)

Time (sec)

PiezometerReadings(mm)

Enlargement 12

Contraction3

4

Long Bend5

6

Short Bend7

8

Elbow9

10

Mitre Bend 1112

Table 2. Raw Data for Gate Valve


50%

Opened

Volume (L)

Time (sec)

Gauge

Reading

(bar)

Red(upstream)

Black(downstream)

70%

Opened Volume (L)

Time (sec)

Gauge

Reading

(bar)

Red(upstream)

Black(downstream)

80%

Opened

Volume (L)

Time (sec)

Gauge

Reading

(bar)

Red(upstream)

Black

(downstream)


69/111


67

Table 3. Minor Head Losses of All Fittings Except Gate Valve


Q (m3/sec)

V (m/s)

V

2

/2g (m)

MinorHeadLosses

(m)

Enlargementh

h +V12/2g- V2

2/2g

Contractionhh +V1

2/2g- V2

2/2g

Long Bend

Short Bend

Elbow

Mitre Bend

Table 4. Loss Coefficients for All Fittings Except Gate Valve


Q (m3/sec)

V (m/s)

V2/2g (m)

Loss

efficie

tsEnlargement

Contraction

Long Bend

Short Bend

Elbow

Mitre Bend

Table 5. Equivalent Minor Head Loss and Loss Coefficient for Gate Valve


50%

Opened

Q (m3/sec)

V (m/sec)

V2/2g (m)

Minor Head

Loss (m)

Loss Coefficient

70%

Opene

dQ (m3/sec)

V (m/sec)V

2/2g (m)

Minor Head

Loss (m)

Loss Coefficient

80%

Opened

Q (m3/sec)

V (m/sec)

V2/2g (m)

Minor Head

Loss (m)

Loss Coefficient


70/111


68

Calculations and Results

Fill in Tables 3 5 with calculated results. Assume that the pipe friction

losses between the upstream and downstream manometer ports are negligible, so the

total head loss is due to minor head losses. Remember the piezometric head is what is

measured with the piezometer (manometer) board on the experimental apparatus.

Questions

1. For Exercise A, prepare plots that show the effect of dynamic head on minor head

loss (i.e. plot graphs of head loss (h) against dynamic head (

), and the effect of flow

rate on loss coefficients (i.e. K against volume flow rateQ).

2. For Exercise B, prepare plots that show the effect of dynamic head on equivalent

head loss (i.e. (h) against (

), and the effect of flow rate on loss coefficients (i.e. K

against volume flow rateQ).

3. Comment on and explain the relationships evident in the plots of Questions 1 and

2. Include a comparison of the loss coefficients and geometry for the four types of

bends.

a. Is it justifiable to treat the loss coefficient as constant for a given

fitting? Explain.

b. How does the loss coefficient for the gate valve vary with the extent of

the opening of the valve? Explain.4. Compare the experimental loss-coefficient values for different fittings to those

found in a fluid mechanics text book (or another source). Be sure to site the

source of the published values.

5. Does the static pressure increase or decrease for the enlargement and contraction?

Explain the increase or decrease in static pressure.


71/111


69


72/111


70


73/111


71


74/111


72


75/111

Hydraulics Lab - ECIV 3122 Experiment (9): Centrifugal Pump

73

Experiment 10: Centrifugal Pump

Introduction:

Pumps fall into two main categories: positive displacement pumps and

rotodynamic pumps.

In a positive displacement pump, a fixed volume of fluid is forced from one

chamber into another. One of the oldest and most familiar designs is the reciprocating

engine, utilising a piston moving inside a cylinder. Steam pumps, the 'nodding

donkey', stirrup pumps and hydraulic rams are all of this type. Animal hearts are also

positive displacement pumps, which use volume reduction of one chamber to force

flow into another chamber.

The FM50 pump is, by contrast, a rotodynamic machine. Rotodynamic (or simply

dynamic) pumps impart momentum to a fluid, which then causes the fluid to move

into the delivery chamber or outlet. Turbines and centrifugal pumps all fall into thiscategory.

