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2013
POLITEKNIK SULTAN AZLAN SHAH liza_anna
[JJ309 FLUID MECHANICS] [Type the abstract of the document here. The abstract is typically a short summary of the contents of the document. Type the abstract of the document here. The abstract is typically a short summary of the contents of the document.]
This workbook published with a goal to ease reference, strengthen understanding, and
increase achievement. So that this objective filled, planning and this book manipulation
are made with very latest curriculum and past year final examination paper that. This
workbook contain inquisition technique with various difficulty level.
Objectives
This module focuses on the following objectives, typically found in syllabus content:
a. Explain clearly the characteristics of fluid
b. Solve problems correctly related to fluid properties, fluid statics and fluid
dynamics
c. Explain the theory of fluid mechanics related to engineering field .
JJ309: Fluid Mechanics
CONTENTS
Unit 1: Fluid Properties Covers characteristics of fluid, pressure gauge measurement, physical properties of fluid, viscosity and compressibility
Unit 2: Fluid Statics Introduces the relationship between pressure and depth, analyze pressure head, buoyancy and pressure.
Unit 3: Fluid Dynamic This topics covers flow, discharge. Mass flow rate in pipe, continuity equation, Bernoulli equation and measurement of fluid motion
Unit 4: Energy Loss In Pipelines This topic cover velocity profile in circular pipe. Type of head loss in pipelines, flow characteristics, head loss equation for rate and pipelines problems
Unit 5: Nozzle This topic covers types and shapes of nozzles, critical pressure ratio, changes in pressure, temperature, maximum mass flow and cross- sectional area
JJ309: Fluid Mechanics
Unit:
Kilo Hekto Deko unit desi centi mili
1 liter = 1000m3
I kg x 9.81 = 1N
1 bar = 105 N/m @ Pa
JJ309: Fluid Mechanics
Unit 1 : Fluid And Properties
1. Define Fluid
2. Compare the characteristics between liquid, gas and solid
a. Liquid
b. Gas
c. Solid
3. Define of pressure
a. Atmospheric
b. Gauge
c. Absolute
d. Vacuum
- The pressure below the atmospheric pressure ( vacuum)
JJ309: Fluid Mechanics
4. Example problem of pressure
a. What is the pressure gauge of air in the cylinder if the atmospheric gauge is
101.3 kN/m2 and absolute pressure is 460 kN/m2.(358.7kN/m2)
b. A Bourdon pressure gauge attached to a boiler located at sea level shows a
reading pressure of 7 bar. If atmospheric pressure is 1.013 bar, what is the
absolute pressure in that boiler (in kN/m2) ?(801 kN/m2)
5. Fluid properties
a. Mass density, ρ is defined as the mass per unit volume.
b. Specific weight, is defined as the weight per unit volume.
JJ309: Fluid Mechanics
c. Specific gravity or relative density, s is the ratio of the weight of the substance to
the weight of an equal volume of water at 4 ºC.
d. Specific volume, v is defined as the reciprocal of mass density. It is used to mean
volume per unit mass.
e. Viscosity
A fluid at rest cannot resist shearing forces but once it is in motion, shearing
forces are set up between layers of fluid moving at different velocities. The
viscosity of the fluid determines the ability of the fluid in resisting these shearing
stresses.
