Fluid Practical

CHAPTER

THREE

FLUID DYNAMICS

3.1. Measurement of Pressure Drop for Flow through Different Geometries

3.2. Determination of Operating Characteristics of a Centrifugal Pump

3.3. Energy Losses in Pipes under Different Flow Conditions

3.4. Viscosity Determination of non-Newtonian Fluids

3.5. Comparison of a Fluid Flow through a Fixed and Fluidized Bed

3.6. Measurement of Pressure Drop in a Packed Tower

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. MEASUREMENT OF PRESSURE DROP FOR FLOW THROUGH DIFFERENT

GEOMETRIES

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

Before the experiment: Read the booklet carefully. Be aware of the safety precautions.

3.1.1. Aim

To investigate the variations in fluid pressure for flow through straight pipes, pipe bends, orifice

and venturi meters.

3.1.2. Theory

In chemical engineering operations, fluids are conveyed through pipelines in which viscous actions

lead to friction between the fluid and the pipe wall. 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. [1]

When a fluid is moving in a closed channel such as a pipe two types of flow can be occurred such

as laminar and turbulent flow. At low velocities, fluid is moving without lateral mixing and there is

no sign of mixing such as eddies or swirl. This type of flow regime is called laminar flow. On the

other hand, at higher velocities lateral mixing occurs with eddies and swirls. This type of flow

regime is called turbulent flow. [2]

The regime of the flow can be predicted using the Reynolds number [3]. The equation that is used

to calculate Reynolds number is shown below:

𝑅𝑒 =𝐷𝑢𝜌

𝜇 (3.1.1)

where,

Re: Reynolds number

D: inside diameter, m

u : mean velocity, m/s

: density of fluid, kg/m3

μ: viscosity of the fluid, kg/m s

3

Bernoulli equation can be applied to find the relation between the velocity difference and the

pressure loss for pipes and fittings, [4]

∆𝑃

𝜌+ 𝑔∆𝑧 +

∆𝑢2

2+ 𝑊 + 𝐹 = 0 (3.1.2)

where,

∆𝑃: pressure drop, Pa

g: gravitational acceleration, m/s2

W: work done or to the system, J

F: frictional dissipation, J

z: elevation, m

3.1.2.1. Pressure Drop in Straight Pipes

The head loss due to friction in straight pipe can be calculated by the expression [5]:

∆𝑃𝑠𝑡 = 4𝑓𝐿𝑢2𝜌

𝐷 (3.1.3)

where

∆𝑃𝑠𝑡 : pressure drop for straight pipe, Pa

D : diameter of pipe, m

f : friction factor

L : length of pipe, m

3.1.2.2. Pressure Drop in Smooth and Sharp Bends

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. The relationship between pressure drop and the velocity can be

derived by using the energy balance and the following equation shows the relation in smooth bend

and sharp bends with a constant, KL: [5]

∆𝑃𝑏𝑒𝑛𝑑 =𝐾𝐿𝜌𝑢2

2 (3.1.4)

4

where,

∆𝑃𝑏𝑒𝑛𝑑 : pressure drop for sharp and smooth bends, Pa

KL : dimensionless factor for sharp and smooth bends

3.1.2.3. Pressure Drop through a Venturi Meter

Venturi meter consists of a throttling section which leads to pressure drop due to the turbulence

created at this section. Fluid velocity can be measured by using Bernoulli equation and equation of

continuity in order to calculate the pressure loss through the pipe. 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 venturi meter [6]. Discharge coefficient of venturi meter (C) is inserted into the

Bernoulli equation for 𝑢2 term, and turned into mean velocity to obtain the following relationship

[5],

∆𝑃𝑣𝑒𝑛𝑡𝑢𝑟𝑖 =𝜌𝑢𝑚

2(1−𝛽4)

2𝐶2 (3.1.5)

where

∆𝑃𝑣𝑒𝑛𝑡𝑢𝑟𝑖 : pressure drop for sharp and smooth bends, Pa

β : dimensionless number relating the diameter of the throttling section of venturi

and inside diameter of the pipe

3.1.2.4. Pressure Drop through an Orifice Meter

An orifice meter consists of a circular disk with a central hole which is bolted between the flanges

on two sections of pipe. Bernoulli’s equation is applied to the fluid as it flows through the orifice of

a reduced area because it is found experimentally that a contracting stream is relatively stable, so

that frictional dissipation can be ignored, especially over a short distances. As a result, as the

velocity of the fluid increases, the pressure will decrease. Applying the mass balance and Bernoulli

equation (energy balance), one can get a relation giving the pressure drop through the orifice meter

as; [4]

