Chapter 3

Chapter 3: FLUID FLOW

1

CHAPTER

THREE

FLUID FLOW

3.1 Fluid Flow Unit

3.2 Pump Test Unit

3.3 Hydraulics bench and accessories

3.4 Flow Curve Determination for Non-Newtonian Fluids

3.5 Fixed and Fluidized Bed

Facts which at first seem improbable will, even in scant

explanation, drop the cloak which has hidden them and

stand forth in naked and simple beauty.

GALILEO GALILEI

2

3.1. FLUID FLOW UNIT

Keywords: Pressure loss, straight pipe, pipe bend, orifice meter, venturi meter.

3.1.1. Object

The object of this experiment is to investigate the variations in fluid pressure for flow in straight

pipes, through pipe bends, fittings, orifice and venturi meters.

3.1.2. Theory

When a fluid flows along a pipe, friction between the fluid and the pipe wall causes a loss of

energy. This energy loss shows itself as a progressive fall in pressure along the pipe and varies

with the rate of the flow. The head loss due to friction can be calculated by the expression:

D

Lufh f

2

4 (3.1.1)

where hf : head loss due to friction, m H2O

D : diameter of pipe, m

f : friction factor

g : acceleration due to gravity, m/sec2

L : length of pipe, m

u : mean velocity, m/sec

: density of fluid, kg/m3

The change of direction forced on a fluid when it negotiates a bend produces turbulence in the

fluid and a consequent loss of energy. The net loss in pressure is greater than that for the same

length of straight pipes. Abrupt changes of direction produce greater turbulence and larger energy

losses than do smoothly contoured changes.


3

When a fluid flows through an orifice or a venturi meter, a loss of pressure energy occurs due to

the turbulence created. A straight line relation exists between the flow rate and the square root of

the pressure drop value, and this principle is utilized in the design of the orifice and venturi

meters.

The internal construction of many pipe fittings leads to the construction of fluid flowing through

them causing turbulence of varying magnitude with a consequent energy loss. This behavior can

be clearly shown using gate and globe valves in comparison with one another. A globe valve will

cause an energy loss even when fully open. Partially closed position of either of these valves

increases appreciably the energy loss across them compared with the fully open position. energy

losses across a fitting are observed in the experiment by noting the pressure drops across each of

these valves.

4

3.1.3. Apparatus

The apparatus used in this experiment is shown in Figure 3.1.1. It consists of 14 main parts.

Figure 3.1.1. The fluid flow unit.

1

2

3

4

5

7

10

8

6

5

9

9

9

9

14 13

12

11 11

1. Pump

2. Flexible joint

3. Water pressure gauge

4. Liquid flowmeter

5. Vent valve

6. Cylindrical vessel (50 lt)

7. Venturi-meter

8. Orifice-meter

9. Make-up joint

10. Staright pipe section

11. Various pipe fittings

12. Gate valve

13. Globe valve

14. Drain valve


5

3.1.4. Experimental Procedure

A. Straight pipes, pipe bends, orifice and venturi meters

1. Select the pipe line on which the experiment will be performed by turning of the isolation

valves for all other horizontal pipe runs.

2. Be sure that water manometers are connected to the pressure tappings read zero.

3. Check that isolating valve on the selected pipe run is fully open.

4. Turn off the flow control valve.

5. Operate the control valve to give successively higher flow rates (9 times) and note

manometer readings for each case.

6. With the same flow rates, repeat the experiment once more to avoid wrong or insufficient

data.

B. Pipe fittings

1. Apply steps 1 through 4 of the procedure (A) and then continue with the following ones.

2. With the valves fully open, operate the control valve to give successively higher flow rates,

noting the manometer readings for each case.

3. Repeat step 2 with the gate valve 1/7, 3/7, and 5/7 closed. Keep the globe valve fully open.

4. With the gate valve fully open, repeat step 2 with the globe valve 1/6, 3/6, and 5/6 closed.

3.1.5. Report Objectives

1. Show the variation of friction loss with respect to flow rate. Calculate theoretical and

experimental losses.