Kinematic viscosity
This ratio is characterized by the kinematic viscosity (Greek letter nu, ν), defined as follows:
Dynamic viscosity, μ
JJ309: Fluid Mechanics
6. Example problems of fluid properties
a. If 5.6 m3 of oil and weights 46000 N ,determine :
i. Mass density ,ρ in unit kg/m3
ii. Specific weight ,ω
iii. Specific gravity of oil , S
(837.33kg/m3,8214.3N/m3,0.837)
JJ309: Fluid Mechanics
b. Get the relative density , density , specific weight and kinematik viscosity
of an oil which are 7.3 m3 in volume , 6500 kg in mass and dynamic
c. Determine the specific volume if it mass is 500g and the volume is 400cm3
(8x10-4m3/kg)
d. Given specific weight of fluid is 6.54 N/litter and its mass is 830 g . Calculate
the following in SI unit
i.Volume of fluid
ii.Specific volume of fluid
iii.Density of fluid (1.245x10-3 m3,1.5x10-3/kg,666.67 kg/m3)
JJ309: Fluid Mechanics
e.Volume and mass for oil are 9.2 m3 and 7300 kg
i. Mass density
ii. Relative density
iii. Specific weight (793.4 kg/m3 , 0.793,7.78x103N/m3)
JJ309: Fluid Mechanics
f. If the mass and volume of air 11.5 kg and 650 cm3, calculate:
i. Mass density
ii. Specific weight
iii. Specific volume
iv. Specific gravity for the air
(17692.31 kg/m3,173558.5N/m3 , 5.352x10-5m3/kg)
JJ309: Fluid Mechanics
g. The volume of engine oil is 5.5m3 and the weight is 50 kN determine
i. Density of oil
ii. Specific weight of oil
iii. Specific volume of oil
iv. Specific gravity
(926.7kg/m3,9091N/m3,1.079x10 -3 m3/kg, 0.9267)
h. Determine the mass density , in SI unit if it s mass is 450g and the volume is
9dm3. (50kg/m3)
JJ309: Fluid Mechanics
i. Determine the specific weight ω ( kN/m2) and specific gravity, s of fluid if the
weight is 100N and the volume is 500cm3
( 20kN/m3, 2.039)
j. The volume of a stone is 1.5 x 10-4 m3. If the relative density of the stone is 2.6,
calculate:
i. The density
ii. The specific weight
iii. The specific volume
iv. The weight
v. The mass
( 2600kg/m3 , 25.506kg kN/m3,3.85 x10-4m3/kg, 3.83 N, 0.39 kg)
JJ309: Fluid Mechanics
k. Given the volume of oil is 3 liter and the weight is 20N, determine the specific
volume, relative density and specific weight of oil.
( 1.471 x10-3m3, 0.68,6670N/m3)
l. Specific gravity of a liquid is 0.85. determine
i. Mass density
ii. Specific volume
(850kg/m3,1.176 x 10-3m3/kg)
JJ309: Fluid Mechanics
Unit 2: Fluid Static
1. If a fluid is within a container then the depth of an object placed in that fluid can
be measured. The deeper the object is placed in the fluid, the more pressure it
experiences
The formula that gives the pressure, p on an object submerged in a fluid is:
ghp
Where,
(rho) - the density of the fluid,
g- the acceleration of gravity
h - the height of the fluid above the object
2. Example Problems:
a. A barometer shows the reading 750mm merkury. Determine;
i. Atmosfera pressure in unit SI
ii. The head of water for that preassure
(100 KN/m2,10.2m)
i. P= ρgh
= 9810 x 13.6 x 075
= 100062N/m2
ii. 100062 = ρgh
h = 10.2m
JJ309: Fluid Mechanics
b. What is the pressure experienced at a point on the bottom of a swimming
pool 9 meters in depth? The density of water is 1.00 x 103
kg/m3.(88.3kN/m2)
c. Assume standard atmospheric conditions. Determine the pressure in kN/m2
for the pressure below: i. depth 6m below under free space water.
ii. At the 9m under surface of oil with specific gravity 0.75.
(58.86kN/m2,66.0 kN/m2)
JJ309: Fluid Mechanics
d. Find the height of water column, h which is equivalent to the pressure , p of
20 N/m2 . Take into consideration specific weight of water , ω is 1000 kg/m2
x 9.81 m/s2 (2.03x10-3m)
e. A fluid in piezometer increased 1.5 m high from point A in a pipeline system .
What is the value of pressure in point A in N/m2 if the fluid is :
i. Mercury with specific gravity 13.6
ii. Salted water with specific gravity 1.24
(200.1240x103N/m2,18.24 x103N/m2)
A
JJ309: Fluid Mechanics
f. Find the head, h of water corresponding to an intensity of pressure, p of 340 000
N/m2. Take into consideration that the mass density, ρ of water is 100kg/m3
(h=34.65m)
g. A Bourdon pressure gauge attached to a boiler located at sea level shows a
reading pressure 10 bar . If atmospheric pressure is 1.01 bar , determine : i. The absolute pressure in kN/m2
ii. The pressure head of water , h
(1101 KN/m2, 112.2m)
JJ309: Fluid Mechanics
3. Pascal’s Law and Hyraulic Jack
iv. State the Pascal’s Law
4. Example :
a. A force, F of 900 N is applied to the smaller cylinder of an hydraulic jack. The
area, a of a small piston is 22 cm2 and the area A of a larger piston is 250
cm2. What load, W can be lifted on the larger piston if :
i. the pistons are at the same level.
ii. the large piston is 0.8 m below the smaller piston.