∆𝑃𝑜𝑟𝑖𝑓𝑖𝑐𝑒 =𝑢2∙𝜌∙(1−𝛽4)

2𝐶2 (3.1.6)

where

∆𝑃𝑜𝑟𝑖𝑓𝑖𝑐𝑒 : pressure drop for orifice meter, Pa

β : dimensionless number relating the diameter of the throttling section of orifice and

inside diameter of the pipe.

C: discharge coefficient of orifice meter

5

Various pipe fittings can be implemented on straight pipes; such as venture meter, orifice meter as

well as smooth and sharp bends. Fluid flow through pipes and fittings can be investigated with

respect to changing liquid flow rate and the effect can be observed via pressure drop.

3.1.3. Experimental Setup

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

1

2

3

4

5

7

10

8

6

5

9

9

9

9

14 13

12

11 11

Figure 3.1.1. The fluid flow unit.

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

6

3.1.4. Procedure

1. Be sure that all isolation valves are open.

2. Set the control valve to 440 gal/h.

3. Report the readings on all water manometers connected to the pressure tappings.

4. Select the pipe line on which the experiment will be performed by turning off the isolation

valves for all other horizontal pipe runs.

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

6. Report the reading on the selected pipe line from the water manometer.

7. Open all isolation valves. Repeat Steps 4-6 for the remaining pipe lines.

8. Operate the control valve from 440-520 gal/h and note manometer readings for each case.

9. With the same flow rates, repeat the experiment once more to avoid vague data.

10.Turn off the flow control valve.

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, pick three values of KL (between 0.2 and 1.0) to determine which one of

these is the most compatible with your experimental results.

3. Draw graphs for experimental and theoretical pressure drop values with respect to volumetric

flow rate to show the effect of flow rate

4. Explain your conclusions.

5. Derive all equations in Appendix.

Safety Issues: Before starting the experiment, be sure to open all the water valves. Wear goggles in

order to prevent water splash from discharge at point 5 in the apparatus. Prevent closing all the

valves at the same time during the experiment.

7

References

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

McGraw-Hill International Book Company, 1967.

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

Chemical Engineering Design, Pergamon Press, Vol. 6, 1983.

3. Bennett, C. O. and J. E. Myers, Momentum, Heat and Mass Transfer, 3rd

Edition, McGraw-Hill

International Book Company, Tokyo, 1987.

4. Wilkes, J. O., Fluid Mechanics for Chemical Engineers, 2nd

Edition, Prentice Hall, 2006.

5. Geankoplis, C. J., Transport Processes and Separation Processes Principles, 4th

Edition,

Prentice Hall, 2003.

6. Munson, B. R., F. D. Young and T. H. Okiishi, Fundamentals of Fluid Mechanics, 4th

Edition,

Wiley, New York, 2002.

Appendix

Table A.1. List of Parameters

Diameter of straight pipe (10-4

m) 254

Length of pipe (10-2

m) 180

Diameter of venturi meter throat (10-2

m) 1.430

Diameter of orifice meter throat (10-2

m) 253

Diameter of pipe with orifice and venturi meter (10-2

m) 381

Area (straight pipe) (10-6

m2) 510

Area (venturi) (10-6

m2) 160

Area (orifice) (10-6

m2) 500

Density (kg/m3) 998.2

Cv (10-3

) 970

Co (10-3

) 630

β (venturi) (10-3

) 380

β (orifice) (10-3

) 664

KL (smooth bend) (10-3

) 800

KL (sharp bend) (10-2

) 440

Area (smooth bend) (10-6

m2) 248

Area (sharp bend) (10-6

m2) 248

8

3.2. DETERMINATION OF OPERATING CHARACTERISTICS OF A CENTRIFUGAL

PUMP

Keywords: Pump, NPSH, cavitation.


3.2.1. Aim

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 discharge 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, hd, is defined as the pressure at the outlet of the pump

plus the velocity head at point of attachment of the gauge, and is given by [1]:

ℎ𝑑 = ℎ𝑑𝑔 + 𝑎𝑡𝑚 +𝑢2

2𝑔 (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

u : velocity at outlet of pump, m/sec

g : gravitational constant, m/sec2

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.