2. For the sharp bend, use at least three values of k (between 0.2 and 1.0) to determine which

one of these is the most compatible with your experimental results.

3. In the case of valves, keep on mind that percentage closure is a parameter.

4. Draw graphs to explain your conclusions.

6

3.1.6. References

1. Bennett, C. O., and J. E. Myers, Momentum, Heat and Mass Transfer, 3rd edition, McGraw-

Hill International Book Company, Tokyo, 1987.

2. Davidson, J. F., and D. Harrison, Fluidization, Academic Press, New York, 1971.

3. Knuii, D., and O. Levenspiel, Fluidization Engineering, John Wiley and Sons Inc., New

York, 1969.

4. McCabe, W. L., and J. C. Smith, Unit Operations of Chemical Engineering, 2nd edition,

McGraw-Hill International Book Company, 1967.

5. Perry, R. H., and D. Green, Perry’s Chemical Engineers’ Handbook, 6th edition, McGraw-

Hill, 1988.

6. Sinnott R. K., J. M. Coulson, and J. F. Richardson, Chemical Engineering, An Introduction

to Chemical Engineering Design, Pergamon Press, Volume 6, 1983.

7. Szckely, J., J. W. Evans, and H. X. John, Gas Solid Reactions, Academic Press Inc., New

York, 1976.


7

3.2. PUMP TEST UNIT

Keywords : Pump, NPSH, cavitation.

3.2.1. Object

The object of this experiment is to determine the Net Positive Suction Head (NPSH) of a

centrifugal pump theoretically and experimentally, and also to investigate the operating curve of

the pump.

3.2.2. Theory

The operating characteristics of a particular centrifugal pump are most conveniently given in the

form of curves of head developed against delivery for various running speeds and throughputs.

The actual head developed is always less than the theoretical one for a number of reasons. The

total discharge head of a pump is defined as the reading of a pressure gauge at the outlet of the

pump plus the barometer reading plus the velocity head at point of attachment of the gauge.

hd = hdg+atm+hvd (3.2.1)

where hd : total discharge head, m of liquid

hdg : gauge reading at discharge outlet of pump, m of liquid

atm : barometric pressure, m of liquid

hvd : velocity head at point of gauge attachment, m of liquid

hdg is measured from the pressure gauge on the outlet side of the pump. A height correction is

necessary due to the position of the gauge above or below the impeller level. The velocity head,

hvd, is calculated from

hv

gvd

2

2 (3.2.2)

where v : velocity at outlet of pump, m/sec

g : gravitational constant, m/sec2

8

Net Positive Suction Head is defined as the amount by which the absolute pressure of the suction

point of the pump, expressed as m of liquid, exceeds the vapor pressure of the liquid being

pumped, at the operating temperature. For any pump there exists a minimum value for the NPSH.

Below this value, the vapor pressure of the liquid begins to exceed the suction pressure causing

bubbles of vapor to form in the body of the pump. This phenomenon is known as cavitation and

is usually accompanied by a loss of efficiency and an increase in noise. For this reason minimum

values of NPSH are important and are usually specified by pump manufacturers.

NPSH = Pressure at pump inlet-vapor pressure of liquid

The pressure at the pump inlet is made up of several pressures:

a) The static head of liquid from pump inlet to liquid surface

b) External pressure above liquid

c) Velocity head i.e. head developed

d) Head due to friction losses in the suction pipework.

The head due to friction losses in the inlet pipework can be calculated from

hf Lv

gdf

4

2

2

(3.2.3)

where f : Fanning friction factor which has correlations with the the Reynold's number

L : Lenght of pipe-corrected to include the effects of bends, elbows, valves,

reducers etc., m

g : gravitational acceleration, m/sec2

d : diameter at the inlet and/or outlet, m

Pressure at pump inlet can also be calculated from Bernoulli's equation,

P

gh

v

g

P

gh

v

gh f

22

22

11

12

2 2 (3.2.4)

where P : pressure, N/m2

: density of the liquid, kg/m3


9

v : velocity, m/sec

h : height, m

hf : friction losses in pipe works

Subscript 1and 2 refer to pump inlet and to surface of liquid reservoir respectively.