Consider the mass density ρ of the liquid in the jack is 103 kg/m3
(10.227 kN,10.423kN)
JJ309: Fluid Mechanics
b. Two cylinders with pistons are connected by a pipe containing water. Their
diameters are 75 mm and 600 mm respectively and the face of the smaller piston
is 6 m above the larger. What force on the smaller piston is required to maintain
a load of 3500 kg on the larger piston?(275.970 N)
JJ309: Fluid Mechanics
c. A diameter of big piston in hydraulic jack is three times bigger than the diameter
of small piston. The small diameter is 630 mm and is used to support a weight of
40 kN. Find the force which is needed to rise up the big piston 2 m above the
small piston. Given the specific gravity of oil is 0.85. (313.18kN)
d. A force , F = 500 N is applied to the smaller cylinder of hydraulic jack . The area, a of
a small piston is 20 cm2 while the area, A of a large piston is 200 cm2 . What mass
can be lifted on the larger piston. (509.68 kg)
JJ309: Fluid Mechanics
e. A hydraulic press has a diameter ratio between the two pistons of 8:1 . The diameter
of the larger piston is 600 mm and it is required to support a mass of 3500 kg . the
press is filled with a hydraulic fluid of specific gravity 0.8 . Calculate the force
required on the smaller piston to provide the required force ;
i. When the two pistons are at same level
ii. When the smaller piston is 2.6 m below the larger piston.
(536.48 N, 627.92 N)
f. A hydraulic jack has diameter cylinder 5 cm and 18 cm. A force has put on small
cylinder to lift the load 1100 kg at bigger cylinder. Determine force F for lift the both
cylinders. (139.85x103N)
JJ309: Fluid Mechanics
h. A area of big piston in hydraulic jack is three times bigger than the area of small
piston. The small diameter is 630 mm and is used to support a weight of 40 KN. Find
the force which is needed to rise up the big piston 2 m above the small piston. Given
the specific gravity of oil is 0.85 (101.6kN)
JJ309: Fluid Mechanics
m. The basic elements of a hydraulic press are shown in Figure i. The plunger has an
area of 3cm2
, and a force, F1, can be applied to the plunger through a lever
mechanism having a mechanical advantage of 8 to 1. If the large piston has an
area of 150 cm2
, what load, F2, can be raised by a force of 30 N applied to the
lever? Neglect the hydrostatic pressure variation. (12 kN)
Figure i
Solution
F2 = 12 kN
JJ309: Fluid Mechanics
n. The diameter of plunger and ram of a hydraulic press are 30 mm and 200 mm respectively. Find the weight lifted by the hydraulic press when the force applied at the plunger is 400N and the difference level between plunger and ram is 0.5 m. Given ρ fluids is 1065 kg/m3 ( 17929.9N)
JJ309: Fluid Mechanics
5. Concept of manometer i.Manometer Simple
ii.Manometer U tube
iii.Manometer Differential
JJ309: Fluid Mechanics
6.Example a. Assume that Patm= 101.3 kN/m2 water flow in pipe and in merkuri in manometer a= 1m h=0.4 m. Determine the absolute pressure. As figure a (38.1kPa)
Figure a
JJ309: Fluid Mechanics
b. A U tube manometer is used to measure the pressure of oil (s= 0.8)
flowing in a pipeline as in figure b. Its right limb is open to the atmosphere
and the left limb is connected to the pipe. The centre of the pipe is 9 cm
below the level of mercury in the right limb. If the difference of mercury
level in the two limbs is 15 cm, determine the gauge pressure of the oil in
the pipe in KPa. (19.541 KPa)
Fig. b
JJ309: Fluid Mechanics
c. Determine absolute pressure at A if Patm = 101.3 kN/m2, h1=20cm,h2= 40 cm as
fig c (45.971KPa)
merkury
figure c.