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

point of the pump exceeds the vapor pressure of the liquid being pumped, at the operating

temperature. For all pumps, there is 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

9

efficiency and an increase in noise. For this reason minimum values of NPSH are important and are

usually specified by pump manufacturers. NPSH can be calculated using [2]:

𝑁𝑃𝑆𝐻 = 𝑃𝑖𝑛 − 𝑃𝑣𝑎𝑝 (3.2.2)

where Pin : Pressure at the pump inlet, N/m3

Pvap : Vapor pressure of the liquid, N/m3

The pressure at the pump inlet is made up of several pressures including the static head of liquid

from pump inlet to the liquid surface, external pressure above liquid, velocity head i.e. the head

developed, and head due to friction losses in the suction pipework [2].

Pressure at the pump inlet can be calculated theoretically from Bernoulli's equation [1],

g

F

g

uz

g

P

g

uz

g

P

22

2

11

1

2

22

2

(3.2.3)

where P : pressure, N/m2

: density of the liquid, kg/m3

u : velocity, m/sec

z : height, m

F : friction losses in pipe works


Subscripts 1 and 2 refer to pump inlet and to surface of liquid reservoir, respectively. By applying

the above equation and considering the fact that the height of the liquid (z2) in the reservoir stays

constant and the velocity at the liquid surface (u2) is zero, [1]

Then

g

F

g

uzz

g

P

g

P

2

2

112

21

(3.2.4)

The head due to friction losses in the inlet pipework can be calculated from [1],

10

𝐹 = 2𝑓𝐹𝑢2 𝐿

𝐷 (3.2.5)

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

u : velocity at the inlet of pump, m/sec


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

etc., m

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

For hydraulically smooth surfaces, in which the pipe wall roughness is not important, the fanning

friction factor is calculated by using the Blasius equation, which provides a correlation for the

experimental observations of turbulent flows with Reynolds numbers below 100,000 [1].

4/1Re079.0 Ff (3.2.6)

Piping installations mostly include a variety of auxiliary hardware such as valves and elbows.

Additional turbulence and frictional dissipation is created by these fittings due to the course change

from a straight line, which results in additional pressure drop comparable to that of the pipeline

itself. The effect of the fittings is introduced in the calculation of the pressure drops simply

recognizing that additional pressure drop caused by the fitting would be produced by a certain

length of pipe. Therefore, the contribution of the fitting is also added into the length of pipe, based

on the equivalent length (L/De) to the fitting [1].

The pressure at the inlet of the pump may be calculated through Bernoulli equation along with the

considerations mentioned above. This allows theoretical NPSH calculation and its comparison with

the experimental one. The operating curve and NPSH values enable to evaluate the working

conditions for the centrifugal pump.

11


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

Figure 3.2.1. Pump test unit apparatus.

1. Manometer (open to atmosphere) 6. Valves

2. Pump 7. Elbow

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

4. Bellows 9. Control valve

5. Flowmeter 10. Liquid feed or vacuum connection

3.2.4. Procedure

1. Get the help of the person in charge to turn on the pump.

2. Open the flow meter 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. Record flow meter reading, inlet pressure, and

outlet pressure.

4. Repeat the experiment for increments of 1/5th full scale value of the flow meter from 2 to

maximum throughput.

12

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

pump.

6. Repeat the experiment.

Safety Issues: Do not attempt to turn on the pump on your own, get the help of the person in

charge. During the experiment, do not set the flow to the zero scale reading for any reason. At the

end of the experiment, be sure that the pump is turned off.


1. Calculate total discharge head for each flow rate, and draw discharge head vs. flow rate graph.

(Note that the conversion of the flow rate scale reading is done as follows:

W(lt/min)=3.317R(scale reading)+8.44.)

2. Calculate NPSH experimentally.

3. Calculate NPSH theoretically. (Note that there is an open gate valve, 4:1 contraction, and a 90o

elbow between the reservoir and the pump inlet.)

4. Comment on the hd vs flow rate graph.

5. Discuss the effects of change in flow rate on these characteristics.

References


edition, Prentice Hall, 2006.

2. Sinnott R. K., Chemical Engineering Design, 3rd

edition, Butterworth-Heinemann, 1999.