By applying the above equation and assuming that the height of the liquid in the reservoir stays

constant,

v2 0

then

P

g

P

gh h

v

gh f

1 22 1

12

2 (3.2.5)

3.2.3. Apparatus

The apparatus used in this experiment is shown in Figure 3.2.1.

Figure 3.2.1. Pump test unit apparatus.

10

1. Manometer(open to atmosphere) 6. Valves

2. Pump 7. Elbow

3. Manometer (water pressure gauge) 8. Spherical buffer vessel

4. Bellows 9. Control valve

5. Flowmeter 10. Vacuum connection or liquid feed


1. Turn on the pump.

2. Open the flowmeter control valve slowly to give a scale reading of approximately 1/5th full

scale value.

3. Allow the unit to settle down for a few minutes. Measure outlet pressure, flowmeter reading

and the height that the liquid discharge to the spherical vessel and the center line of the

pump.

4. Repeat the experiment for increments of 1/5th full scale value of the flowmeter from 0 to

maximum throughput.

5. Measure distance between liquid level in spherical vessel and the center line of the pump.

6. Duplicate your data.


1. Calculate total discharge head and show the variation of this value with respect to

throughputs.

2. Calculate NPSH theoretically and experimentally and express the effects of change in

flowrates on these characteristics.

3.2.6. References

1. Bennett, C.O., and J. E. Myers, Momentum, Heat and Mass Transfer, 3rd edition, McGraw-

Hill, 1983.

2. McCabe, W. L., J. C. Smith, and P. Harriot Unit Operations of Chemical Engineering, 4th

edition, McGraw-Hill, 1987.


11

3. Perry, R. H., and D. Green, Perry's Chemical Engineers’ Handbook, 6th edition, McGraw-

Hill, 1988.

12

3.3. HYDRAULICS BENCH AND ACCESSORIES- ENERGY LOSES IN PIPES

Keywords: Fluid mechanics, head loss, flow in pipes, friction in pipes

3.3.1. Object

The object of this experiment is to investigate the head loss due to friction in the flow of water

through a pipe and to determine the associated friction factor. Both variables are to be

determined over a range of flow rates and their characteristics identified for both laminar and

turbulent flows.

3.3.2 Theory

A basic momentum analysis of fully developed flow in a straight tube of uniform cross-section

shows that the pressure difference (p1 – p2) between two points in the tube is due to the effects of

viscosity (fluid friction). The head-loss Δh is directly proportional to the pressure difference

(loss) and is given by

ρg

ppΔh 21

(3.3.1)

and the friction factor, f, is related to the head-loss by the equation

2gd

fLvΔh

2

(3.3.2)

where d is the pipe diameter and, in this experiment, Δh is measured directly by a manometer

which connects to two pressure tappings a distance L apart; v is the mean velocity given in terms

of the volume flow rate Qt by

2

t

Πd

4Qv

(3.3.3)

The theoretical result for laminar flow is


13

Re

64f

(3.3.4)

where Re = Reynolds number and is given by

ν

vdRe

(3.3.5)

and υ is the kinematic viscosity.

For turbulent flow in a smooth pipe, a well-known curve fit to experimental data is given by

0.250.316Ref (3.3.6)

14

3.3.3. Apparatus

Other than the main apparatus, a stopwatch to allow us to determine the flow rate of water, a

thermometer to measure the temperature of the water and a measuring cylinder for measuring

flow rates are all needed.


Setting-up for high flow rates

The test rig outlet tube must be held by a clamp to ensure that the outflow point is firmly

fixed. This should be above the bench collection tank and should allow enough space for

insertion of the measuring cylinder.

Join the test rig inlet pipe to the hydraulic bench flow connector with the pump turned off.

Close the bench gate-valve, open the test rig flow control valve fully and start the pump.

Now open the gate valve progressively and run the system until all air is purged.

Open the Hoffman clamps and purge any air from the two bleed points at the top of the Hg

manometer.


15

Setting up for low flow rates (using the header tank)

Attach a Hoffman clamp to each of the two manometer connecting tubes and close them

off.