water
JJ309: Fluid Mechanics
d. For a gauge pressure in pipe is 5kN/m2, determine the specific gravity of
the liquid B in the figure given below. (6.54)
12cm
water
Liquid B
JJ309: Fluid Mechanics
e. Find the level of h if P1 is absolute pressure 150kN/m2, ρm= 13.6 x103 kg/m2
and in pipe is water in fig. e. (0.401m)
Fig. e
500mm
h
m
JJ309: Fluid Mechanics
f. One end of a manometer contain mercury is open to atmosphere, while the
other end of the tube is connected to pipe in which a fluid of specific gravity
0.85 is flowing. Find the gauge pressure the fluid flowing in pipe.
(26.271kN/m2)
Fig.f
JJ309: Fluid Mechanics
g. A U tube manometer measures the pressure difference between two
points A and B in a fluid as shown in Figure d. The U tube contains
mercury. Calculate the difference in pressure at pipe A and B if h1 = 160
cm, h2 = 50 cm and h3 = 80 cm. The liquid at A and B is water ρ =
1000kg/m3 and the specific gravity of mercury is 13.6.1 (53955N/m2)
Figure g
JJ309: Fluid Mechanics
h. The figure e below shown a U tube manometer . The specific gravity of mercury is
13.6 . If the pressure difference between point B and A is 47 kN/m2 , h = 12cm
and a = 43 cm , determine the height of b .(3.71m)
Figure h
b
a
water
merkury
JJ309: Fluid Mechanics
i. A manometer U tube is using to measure between A and B in pipe has water and in
manometer has mercury. Determine the differential pressure between pipe A and B, if
a =150 cm, b = 70 cm and c = 45 cm. Figure f (47.77kN/m2)
Figure i
JJ309: Fluid Mechanics
j. Figure g shown U tube manometer. If the differential of pressure between X andY is
50KN/m2 , h=2m and a=0.85m determine b (0.4719m)
Figure j
JJ309: Fluid Mechanics
k. he fig. k shows a differential manometer connected at two points A nd B. At A
air pressure is 100kN/m2. Find the absolute pressure at B
Figure k
(84.28kPa)
JJ309: Fluid Mechanics
l. A U-tube manometer is connected to a closed tank containing air and water as shown in Figure h. At the closed end of the manometer the absolute air pressure is 140kPa. Determine the reading on the pressure gage for a differential reading of 1.5-m on the manometer. Express your answer in gauge pressure value. Assume standard atmospheric pressure and neglect the weight of the air columns in the manometer. (64.5 kPa)
Figure l
JJ309: Fluid Mechanics
m. A U-tube manometer contains oil, mercury, and water as shown in Figure i. For the column heights indicated what is the pressure differential between pipes A and B? (-15.1kPa )
Figure m
JJ309: Fluid Mechanics
n. A U-tube manometer is connected to a closed tank as shown in Figure j. The air pressure in the tank is 120 Pa and the liquid in the tank is oil (γ = 12000
N/m3
). The absolute pressure at point A is 20 kPa. Determine: (a) the depth of oil, z, and (b) the differential reading, h, on the manometer. Patm = 101.3 kPa (z = 1.66 m, h = 1.33 m )
Figure n
JJ309: Fluid Mechanics
o. The inverted U-tube manometer of Figure k contains oil (SG = 0.9) and water as shown. The pressure differential between pipes A and B, p
A − p
B, is −5 kPa. Determine
the differential reading, h. (0.46 mm )
Fig.o
JJ309: Fluid Mechanics
o. In the figure below, fluid Q is water and fluid P is oil (specific gravity = 0.9). If h =
69 cm and z = 23 cm, what is the difference in pressure in kN/m2 between A and
B?(-1.579kN/m2)
JJ309: Fluid Mechanics
p. Figure m belows shows a u-tube manometer that used to measure the pressure
difference between pipe P and pipe Q that contains water. If the fluid in u-tube is
oil with specific gravity 0f 0.9, calculate the pressure difference between these two
pipes in kN/m3 . Given M =80 cm and
N = 25 cm.(1667.7 Pa)
Figure p
JJ309: Fluid Mechanics
r. For the inclined-tube manometer of Figure n, the pressure in pipe A is 8 kPa. The