13

3.3. ENERGY LOSSES IN PIPES UNDER DIFFERENT FLOW CONDITIONS

Keywords: Head loss, flow in pipes, friction in pipes.

Before the experiment: Read the booklet carefully. Be aware of the safety issues. See your TA.

3.3.1. Aim

To investigate the head loss due to friction in the flow of water through a pipe and to determine the

associated friction factor over a range of flow rates for both laminar and turbulent flows.

3.3.2. Theory

For incompressible, Newtonian, isothermal fluids, the energy balance between two points in

continuous flow can be described by the Generalized Bernoulli’s Equation (Wilkes, 2006):

∆ (𝑢𝑚

2

2) + 𝑔∆𝑧 + (

∆𝑃

𝜌) + 𝑤 + 𝐹 = 0 (3.3.1)

Where, 𝑢𝑚 denotes mean velocity of fluid along the pipe, 𝑔 is gravitational acceleration, 𝑧 is

elevation, 𝑃 is pressure, 𝜌 is density, 𝑤 is work on the system and 𝐹is frictional dissipation.

Considering constant pipe diameter and no work term, the equation simplifies to:

𝑔∆𝑧 + (∆𝑃

𝜌) + 𝐹 = 0 (3.3.2)

In this case, the head loss and gain of a system is therefore dependent on elevation change and

pressure difference between two points. Head loss is caused by frictional dissipation, defined

as − 𝐹𝑔⁄ , and denoted as ∆ℎ:

∆ℎ = ∆𝑧 + (∆𝑃

𝜌𝑔) = −

𝐹

𝑔) (3.3.3)

and the Fanning friction factor, 𝑓𝐹, is related to the head-loss by the equation:

14

∆ℎ = −𝐹

𝑔=

2𝑓𝐹𝑢𝑚2 𝐿

𝑔𝐷 (3.3.4)

Where L denotes length of pipe between two measurement points and D denotes pipe diameter.

The theoretical result for laminar flow is given as follows (Wilkes, 2006):

𝑓𝐹 =16

𝑅𝑒 (3.3.5)

where Re = Reynolds number and is given by:

𝑅𝑒 =𝜌 𝑢𝑚𝐷

𝜇=

𝑢𝑚𝐷

𝜈 (3.3.6)

and 𝜈 is the kinematic viscosity, which is ratio of viscosity over density of fluid. For turbulent

regime the roughness of pipe itself comes into play. Colebrook and White equation can be used to

estimate fanning friction factor for turbulence. This correlation is available as a graph:

Figure 3.3.1. Fanning friction factor vs. Reynolds number [1].

15

In the experiment, investigation of pressure drop and head loss due to frictional losses will be made

in both laminar and turbulent flow regimes.

Table 3.3.1. Kinematic viscosity of water at atmospheric pressure.

Temperature

(℃)

Kinematic Viscosity

(m2/s × 10

-6)

Temperature

(℃)

Kinematic Viscosity

(m2/s × 10

-6)

0 1.793 25 0.893

1 1.732 26 0.873

2 1.674 27 0.854

3 1.619 28 0.836

4 1.568 29 0.818

5 1.520 30 0.802

6 1.474 31 0.785

7 1.429 32 0.769

8 1.386 33 0.753

9 1.346 34 0.738

10 1.307 35 0.724

11 1.270 36 0.711

12 1.235 37 0.697

13 1.201 38 0.684

14 1.169 39 0.671

15 1.138 40 0.658

16 1.108 45 0.602

17 1.080 50 0.554

18 1.053 55 0.511

19 1.027 60 0.476

20 1.002 65 0.443

21 0.978 70 0.413

22 0.955 75 0.386

23 0.933 80 0.363

24 0.911 85 0.342


Figure 3.3.2. The experimental apparatus.

16

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. 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.

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).

17

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 using 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.

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.

Safety Issues: No chemicals are required. Make sure to unplug the device after completing the

experiment.


1. Plot f versus Re from experimental data.

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

3. Plot ln(∆ℎ) vs ln (𝑢𝑚)

4. Identify the laminar and turbulent flow regimes, and determine 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 dependence of head loss upon flow rate in the laminar and turbulent regions of flow?