Pumps

Turbo-hydraulic (Kinetic) pumps Positive Displacement Pumps

Centrifugal Propeller Jet Screw Reciprocating

Pump (Radial) (Axial) (Mixed)

Description:

The apparatus consists of a tank and pipework which delivers water to and from a

small centrifugal pump. The unit is fitted with electronic sensors which measure the

process variables. Signals from these sensors are sent to a computer via an interface

device, and the unit is supplied with data

logging software as standard.

Pump speed and outlet pressure may

be varied to allow the collection ofperformance data over a range of

parameters. The inlet (suction) head

pressure may be adjusted to investigate

the onset of cavitation. An alternative

impeller is also supplied so that the effect

of impeller design may be studied.

For more Details refer to Instruction

Manual FM50.

Figure 1: Centrifugal Pump Demonstration Unit


76/111


74

Exercise B

Objective

To create head, power and efficiency characteristic curves for a centrifugal

pump.

Theory

One way of illustrating pump characteristics is to construct contour lines of

constant power or efficiency on a graph of pump head plotted against pump

discharge. These allow engineers to see the maximum efficiency of a pump

over a range of operating parameters, which can assist in the selection of an

appropriate pump to suit particular conditions. An example is given in Figure

2.

Figure 2

Equipment Set Up

If the equipment is not yet ready for use, proceed as follows:

Ensure the drain valve is fully closed.

If necessary, fill the reservoir to within 20cm of the top rim.

Ensure the inlet valve and gate valve are both fully open.

Ensure the equipment is connected to the IFD7 and the IFD7 is connected to a

suitable PC. The red and green indicator lights on the IFD7 should both be

illuminated.

Ensure the IFD7 is connected to an appropriate mains supply, and switch on

the supply.

Run the FM50-304 software. Check that 'IFD: OK' is displayed in the bottom

right corner of the screen and that there are values displayed in all the sensor

display boxes on the mimic diagram.


77/111


75

Procedure

Switch on the IFD7.

Switch on theFM50pump within the software using the Pump On button.

In the software, rename the current (blank) results table to '50%' (this will be

the only table if results from Exercise A are not available).

On the mimic diagram of the software, set the pump speed to 50%.

The interface will increase the pump speed until it reaches the required setting.

Allow water to circulate until all air has been f1ushed from the system.

Partially closing and opening the inlet and gate valves a few times will help in

priming the system and eliminating any bubbles caught within the valve

mechanism. Leave the inlet valve fully open.

Close the gate valve to give a flow rate Q of 0. (Note that the pump may not

run well with the gate valve closed or nearly closed, as the back pressure

produced is outside normal operating parameters. The pump should begin to

run more smoothly as the experiment progresses).

Select the icon to record the sensor readings and pump settings on the

results table of the software.

Open the gate valve to allow a low flow rate. Allow sufficient time for the

sensor readings to stabilise then select the icon to record the next set of

data.

Open the gate valve in small increments, allowing the sensor readings to

stabilise then recording the sensor and pump data each time.

Create a new results sheet by selecting the icon (you may also wish to

save the results at this time to avoid losing the data in the event of problems).

Close the gate valve.

Set the pump to 60%.

Select the icon to record the sensor readings and pump settings on the new

results table.

Repeat as before, opening the gate valve in small increments and allowing the

sensor readings to stabilise then recording the sensor and pump data each time.


Repeat the procedure at 70%, 80%, 90% and 100%. Create a new results sheet

for each setting (and save the results if desired- the same file may be

overwritten each time as more data is added). For convenience, rename each

sheet of results in the software with the pump setting.

Ensure the results are saved after taking the final set of results.

Switch the pump off. If not proceeding directly to another exercise then switchoff the IFD7 and close the FM50 software.


78/111


76

Results

On the same graph plot Total Head H t against Flow Rate Q for each setting.Graphs may be produced using the software graph facility, in which case theresulting graph with multiple plots must be printed. Alternatively the resultsmay be imported into a more sophisticated spreadsheet program that allows

the following procedure to be performed.

Select a value for efficiency, for example 40%. On each line plotted, mark thepoints at which an efficiency of 40% is achieved (the data is unlikely toinclude recorded points at which the efficiency is exactly 40%, so estimate the

points based on the values obtained). Where the pump performance at aparticular setting does not ever correspond to the efficiency chosen, notewhether the efficiency would lie above the line or to the right of the pump

performance curve. Join the marked points to form a smooth curve.