With the system fully purged of air, close the bench valve, stop the pump, close the outflow

valve and remove Hoffman clamps from the water manometer connections.

Disconnect test section supply tube and hold high to keep it liquid filled.

Connect bench supply tube to header tank inflow, run pump and open bench valve to allow

flow. When outflow occurs from header tank snap connector, attach test section supply

tube to it, ensuring no air entrapped.

When outflow occurs from header tank overflow, fully open the outflow control valve.

Slowly open air vents at top of water manometer and allow air to enter until manometer

levels reach convenient height, then close air vent. If required, further control of levels can

be achieved by use of hand-pump to raise manometer air pressure.

Taking a Set of Results

Running high flow rate tests

Apply a Hoffman clamp to each of the water manometer connection tubes (essential to

prevent a flow path parallel to the test section).

Close the test rig flow control valve and take a zero flow reading from the Hg manometer,

(may not be zero because of contamination of Hg and/or tube wall).

With the flow control valve fully open, measure the head loss “h” Hg shown by the

manometer.

Determine the flow rate by timed collection and measure the temperature of the collected

fluid. The Kinematic Viscosity of Water at Atmospheric Pressure can then be determined

from the table.

Repeat this procedure to give at least nine flow rates; the lowest to give “h” Hg = 30mm

Hg, approximately.

Running low flow rate tests

Repeat procedure given above but using water manometer throughout.

16

With the flow control valve fully open, measure the head loss “h” shown by the

manometer.

Determine the flow rate by timed collection and measure the temperature of the collected

fluid. The Kinematic Viscosity of Water at Atmospheric Pressure can then be determined

from the table provided in this help text.

Obtain data for at least eight flow rates, the lowest to give h = 30mm, approximately.


1) Plot f versus Re.

2) Plot ln(f) versus ln(Re).

3) Plot ln(head loss) vs ln (velocity)

4) Identify the laminar and turbulent flow regimes, what is the critical Reynolds Number.

5) Assuming a relationship of the form f = KRen calculate these unknown values from the

graphs you have plotted and compare these with the accepted values shown in the theory

section.

6) What is the cumulative effect of experimental errors on the values of K and n?

7) What is the dependence of head loss upon flow rate in the laminar and turbulent regions

of flow?

8) What is the significance of changes in temperature to the head loss?

3.3.6. References

Wilkes, O. J., 1999, Fluid Mechanics for Chemical Engineers, Prentice Hall, New Jersey


17

3.4. FLOW CURVE DETERMINATION FOR NON-NEWTONIAN FLUIDS

Keywords: Newtonian, non-Newtonian flow, viscosity, apparent viscosity, shear rate.

3.4.1. Object

The object of the experiment is to determine the apparent viscosity, a, as a function of shear rate

and to investigate the effect of diameter and the length of the glass capillaries on flow curves.

3.4.2. Theory

The volume rate of flow „Q‟ of a Newtonian liquid in a horizontal capillary tube under steady,

fully developed and laminar conditions is described by the equation:

Q = R4(-P')

8 (3.4.1)

with

L

ΔPconstant

dx

dPP (3.4.2)

where , P, L and R are the viscosity, pressure drop across the capillary, length and radius of

the capillary, respectively. The pressure drop across the capillary tube in the set up is also given

by:

P= gh(t) (3.4.3)

where ‘‟ is the liquid density, and ‘g’ is the acceleration due to gravity. The change of ‘h’ with

respect to time can be expressed as:

18

dh(t)

dt- =

Q

A = R4( gh(t))

8LA (3.4.4)

where ‘A’ is the cross sectional area of the burette. Integration of Equation (3.4.4) gives:

ln [h(t)] =

R4( g)

8LA + C =

B

t + C = mt +C

(3.4.5)

where

B = R4g

8LA (3.4.6)

m = d ln [h(t)]

dt =

B

(3.4.7)

log [h(t)] vs t plots for such liquids are thus expected to be linear having negative slopes (which

may be used to estimate viscosity for Newtonian liquids).