References



18

3.4. VISCOSITY DETERMINATION OF NON-NEWTONIAN FLUIDS

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


3.4.1. Aim

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

Fluids can be classified as Newtonian and non-Newtonian. Newtonian fluids obey the Newton’s law

of viscosity. According to the Newton’s law of viscosity, shear stress is directly proportional to the

velocity gradient defined as shear rate [1]:

τw=μγ̇w (3.4.1)

where γ̇w, 𝜏𝑤, and μ are shear rate, shear stress, and viscosity of the fluid, respectively.

Water, oil and air are considered as Newtonian fluids since they have constant viscosity and almost

no elasticity. Fluids that do not obey Newton’s law of viscosity are non-Newtonian fluids.

Ketchup, custard, toothpaste, blood and paint are non-Newtonian fluids due to their viscoelastic

properties, unsteady viscosity and high elasticity [2].

For incompressible Newtonian fluids the expression for the shear stress is given by Eq. 3.4.1. The

generalized Newtonian fluid model is obtained by replacing the constant viscosity μ by the non-

Newtonian viscosity ηa, a function of shear rate [1]:

τw=ηaγ̇w (3.4.2)

with

ηa=ηa(γ̇w) (3.4.3)

19

Rabinowitsch-Mooney equation is one of the few methods to describe the shear rate of an

incompressible, non-Newtonian fluid with laminar and steady flow regime, as a function of shear

stress [3].

γ̇w=f(τw)= (3Q

πR3) +τw [

d(Q (πR3))⁄

dτw] (3.4.4)

where Q and R are volumetric flow rate and radius of the capillary, respectively. This expression

can be also expressed as:

γ̇w= [3n'+1

4n'] Г (3.4.5)

where Г=4Q/(πR3) and n'= d(lnτw) d(lnГ)⁄ , that is the gradient of the ln τw vs. ln Г curve.

Shear stress at the wall (𝜏𝑤) is defined for all fluids as [2]:

τw=D ΔP

4L (3.4.6)

where ‘D’ and ‘L’ are diameter and length of the capillary, respectively. Pressure drop (ΔP) within

the capillary at any time point is given by:

ΔP=gh(t) (3.4.7)

where ‘’ is the density of the fluid, ‘g’ is the acceleration of the gravity, and ‘h’ is the height of the

liquid above.

Volumetric flow rate (Q) can be evaluated from Equation 3.4.8:

Q=-Adh(t)

dt (3.4.8)

where ‘A’ is the cross sectional area and ‘t’ is the time in the latter one. Negative sign is required in

the second equation to satisfy the sign convention. Volumetric flow rate can be calculated through

the evaluation of time derivative at each time point in the h(t) vs. t graph.

20

The calculation of the gradient of the ln τw vs. ln Г curve by taking the derivative of that curve at

each point enables the calculation of the apparent viscosity. The change of apparent viscosity with

time and shear rate can be investigated, thereby.


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

Figure 3.4.1. The experimental setup for non-Newtonian fluid flow in a capillary tube.

3.4.4. 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 0.5% (wt.) carboxymethyl cellulose sodium (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 time.

4. Record the time for every 1 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

Safety Issues: Carboxymethyl cellulose sodium (CMC) solution is used in the experiment. CMC is

hazardous in case of skin contact (irritant), of eye contact (irritant), and of ingestion. Use splash

goggles, lab coat, and gloves during the experiment. In case of skin contact with CMC, wash

immediately with plenty of water and seek medical attention for irritation. In case of eye contact,

remove any contact lenses, flush eyes with water and seek medical attention. Seek immediate

medical attention in case of inhalation of CMC. In addition, please be careful while working with

glass capillaries to avoid injury. In the case of glass breaking, use glass waste container and inform

the person in charge.


1. Derive Equation (3.4.5).

2. Plot h(t) vs t graph using experimental data.

3. Plot apparent viscosity vs time graphs.

4. Plot apparent viscosity vs shear rate graphs.

References

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

22

3.5. COMPARISON OF A FLUID FLOW THROUGH A FIXED AND FLUIDIZED BED

Keywords: Fixed bed, fluidized bed, Ergun equation, Blake-Kozeny equation, head loss.