Repeat for other efficiency values. for example 35%.45% and 5090. to give a

family of efficiency curves.

Create and/or print a second head-flow rate graph for all pump frequencies.

Using the same procedure as for drawing contour lines of constant efficiency,

produce curves for constant mechanical power.

Conclusion

Examine and describe the shapes of the efficiency and power curves obtained.Are the shapes consistent? How do they relate to the head-flow rate

characteristic? How do the efficiency and power curves relate to each other?

Compare the results to the example pump curves presented in the theory

section. How does the pump in the example compare to the pump on the FM50in terms of capacity, power, and efficiency?


79/111


77

Calculations

Table 1: Example of data taken from the Software (Setting 50%)

SampleNumber

NotesPump

Setting

S[%]

PumpSpeed

n[rpm]

WaterTemperature

T[C]

InletPressure

Pin[kPa]

OutletPressure

Pout[kPa]

MotorTorque

t[Nm]

FlowRate

Q[l/s]

Densityof

water

[kg/m]

1 50 750 26.7 2.6 18.5 0.62 0.04 997

2 50 750 27.2 2.7 18.3 0.64 0.12 996

3 50 750 26.7 2.3 17.7 0.64 0.21 997

4 50 750 26.9 2.2 17.0 0.66 0.29 997

5 50 750 27.1 1.6 15.4 0.65 0.40 997

6 50 750 27.4 1.3 14.0 0.67 0.49 996

7 50 750 26.7 0.9 13.1 0.66 0.54 997

8 50 750 27.0 0.3 11.0 0.67 0.60 997

9 50 750 26.6 0.2 10.1 0.69 0.64 997

10 50 750 26.7 -0.4 9.5 0.68 0.66 99711 50 750 26.8 -0.6 8.6 0.68 0.69 997

12 50 750 27.1 -0.9 8.1 0.68 0.72 996

13 50 750 26.7 -1.1 7.1 0.67 0.74 997

14 50 750 27.1 -1.0 7.2 0.70 0.76 996

15 50 750 26.7 -1.1 6.5 0.68 0.76 997

16 50 750 27.5 -1.0 6.2 0.69 0.76 996

17 50 750 27.1 -1.2 6.2 0.72 0.77 996

18 50 750 26.7 -1.2 6.2 0.70 0.77 997

19 50 750 27.4 -1.2 6.4 0.68 0.76 996

Table 1 (Cont.): Example 50% setting (n = 750 rpm)

InletVelocity

Vin[m/s]

OutletVelocity

Vout[m/s]

StaticHead

Hs[m]

VelocityHead

Hv[m]

ElevationHead

He[m]

TotalHead

Ht[m]

HydraulicPower

Ph[W]

MechanicalPower

Pm[W]

PumpEfficiency

E[%]

PredictedFlowRate[l/s]

0.090 0.162 1.627 0.001 0.075 1.70 0.7 48.4 1.3 0.03

0.275 0.495 1.596 0.009 0.075 1.68 2.0 50.5 3.9 0.08

0.491 0.885 1.570 0.028 0.075 1.67 3.5 50.3 6.9 0.14

0.675 1.218 1.516 0.052 0.075 1.64 4.7 52.1 9.0 0.20

0.919 1.657 1.413 0.097 0.075 1.58 6.2 50.8 12.2 0.27

1.135 2.046 1.302 0.148 0.075 1.52 7.3 52.7 13.9 0.33

1.256 2.266 1.250 0.181 0.075 1.51 8.0 51.8 15.5 0.36

1.378 2.485 1.097 0.218 0.075 1.39 8.1 52.6 15.5 0.40

1.468 2.647 1.020 0.247 0.075 1.34 8.4 54.4 15.4 0.42

1.531 2.761 1.012 0.269 0.075 1.36 8.8 53.2 16.6 0.44

1.594 2.875 0.935 0.292 0.075 1.30 8.8 53.3 16.5 0.46

1.653 2.980 0.919 0.313 0.075 1.31 9.2 53.4 17.2 0.48

1.716 3.094 0.837 0.338 0.075 1.25 9.1 52.8 17.2 0.50

1.747 3.151 0.839 0.350 0.075 1.26 9.4 54.9 17.1 0.51

1.747 3.151 0.777 0.350 0.075 1.20 8.9 53.1 16.8 0.51

1.747 3.151 0.733 0.350 0.075 1.16 8.6 54.2 15.9 0.51

1.774 3.199 0.757 0.361 0.075 1.19 9.0 56.2 16.0 0.51

1.774 3.199 0.754 0.361 0.075 1.19 9.0 55.1 16.2 0.511.747 3.151 0.775 0.350 0.075 1.20 8.9 53.8 16.5 0.51