In the case of non-Newtonian liquid, the shear stress, is not linearly related to the shear

rate and the 'apparent' viscosity is a function of the shear rate. Rabbinowitsch and Mooney

have presented an extremely ingenious method of analyzing experimental data on flow through

capillaries under these conditions. Their final equations are given by the following equations:

w = R P2L

(3.4.8)

and

1

a(w) = w

w = e +

w

4 de

dw (3.4.9)

Here, w and w are the shear stress and the shear rate at the capillary wall any time t, e, is

defined by:


19

e = 4Q

R3w

= 8QL

R4P (3.4.10)

Equation (3.4.3) may still be used to estimate „P‟ as a function of time, and the flow, Q, can

easily be determined experimentally at different times, using

Q = - A dh(t)

dt (3.4.11)

Thus both ‘w’ and ‘e’ can be obtained as functions of time from a single experiment on flow

through the capillary. Plots of e vs w can be made and both ‘a’ and ‘w’ can be obtained for a

particular time. Thus, the function a (w) can be determined. This is identical to a ( ), since the

apparent viscosity is a material property.

Because of errors introduced in computing the slopes of Equation (3.4.9) curve-fitting

experimental data is suggested using

h(t) = h0 exp {-kt + (a + bt)2} (3.4.12)

where h0 is the height of the meniscus at time t=0 and k, a, and b are constants. The

corresponding form of the Equation (3.4.9) is then

dt

dm

4m

11

Bρ

m

τ

γ

)(γη

12

w

w

wa

(3.4.13)

where

bt)(a2bkdt

d(lnh)m (3.4.14-a)

dmdt

= 2b2 (3.4.14-b)

and ‘B’ is given by Equation (3.4.6).

20

The method of analysis of experimental data h(t), on any system, is to obtain „k‟, „a‟, and „b‟ by

Excel Solver.

3.4.3. Apparatus

The apparatus used in this experiment is shown in Figure 3.4.1:

Figure 3.4.1. The experimental setup.


1. Take a glass capillary 0.8 mm in diameter, 20 cm in length, and attach it to a 50 ml burette.

2. Fill the burette with 0.13 % (wt) CMC solution previously prepared and note the height of

the solution (h0).

3. Open the valve of the burette and start the stopwatch at the same tine.

4. Record the time for every 4 ml level drop of the solution.

5. Repeat the above procedure for the capillaries having diameter of 0.8 mm and lengths of 30,

39.6 cm, and for the capillaries having diameter of 1.2 mm and lengths of 20, 30, 39.6 cm.


21


1. Prove the Equation (3.4.13).

2. Plot log [h(t)] vs t graph using experimental data and excel solver parameters.

3. Plot viscosity vs time graphs.

4. Plot viscosity vs shear rate graphs.

3.4.6 References

1. Bird, R. B., W. E. Steward, and E. N. Lightfoot, Transport Phenomena, 1st edition, John

Wiley and Sons Inc., New York, 1960.

2. Fery, J. D., Viscoelastic Properties of Polymers, 2nd edition, John Wiley and Sons Inc.,

New York, 1960.

3. McCrum, N. G., C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering,

Oxford University Press, New York, 1961.

4. Nielsen, K. L., Methods in Numerical Analysis, 1st edition, Macmillan, New York, 1960.

22

3.5. FIXED AND FLUIDIZED BED APPARATUS

Keywords: fixed bed, fluidized bed, Ergun equation, Carman-Kozeny equation, head loss

3.5.1. Object

EXPERIMENT A

To investigate the characteristics associated with water flowing vertically upwards through a bed

of granular material as follows:

To determine the head loss (pressure drop)

To verify the Carman-Kozeny equation

To observe the onset of fluidization and differentiate between the characteristics of a

fixed bed and a fluidized bed

To compare the predicted onset of fluidization with the measured head loss

EXPERIMENT B

The object of this experiment is to investigate the characteristics associated with air flowing

vertically upwards through a bed of granular material as above.

3.5.2. Theory

The pressure drop required for a liquid or a gas to flow through the column at a specified flow

rate is calculated by Ergun Equation.