3.5.1. Aim

To investigate the characteristics associated with water (case A) and air (case B) flowing vertically

upwards through a bed of granular material as follows:

To determine the head loss (pressure drop)

To verify the Blake-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

3.5.2. Theory

The upward flow of fluid through a bed of particles is a situation encountered both in nature and in

industry. Examples for natural phenomena are the movement of ground water, the movement of

crude petroleum or natural gas through porous media. Flow through packed beds encounters in

several areas of chemical engineering, such as the flow of gas through a tubular reactor containing

catalyst particles or the flow of water through cylinders packed with ion-exchange resin in order to

produce deionized water. In the case of flow through a packed bed, the prediction of the

corresponding pressure drop for certain flow rate is usually necessary, especially if the particles are

small. To determine the pressure drop for a liquid or a gas to flow through the column at a specified

flow rate, the Ergun equation can be expressed in the form: [1]

3

2

(1 )150 1.75

( ) (1 ) Re

p

sm

DP

L V

(3.5.1)

For laminar flow in packed beds, i.e. the case for low Reynolds numbers, the Blake-Kozeny

equation is obtained by ignoring one term (turbulent term) in Ergun equation. For Re < 10, this

equation is generally good:

23

3

2

(1 )150

( ) (1 ) Re

p

sm

DP

L V

(3.5.2)

For highly turbulent flow, Re > 1000, the Burke-Plummer equation obtained by ignoring laminar

contribution [2].

Table 3.5.1. Nomenclature and some specifications.

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

0.275 mm (case B)

L Height of bed

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 (case A)

0.343 (case B)

Re Average Reynolds’ number based on superficial velocity Re = Dp.Vsm. /

Vsm Average superficial velocity (m/s) sm

QV

A

Q Volumetric flow rate of the fluid

A Cross-sectional area of the bed

The phenomenon of fluidization occurs if the pressure drop due to the flow through the bed is

equivalent to the weight of the bed. Thus, the bed is loosened and the particle-fluid mixture behaves

as the same fluid. In fluidized packed-bed, gas or liquid can be used as fluid. The high rate of solid

mixing that accompanies fluidization is utilized in various industrial operations such as catalytic

cracking in petroleum industry, catalyst regeneration, solid-gas reactors, combustion of coal,

roasting of ores, drying, and gas adsorption operations. The most important advantages of fluidizing

a bed where the solid particles are used to catalyze a reaction is excellent contact of the solid and

the fluid, i.e. nearly uniform temperatures even in highly exothermic reaction.

In case of flow through packed-bed, when the flow rate of fluid is gradually increased from zero to

its maximum value, the onset of fluidization and the characteristics of a solid bed are investigated.

At first, when there is no flow, the pressure drop is zero, and the bed has a certain height. As the

flow rate of fluid increases, the pressure drop gradually increases, but the bed height is constant

24

(Figure 3.5.1). In this region, the pressure drop through the bed can be described by the Ergun

equation. After the flow rate reaches a certain value (point A), the bed starts increasing and

continues to expand in height, but the pressure drop remains constant with increasing flow rates.

This is defined as the point of fluidization and it occurs at minimum fluidization velocity (vf). After

fluidization, the constant bed height is larger than the bed height in the initial state since the bed

returns a more loosely packed state if the flow rate of fluid decreases from its maximum value to

zero [3].

Figure 3.5.1. Pressure drop and bed height vs. superficial velocity [3].

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 (3.5.3)

The pressure drop across a fixed bed is predicted by using Ergun equation and the equations above:

2 2

2 3 3

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

p w p

L V L Vh

D g D g

(case A) (3.5.4)

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

(case B) (3.5.5)

25

The fluidization occurs when the particles begin to separate from each other and float in the fluid.

This velocity at fluidization point can be calculated by balancing upward force exerted by the fluid

on the particles and the net weight of the bed, and ignoring small frictional force on the wall.

Upward force on the particles is:

𝐹𝑢𝑝𝑤𝑎𝑟𝑑 = ∆𝑃 ∙ 𝐴 (3.5.6)

Net weight of the particles is:

𝐹𝑛𝑒𝑡 𝑤𝑒𝑖𝑔ℎ𝑡 = 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 ∙ (𝜌𝑠 − 𝜌𝑓𝑙𝑢𝑖𝑑) ∙ g (3.5.7)

where 𝜌𝑓𝑙𝑢𝑖𝑑 is the density of air or water, g is gravity, and the volume of particle is (1 − 𝜀)𝐴𝐿.

