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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.
Chapter 3: FLUID FLOW
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
Chapter 3: FLUID FLOW
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.
Chapter 3: FLUID FLOW
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
Chapter 3: FLUID FLOW
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
3.2.4. Experimental Procedure
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.
3.2.5. Report Objectives
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.
Chapter 3: FLUID FLOW
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
Chapter 3: FLUID FLOW
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.
3.3.4. Experimental Procedure
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.
Chapter 3: FLUID FLOW
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.
3.3.5. Report Objectives
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
Chapter 3: FLUID FLOW
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:
Chapter 3: FLUID FLOW
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.
3.4.4. Experimental Procedure
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.
Chapter 3: FLUID FLOW
21
3.4.5. Report Objectives
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)
Chapter 3: FLUID FLOW
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.
Chapter 3: FLUID FLOW
25
3.5.4. Experimental Procedure
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
3.5.5. Report Objectives
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.