80/111


78

Table 1 (Cont.): 50% setting (n = 750 rpm)

PredictedTotalHead[m]

VapourPressure

Pv[kPa]

Net +veSuction Head

Available[m]

PipeLength

L[m]

PipeDiameter

d[m]

Coefficientk

[-]

CoefficientC

[-]

SystemHeadLoss[m]

WalkthroughQuestions

Score[%]

0.757 36.64 6.73 0.916 0.032 4.9 140 0.06

0.746 37.33 6.68 0.916 4.9 0.21

0.743 36.64 6.72 0.916 4.9 0.40

0.730 36.89 6.71 0.916 4.9 0.58

0.704 37.14 6.67 0.916 4.9 0.86

0.678 37.58 6.64 0.916 4.9 1.13

0.669 36.70 6.72 0.916 4.9 1.29

0.618 37.08 6.66 0.916 4.9 1.46

0.597 36.57 6.73 0.916 4.9 1.60

0.603 36.64 6.69 0.916 4.9 1.69

0.578 36.82 6.68 0.916 4.9 1.79

0.581 37.20 6.63 0.916 4.9 1.88

0.555 36.64 6.69 0.916 4.9 1.98

0.562 37.20 6.65 0.916 4.9 2.04

0.534 36.70 6.69 0.916 4.9 2.04

0.515 37.65 6.60 0.916 4.9 2.04

0.530 37.20 6.64 0.916 4.9 2.08

0.529 36.64 6.70 0.916 4.9 2.08

0.533 37.58 6.59 0.916 4.9 2.04

Figure 3: Pump Curves for different velocities

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

TotalHeadHt[m]

Flow Rate Q [l/s]

Pump Curves for different velocities (rpm)

725

955

1525

155

1325

1255


81/111


79

Exercise C

Objective

To investigate the use of the affinity laws in predicting the head-flow

characteristic for a pump.

Theory

When selecting a pump for a system, it is seldom practical to test the

performance of every size of pump in a manufacturer's range at all speeds at

which it may be designed to run. It is therefore useful to have a mathematical

solution that allows assumptions can be made about operating characteristics

of a pump running at one speed, impeller size, etc. from experimental results

taken at another.

The multiple curves obtained from plotting measured pump characteristics on

dimensional axes can be reduced to a single curve if appropriate dimensionless

groups are used. Provided the effects of t1uid viscosity on pump performance

are small, and that cavitation is not occurring, the characteristic of a given type

and shape of pump may be represented by: where n is the pump speed (rpm or Hz), and D is the impeller diameter (m)

For a single curve of the type suggested by this equation to represent more

than one operating condition of the particular type of pump, the criterion ofdynamic similarity must be fulfilled. That is, all fluid velocities at

corresponding points within the machine are in the same direction and

proportional to impeller speed. When this is the case, as for a particular pump

operated at different speeds, a simple graph of data is formed, as depicted in

Figure 4:

Figure 4: Dimensionless head-discharge characteristic of a particular centrifugal pump

operated at different speeds


82/111


80

The dimensionless equation given previously is the basis from which the

affinity laws are derived. The affinity laws allow the performance of

geometrically similarpumps of different sizes or speeds to be predicted

accurately enough for practical purposes.

The methods used for deriving the affinity laws will not be presented here, but

the laws are as follows:

Power Coefficient Flow Coefficient Head Coefficient

These Laws are most often used to calculate changes in now rate, head and

power of a pump when the size, rotational speed or fluid density is changed.