The pressure drop across a fluidized bed is predicted by balancing the equation 3.5.6 and 3.5.7:

(1 ) ( )s wP L g (case A) (3.5.8)

(1 ) ( )s aP L g (case B) (3.5.9)

(1 )

( )s w

w

h L

mm H2O (case A) (3.5.10)

(1 )( )s a

w

h L

mm H2O (case B) (3.5.11)

Particulate and bubbling regimes are observed in fluidization. Generally, particulate fluidization

occurs in liquids, the bed expands uniformly, and bubbling fluidization occurs in gas-solid packed-

bed [4].

In this experiment, the characteristics of water and air flowing vertically upward through two

different columns, which are packed with coarse and fine granular materials respectively, will be

investigated. Pressure drop in packed beds will be measured by using water manometer

experimentally and be estimated by using Ergun equation. The velocity at fluidization point will be

determined experimentally and theoretically.

26


Fixed and Fluidized Bed Apparatus with the water circuit filled with coarse ballotini (case A)

Fixed and Fluidized Bed Apparatus with the air circuit filled with fine ballotini (case B)

Figure 3.5.2. Fixed and fluidized bed apparatus.

3.5.4. Procedure

CASE A

1. Measure the height of the water test column packed with coarse grade of ballotini.

2. Check that the water flow control valve is closed.

3. Check that there are no air bubbles in the water manometer, the water levels in the manometer

read zero, if not, adjust the level accordingly.

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.

CASE B

1. Measure the height of the air test column packed with fine grade of ballotini.

2. Close the air flow control valve.

27

3. Check that there are no air bubbles in the water manometer, the water levels in the manometer

read zero, if not, adjust the level accordingly.

4. Switch on the air pump.

5. 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.

6. Repeat the experiment two more times.

Safety Issues: Check the level of water in the tank for case A. Be sure that all valves are closed and

all the electronic devices are unplugged at the end of the experiment.


1. Derive all equations (3.5.4) - (3.5.11) in Theory section.

2. Draw the graph of bed height (mm) and pressure drop (mm H2O) against water and air flow rate

from the experimental values obtained in case A and in case B, respectively, and estimate

experimental fluidization point for both cases.

3. Calculate superficial velocity, Reynolds number, hfixed (mm H2O), hfluidized (mm H2O), for each

flow rate and both cases. Compare these predicted pressure drops with experimental ones.

4. Calculate theoretical fluidization point for both cases by equating (3.5.4) & (3.5.10), (3.5.5) &

(3.5.11). By using flow rates at experimental and theoretical fluidization point, calculate percent

error and discuss reasons for discrepancies between these values.

5. Calculate hfixed (mm H2O) by using Blake-Kozeny equation, compare with experimental values.

References

1. Wilkes, O. J., Fluid Mechanics for Chemical Engineers, 2nd

Edition, Prentice Hall, New Jersey,

2006.

2. Bird, R. B., W. E. Steward and E. N. Lightfoot, Transport Phenomena, 2nd

Edition, John Wiley

and Sons Inc., New York, 2002.

3. McCabe W.E., J.C. Smith and P. Harriott, Unit Operations of Chemical Engineering, McGraw

Hill, New York, 2001.

4. Perry R.H., D.W. Green, and J.O. Maloney, Perry’s Chemical Engineers Handbook, 7th

Edition.

McGraw-Hill, New York, 1997.

28

3.6. MEASUREMENT OF PRESSURE DROP IN A PACKED TOWER

Keywords: Packed tower, pressure drop, Ergun’s correlation, Leva correlation, Bernoulli

equation, counter-current flow.


3.6.1. Aim

The aim of this experiment is to demonstrate the effect of variations in the liquid and gas feed rates

on the pressure drop in a counter-current packed tower gas absorber. The characteristics of a gas

absorption column will be studied to determine (1) the pressure drop across the dry column as a

function of air flow rate and (2) the pressure drop across a wet column as a function of air flow rate

and water flow rate.

3.6.2. Theory

Packed tower absorbers are frequently used to strip out one component of a gas stream. In gas

absorption, a gas stream containing a transferable solute comes into contact with a non-volatile

liquid containing little or no solute. The gas and liquid streams may be arranged in co-current or

counter-current flow. The former is common when the absorbed gas reacts chemically in the liquid

phase, but in general countercurrent flow is used. Countercurrent flow ensures that the depleted gas

about to leave the column encounters fresh liquid, the best possible absorbent. Near the bottom of

the column, the liquid already contains some dissolved gas but it encounters the fresh gas and

further transfer is possible due to the high concentration gradient. Variations in operating conditions

are possible since each stream may be perfectly mixed, partly mixed or unmixed. The process is

assumed to be isothermal [1].