fluid in both pipes A and B is water, and the gage fluid in the manometer has a
specific gravity of 2.6. What is the pressure in pipe B corresponding to the
differential reading shown?(5.51kPa )
fig.r
JJ309: Fluid Mechanics
s. A piston having a cross-sectional area of 0.07 m2
is located in a cylinder containing water as shown in Figure o. An open U-tube manometer is connected to the cylinder as shown. For h
1 = 60 mm and h = 100 mm, what is the value of the applied force, P,
acting on the piston? The weight of the piston is negligible (892.7 N)
Fig. s
JJ309: Fluid Mechanics
7. Pressure Measurement
Piezometer, Barometer
Bourdon gauge
Sketch important parts of bourdon gauge
Explain mechanism of a bourdon gauge
JJ309: Fluid Mechanics
8. Buoyancy
Define Buoyancy Force
Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object Buoyant Force=Weight of Displaced Fluid
R2
R 1 = R2
ρ1 g1 v1 = ρ2 g2 v2
R1
JJ309: Fluid Mechanics
9. Example Question
a. A rectangular pontoon has a width B of 6 m, a length l of 12 m, and a draught D of
1.5 m in fresh water (density 1000 kg/m3). Calculate :
a) the weight of the pontoon b) its draught in sea water (density 1025 kg/m3) c) the load (in kiloNewtons) that can be supported by the pontoon in fresh
water if the maximum draught permissible is 2 m. (1059.5kN, 1.46m, 14126kN,353.1kN)
JJ309: Fluid Mechanics
b. 8 cm side cube weighing 4N is immersed in a liquid of relative density 0.8
contained in a rectangular tank of cross- sectional area 12cm x 12cm. If the tank
contained liquid to a height of 6.4 cm before the immersion determine the levels of
the bottom of the cube and the liquid surface. (x =0.0796m)
i. The raw oil flowed through a pipe with a diameter of 40 mm and entered a pipe a
diameter of 25mm. The volume flow rate is at 3.75 liter/s. Calculate the flow
velocity of both pipes and the density of raw oil if the mass flow rate is 3.23 kg/s.
(v1=2.984m/s, v2=7.46m/s,861.3kg/m3)
JJ309: Fluid Mechanics
Energy of a flowing fluid
a. Potential energy Potential energy per unit weight = z
b. Pressure energy (Pressure Head)
pressure energy per unit weight =
p =
g
p
c. Kinetic energy
Kinetic energy per unit weight =g
v
2
2
Total energy per unit weight = g
vpz
2
2
Bernoulli’s Theorem,
Total energy per unit weight at section 1 = Total energy per unit weight at section 2
g
vpz
g
vpz
22
222
2
111
The limits of Bernoulli’s Equation
Bernoulli’s Eqution is the most important and useful equation in fluid mechanics. It may
be written,
2
2
21
1
2
11
22
p
g
vz
p
g
vz
Bernoulli’s Equation has some restrictions in its applicability, they are :
the flow is steady
the density is constant (which also means the fluid is compressible)
friction losses are negligible
JJ309: Fluid Mechanics
the equation relates the state at two points along a single streamline (not conditions on two different streamlines).
Application of Bernoulli equation
a. Water flows through a pipe 36 m from the sea level as shown in figure a.
Pressure in the pipe is 410 kN/m2 and the velocity is 4.8 m/s. Calculate total
energy of every weight of unit water above the sea level. (78.96J)
b. A pipe measure 15 m length, supplying water to a house that located on a hill,
5.5 m above sea level . Diameter of the pipe is 30 cm . If the water velocity is 2
m/s, calculate the total energy . The water pressure is 5000 Pascal .(6.21m)
36
m
Figure a
m
JJ309: Fluid Mechanics
c.
Figure b
A bent pipe labeled MN measures 5 m and 3 m respectively above the datum
line. The diameter M and N are both 20 cm and 5 cm. The water pressure is 5
kg/cm2. If the velocity at M is 1 m/s, determine the pressure at N in kg/cm2.
d. Ventury meter is flow meter device. Sketch and main part of horizontal ventury
meter.