The following formulae are derived from the above considerations, and allow

calculation of total head H, and power Pm at one speed n. to be deduced from

those measured at another speed n2: More generally, the relationship between two geometrically similar machines

with characteristic diameters D1 and D2 operating at rotational speeds n1 and

n2 is shown in Figure 5. For any two points at which values of (gH / n2D2) and

(Q / nD3) are the same, it follows that:

and These are termed corresponding points.

The power coefficient and the resulting efficiency E can be compared in

a similar manner.

Figure 5:Relationship of performance characteristics for geometrically similar machinesoperating at different speeds


83/111


81

Equipment Set Up

If the results from Exercise B are available then no further data is required.

Ensure you understand the Theory section then proceed directly to the results.

This experiment may be undertaken directly following another experiment, inwhich case the equipment will already be prepared and need only be switched

back out of standby mode again.

If the equipment is not yet ready for use, proceed as follows:


If necessary, fill the reservoir to within 20cm of the top rim. Ensure the inlet

valve and the gate valve are both fully open.



illuminated.


the supply.



display boxes on the mimic diagram

Procedure

The results from Exercise B may be used to perform the calculations and to

create the graphs for this exercise. Where these results are available, no further

data is required. Proceed directly to the Results section. If results are not

available, proceed as follows:

Switch on the IFD7.

Switch on the FM50 pump within the software.

In the software, set the pump to 50%.

Allow water to circulate until all air has been flushed from the system. Close

the gate valve to give a flow rate Q of 0.



Open the gate valve to give a very low flow rate. Allow sufficient time for the

sensor readings to stabilise then select the icon to record the next set of

data.

Open the gate valve in small increments, allowing the sensor readings to

stabilise then recording the sensor and pump data each time.

Create a new results sheet by selecting the icon (you may also wish to

save the results at this time to avoid losing the data in the event of problems).

Set the pump to 70%.



84/111


82

Select the icon to record the sensor readings and pump settings on the new

results table.

Open the gate valve to give a very low flow rate. Allow sufficient time for the

sensor readings to stubilise, then select the icon to record the next set of

data.Repeat, opening the gate valve in small increments and allowing the sensor

readings to stabilise, then recording the sensor and pump data each time.

Ensure the results are saved using 'Save' or 'Save As .. .' from the software File

menu after taking the final set of results.

Switch off the FM50 within the software using the Power On/Standby button.

Switch off the IFD7.

Results

The results taken at 70% will be used with the affinity laws to give predicted

results at 50%. This will then be compared to the actual results at 50%.The software uses the affinity laws and to calculate the predicted values of Ht2 at predicted flow rates Q2 and 50%

setting from the measured values of Htl and Q1 and the values n1 = 70 and n2 =

50.

Plot a graph of Predicted Head against Predicted Flow Rate.

Plot the measured Total Head at 50% against measured Flow Rate at 50% (if

the data is exported into a dedicated spread sheet package or similar then itmay be possible to plot both graphs on the same axes).

Conclusion

Compare the predicted results at 50% with the measured results. How accurate

were the values obtained using the affinity laws? Discuss the advantages and

disadvantages of this technique for pump system design


85/111


83

Calculations

Table 2: Data for 50% Setting and 70% setting from software

Practical

70% = 1050 rpm 50% = 750 rpm

SampleNumber

FlowRate

Q[l/s]

TotalHead

Ht[m]

FlowRate

Q[l/s]

TotalHead

Ht[m]

1 0.08 3.41 0.04 1.70

2 0.15 3.38 0.12 1.68

3 0.27 3.26 0.21 1.67

4 0.43 3.26 0.29 1.64

5 0.56 3.11 0.40 1.58

6 0.66 2.99 0.49 1.527 0.76 2.88 0.54 1.51

8 0.82 2.79 0.60 1.39

9 0.89 2.68 0.64 1.34

10 0.93 2.63 0.66 1.36

11 1.00 2.58 0.69 1.30

12 1.01 2.52 0.72 1.31

13 1.04 2.42 0.74 1.25

14 1.04 2.33 0.76 1.26

15 1.06 2.44 0.76 1.20

16 1.05 2.34 0.76 1.16

17 1.06 2.34 0.77 1.19

18 1.08 2.38 0.77 1.1919 1.08 2.35 0.76 1.20

20 1.06 2.34

Figure 6

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.50 1.00 1.50

TotalHeadHt[m]