3

2

(1 )150 1.75

( ) (1 ) Re

p

sm

DP

L V

(3.5.1)

Carman-Kozeny equation:

3

2

(1 )150

( ) (1 ) Re

p

sm

DP

L V

(3.5.2)


23

Dp Size of the particle/ballotini 0.460 mm (Exp. A)

0.275 mm (Exp. B)

L Height of bed 0.3 m

ρs Particle density 2960 kg/m3

Dynamic viscosity of the fluid (water or air) Ns/m2

d Bed diameter 0.05 m

Density of the fluid (water or air) (kg/m3)

Void fraction of the bed 0.470 (Exp. A)

0.343 (Exp. B)

Re = Average Reynolds‟ number based on superficial velocity

Re = Dp.Vsm. / (3.5.3)

Vsm = Average superficial velocity (m/s)

sm

QV

A (3.5.4)

where Q is the volumetric flow rate of the fluid and A is the cross-sectional area of the bed

As the pressure drop (h) across the fixed bed is measured in mm H2O, then

310

h

g

P

w where g = 9.81m/s

2 (Exp. A) (3.5.5)

310

h

g

P

ww

a

where g = 9.81m/s

2 (Exp. B) (3.5.6)

Predicted pressure drop across a fixed bed:

2 2

2 3 3

150 (1 ) ( ) 1.75 ( ) (1 ) sm w sm

p w p

L V L Vh

D g D g

(Exp. A) (3.5.7)

2 2

2 3 3

150 (1 ) ( ) 1.75 ( ) (1 ) sm a sm a

p w p w

L V L Vh

D g D g

(Exp. B) (3.5.8)

24

Predicted pressure drop across a fluidized bed:

(1 ) ( )s wP L g (Exp. A) (3.5.9)

(1 ) ( )s aP L g (Exp. B) (3.5.10)

(1 )

( )s w

w

h L

(Exp. A) (3.5.11)

(1 )( )s a

w

h L

(Exp. B) (3.5.12)

3.5.3. Apparatus

CEL with the water circuit filled with coarse ballotini (Exp. A)

CEL with the air circuit filled with fine ballotini (Exp. B)

Figure 3.5.1. Fixed and Fluidized Bed Apparatus.


25


Experiment A

1. Fill the water test column to a height of 300 mm with the coarse grade of ballotini.

2. Close the water flow control valve.

3. Check that there are no air bubbles in the water manometer or the tubing connected to it.

4. Switch on the water pump.

5. Adjust the water flow rate in increments of 0.1 l/min from 0.1l/min to maximum flow

rate. At each setting allow the conditions to stabilize then record the height of bed, the

differential reading on the manometer, and state of bed. Tabulate results.

6. Repeat the experiment two more times.

Note: For coarse ballotini = 0.471 and Dp= 0.460 mm.

Experiment B

7. Fill the air test column to a height of 300 mm with the fine grade of ballotini.

8. Close the air flow control valve.

9. Check that the water levels in the manometer read zero, if not, adjust the level

accordingly.

10. Switch on the air pump.

11. Adjust the air flow rate in increments of 1.0 l/min from 1 l/min to maximum flow rate. At

each setting allow the conditions to stabilize then record the height of bed, the differential

reading on the manometer, and state of bed. Tabulate results.

12. Repeat the experiment two more times.

Note: For fine ballotini = 0.343 and Dp= 0.275 mm.

26


1. Derive all equations (3.5.7) - (3.5.12) in Theory section.

2. Draw the graph of water and air flow rate against bed pressure drop (ΔP) from the

experimental values obtained in Part A and in Part B, respectively, and estimate

experimental fluidization point for both cases.

3. Calculate superficial velocity, Reynolds number, hfixed, ΔPfixed, hfluidized, ΔPfluidized for each

flow rate.

4. Calculate theoretical fluidization point for both cases by equating (3.5.7) & (3.5.11),

(3.5.8) & (3.5.12). Show your error calculations and give reasons for discrepancies

between these values.

Chapter 3

Documents

total discharge

head loss

chemical engineering

shear rate

flow rate

head due

experimental

experimental