5 m 5 m
3 m
JJ309: Fluid Mechanics
e. A venturimeter is used to measure liquid flow rate of 7500 litres perminute. The
difference in pressure across the venturimeter is equivalent to 8 m of the flowing
liquid. The pipe diameter is 19 cm. Calculate the throat diameter of the
venturimeter. Assume the coefficient of discharge for the venturimeter as
0.96.(11.14 cm)
m/s
JJ309: Fluid Mechanics
f. A Venturi meter is 50 mm bore diameter at inlet and 10 mm bore diameter at the
throat. Oil of density 900 kg/m3 flows through it and a differential pressure head of 80 mm is produced. Given Cd = 0.92, determine the mass flow rate in kg/s
( 0.0815 kg/s)
JJ309: Fluid Mechanics
g. A Venturi meter is 60 mm bore diameter at inlet and 20 mm bore diameter at the throat. Water of density 1000 kg/m3 flows through it and a differential pressure head of 150 mm is produced. Given Cd = 0.95, determine the flow rate in dm3/s. (0.515 dm3/s)
JJ309: Fluid Mechanics
h. Calculate the differential pressure expected from a Venturi meter when the flow rate
is 2 dm3/s of water. The area ratio is 4 and Cd is 0.94. The inlet cross section area . is 900 mm2.(41916 Pa)
JJ309: Fluid Mechanics
i. Calculate the mass flow rate of water through a Venturi meter when the differential pressure is 980 Pa given Cd = 0.93, the area ratio is 5 and the inlet cross section area. is 1000 mm2. (0.2658kg/s)
JJ309: Fluid Mechanics
j. Calculate the flow rate of water through an orifice meter with an area ratio of 4 given
Cd is 0.62, the pipe area is 900 mm2 and the differential pressure is 586 Pa.
(0.156 dm3/s).
JJ309: Fluid Mechanics
j. A horizontal Venturi meter with 0.15 m in diameter at the entrance is use to
measures flow rate of oil . Specific gravity for oil is 0.9 . The difference of level in
manometer is 0.2 m. Calculate the throat diameter if velocity at the entrance is
3.65 m/s . Find the actual rate of flow , assuming a coefficient of discharge is 0.9
.(2.82m,0.099m,0.058m3/s)
JJ309: Fluid Mechanics
k. A meter ventury with diameter of 400 mm at the inlet and 200 mm at the throat .
It is horizontal and used to measure the water flow rate . A differential
manometer is used and shown the different level reading of 60 mm . Calculate
the real discharge . Given Cd = 0.95 .(0.119m3/s)
JJ309: Fluid Mechanics
l. A metre venturi that in a situation horizontal have neck diametrical 150 mm set
within water main pipe that diametrical 300 mm. Discharge coefficient this metre
venturi is 0.982 .Determine height difference mercury column in manometer
differential if flow rate is 0.142 m3 / s (0.254m)
JJ309: Fluid Mechanics
m. Horizontal a meter venturi have diameter 250 mm in inlet and 150 mm in neck
area. Manometer mercury connected to metre venturi show flow level difference
reading 55 mm. Determine rate coefficient if real discharge water which flowed is
0.063 m3 / s .(0.9)
JJ309: Fluid Mechanics
n. A metre venturi have diameter 400 mm in section enter and 200 mm in neck area.
It is prestigious horizontal and used to measure rate of flow water . Manometer
differential mercury / water used and show level difference 60 mm. Determine rate
of actual flow rate of water . Assume Cd = 0.95 .(0.1187m3 / s)
JJ309: Fluid Mechanics
o. A meter venturi horizontal used to measure fluid flow from a tank. Inlet and neck
venturi have diametrical 76 mm and 38 mm. 2200 kg water ran in 4 minutes.
Difference reading in mercury level in U-tube is 266 mm. Calculate coefficient of
flow rate. Mercury specific gravity13.6.(0.965)
JJ309: Fluid Mechanics
p. Diameter for entry of meter ventury horizontal was 0.2 m and diameter in neck
area was 0.1 m. It used to measure flow rate oil that density comparison 0.8.
Mercury manometer difference / oil is using are showing reading 0.2 m, determine
i. Oil flow velocity
ii. Discharge in theory
iii. Actual discharge discharge coefficient, Cd = 0.9