Flow Rate Q [l/s]

Practical

70% = 1050 rpm

50% = 750 rpm


86/111


84

Using Similarity Laws to calculate Q and Ht for 50% and Table 3: Data for 70% setting from software and 50% Setting from Similarity Laws

Similarity Laws70% = 1050 rpm Calculated 50% = 750 rpm

SampleNumber

FlowRate

Q[l/s]

TotalHead

Ht[m]

FlowRate

Q[l/s]

TotalHead

Ht[m]

1 0.08 3.41 0.06 1.74

2 0.15 3.38 0.10 1.72

3 0.27 3.26 0.19 1.66

4 0.43 3.26 0.30 1.66

5 0.56 3.11 0.40 1.596 0.66 2.99 0.47 1.53

7 0.76 2.88 0.54 1.47

8 0.82 2.79 0.59 1.42

9 0.89 2.68 0.64 1.37

10 0.93 2.63 0.66 1.34

11 1.00 2.58 0.71 1.32

12 1.01 2.52 0.72 1.29

13 1.04 2.42 0.74 1.23

14 1.04 2.33 0.74 1.19

15 1.06 2.44 0.76 1.24

16 1.05 2.34 0.75 1.19

17 1.06 2.34 0.76 1.19

18 1.08 2.38 0.77 1.22

19 1.08 2.35 0.77 1.20

20 1.06 2.34 0.76 1.19

Figure 7

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.50 1.00 1.50

TotalHeadHt

[m]

Flow Rate Q [l/s]

Affinity Laws

70% = 1050

rpm

Calculated

50% = 750

rpm


87/111


85

Exercise D

Objective

To investigate the effect of changing inlet head on pump performance.

Method

By varying the pressure at the inlet to the pump using a manual valve to

control the available flow.

Theory

In both the design and operation of a rotodynamic machine, careful attention

has to be paid to the fluid conditions on the suction side. In particular, it is

important to check the minimum pressure that can arise at any point to ensurethat cavitation does not take place.

Cavitation

If the pressure at any point is less than the vapour pressure of the liquid at the

temperature at that point, vaporisation will occur. This is most likely to arise in

the suction side where the lowest pressures are experienced. The vaporised

liquid appears as bubbles within the liquid, and these subsequently collapse

with such force that mechanical damage may be sustained. This condition,known as cavitation, is accompanied by a marked increase in noise and

vibration in addition to the loss of head.

suction pipe.

:FM 51


88/111


86

Exercise E

Objective

To obtain a Head - Flow curve for the piping system through which the fluid is

to be pumped. To determine the operating point of the pump.

Theory

System analysis for a pumping installation is used to select the most suitable

pumping units and to define their operating points. System analysis involves

calculating a head - flow curve for the pumping system (valves, pipes, fittings

etc.) and using this curve in conjunction with the performance curves of the

available pumps to select the most appropriate pump(s) for use within the

system.

The system curve is a graphic representation of the flow rate in the system with

respect to system head. It represents the relationship between flow rate and

hydraulic losses in a system. Such losses are due to the system design (e.g.

bends and fittings, surface roughness) and operating conditions (e.g.

temperature).

Assuming that

Flow velocity is proportional to volume now rate

Losses in the system are proportional to the square of the now velocity

it follows that system head loss must be proportional to the square of thevolume flow rate, and the system head - now graph will therefore be parabolic

in shape.

Calculations

Table 4

System Curve

Sample

Number

Pump

SettingS[%]

Pump

Speedn[rpm]

Flow

RateQ[l/s]

Total

HeadHt[m]

1 100 1500 1.49 4.28

2 90 1350 1.36 3.78

3 80 1200 1.22 3.03

4 70 1050 1.08 2.33

5 60 900 0.92 1.71

6 50 750 0.77 1.16

7 40 600 0.61 0.74

8 30 450 0.46 0.38

9 20 300 0.30 0.15

10 10 150 0.13 -0.0111 0 0 0.00 -0.05


89/111


87

Table 5

Pump Curve

SampleNumber

PumpSetting

S[%]

PumpSpeed

n[rpm]

FlowRate

Q[l/s]

TotalHead

Ht[m]

1 70 1050 1.08 2.28

2 70 1050 1.02 2.38

3 70 1050 1.00 2.55

4 70 1050 0.97 2.60

5 70 1050 0.92 2.69

6 70 1050 0.85 2.74

7 70 1050 0.80 2.86

8 70 1050 0.69 2.89

9 70 1050 0.61 3.10

10 70 1050 0.49 3.16

11 70 1050 0.35 3.28

12 70 1050 0.24 3.3413 70 1050 0.13 3.39

14 70 1050 0.09 3.41

Figure 8

:pump curvesystem curve

flow(outlet valve fully opened.)

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

0.00 0.50 1.00 1.50 2.00TotalHeadHt[m]

Flow Rate Q [l/s]

Operating Point

Pump Curve

System Curve

Operating Point


90/111

Hydraulics Lab - ECIV 3122 Experiment (10): Series & Parallel Pumps

88

Experiment 11: Series and Parallel Pumps

Introduction to the Equipment

The apparatus consists of a tank and pipework which delivers water to and

from two identical centrifugal pumps. The unit is fitted with electronic sensorswhich measure the process variables. Signals from these sensors are sent to a

computer via an interface device, and the unit is supplied with data logging

software as standard.

The speed of one of the pumps may be varied to allow the collection of

performance data over a range of parameters. Outlet pressures may be varied

to control the flow rate. Flow through the system may be set to allow single

pump operation, series pump operation or parallel pump operation.

Figure 1: Series and Parallel Pumps Demonstration Unit

Pumps

The two pumps are motor-driven centrifugal pumps. On pump 1 the speed ofthe motor is adjustable to give a range of 0 to 100%, allowing operation as asingle pump for pump performance analysis. Pump 2 is an identical model butis run at its design speed, which is equivalent to a setting of 80% on thevariable-speed pump for a 50Hz electrical supply, or 100% for a 60 Hz supply.The pump bodies and cover plates are made from clear acrylic, allowing the

impellers to be observed.

Inlet valve

A manual ball valve controls the inlet (suction) head supplied to the pumps.This valve should be fully open except when investigating the effect of inlet

pressure on pump performance and cavitation formation.


91/111


89

Setting the flow path

The system may be configured to drive flow

using single, series or parallel pumps. The

system valves are as shown:

Valves should be set to configure the system as follows. The software should also be

set to the corresponding flow path to ensure that the correct calculations are

performed.

Single Pump:

Series Pumps:

Parallel Pumps:


92/111


90

Exercise F

Objective

To investigate the result on discharge and total head of operating pumps in

series.

Theory

A single pump may be insufficient to produce the performance required.

Combining two pumps increases the pumping capacity of the system. Two

pumps may be connected inseries, so that water passes first through one pump

and then through the second. When two pumps operate in series, the flow rate

is the same as for a single pump but the total head is increased. The combined

pump head-capacity curve is found by adding the heads of the single pump

curves at the same capacity.

Figure 2

Equipment Set Up


If necessary, fill the reservoir to within 10 cm of the top rim.

Check that both pumps are fitted with similar impellers (the impellers may be

viewed through the clear cover plate of each pump).

Ensure the inlet valve and gate valve are both fully open.

Set the 3-way valve for flow in series (the earlier experiments have all usedthis valve set for flow in parallel).



illuminated.


the supply. Switch on the IFD7.



display boxes on the mimic diagram.


93/111


91

Procedure

Both pumps must be used at the same setting in this experiment, to ensure

identical performance. As the speed of Pump 2 is fixed at its design

operational point, Pump 1 should be set to match - select 80% for a 50Hz

electrical supply, or 100% for 60 Hz.Allow water to circulate until all air has been flushed from the system.

If results are already available for a single pump across its full flow range,

load those results into the software now and jump to the section of this

exercise using two pumps. If results are not available then proceed as follows:

Single pump performance:

Close Pump 2 outlet valve and open Pump 1 outlet valve.

In the software, on the mimic diagram, set the 'Mode' to 'Single' by selecting

the appropriate radio button.

Rename the results sheet to 'Single'.



Close the gate valve to reduce the flow by a small amount. Select the icon

again.

Continue to close the gate valve to give increment

ملزمة-Hydraulics-Lab-2

Documents