The pressure losses accompanying the flow of fluids through columns packed with granular

material are caused by simultaneous kinetic and viscous energy losses. The essential factors

determining the energy loss, i.e. pressure drop, in packed beds are:

1. Rate of fluid flow

2. Viscosity and density of the fluid

3. Closeness and orientation of packing

4. Size, shape and surface properties of the particles

29

The first two variables concern the fluid, while the latter two the solids. Packed towers used for

continuous countercurrent contact of liquid and gas are vertical columns that have been filled with

packings. The liquid is distributed over and trickles down through the packed bed, thus presenting a

large surface to contact the gas. The frictional losses increase as the gas flow rate is increased. Since

both the gas and the liquid are competing for the free cross-sectional area left by packing, an

increase in liquid flow rate will also result in an increase in the frictional losses. At high gas flow

rates, the frictional drag of the gas on the liquid prevents the liquid from draining down the tower.

As a result, flooding occurs due to accumulation of the liquid. The pressure drop in this condition is

extremely high. In ordinary operation of a packed tower the liquid circulated over the packing

occupies an appreciable fraction of the void volume and reduces the mean free cross-section of area

open to passage of the gas. Thus, in columns with wet packings, at a seemingly constant superficial

gas velocity, the actual gas velocity is increased, and the pressure drop is appreciably greater than

when the packing is dry. For dry packing, pressure drop across the absorption tower can be

calculated theoretically by Ergun equation [2]:

𝑓𝑝 = −∆𝑝

𝜌=

150𝑈0𝜇𝐿(1 − 𝜖)2

𝜌𝐷𝑝2𝜖3

+1.75𝑈0

2𝐿(1 − 𝜖)

𝐷𝑝𝜖3 (3.6.1)

where

∆𝑝 : Pressure drop

𝑈0 : Velocity of fluid

𝐿 : Length of the bed

𝐷𝑝 : Equivalent spherical diameter of the packing defined by: 𝐷𝑝 = 6 ∗𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

𝜌 : Density of the fluid

𝜇 : Dynamic viscosity of the fluid

𝜖 : Void fraction of the bed

For the required pressure drop calculations, Leva correlation is used [3]:

∆𝑝 = 𝑐210𝑐3𝑢𝑡𝜌𝑔𝑈𝑡2 (3.6.2)

where

∆𝑝 : Pressure drop

𝑈𝑡 : Superficial gas velocity

𝜌𝑔 : Gas density

𝑢𝑡 : Liquid superficial velocity

30

C2 and C3 are specified constants. The values of these constants are dependent on the packing type.

For 3/8 inch Raschig ring values, C2 is 7.03 and C3 is 0.084.

In this experiment, the effect of liquid and gas flow rates on the pressure drop will be investigated

for dry and wet packed tower separately. By using Ergun’s correlation for dry columns and Leva

correlation for wetted columns, the comparison between the experimental and theoretical results

will be obtained.


The apparatus is shown in Figure 3.6.1. The unit consists of a 3’’ (7.6 cm) column section filled to a

height of 150 cm with (3/8)’’ Raschig rings. Air and water are the feed materials.

Figure 3.6.1. Gas absorption apparatus.

1.) Liquid inlet 8.) Pressure tap point

2.) Liquid flow meter 9.) Gas vent

3.) Liquid control valve 10.) Packed tower

4.) Liquid flow line 11.) Liquid exit

5.) Gas inlet 12.) Liquid seal

6.) Gas flow meter 13.) Drain valve

7.) Gas control valve

31

3.6.4. Procedure

1. Check that air pressure manometer reading is zero.

2. Open the gas flow control valve and set the gas flow rate to 30 L/min.

3. Allow the column to settle down and measure the pressure difference.

4. Remeasure the pressure difference at gas flow rates; 40 L/min, 50 L/min, 60 L/min.

5. Close the gas control valve, and then open the liquid (water) feed control valve.

6. Set the liquid flow rate to 0.3 L/min, open the gas flow control valve, set the gas flow rate to 30

L/min.

7. Allow the column to reach steady-state operation and then read the pressure difference on the

manometer.

8. With the same liquid flow rate, repeat the same procedure at 40-50-60 L/min gas flow rates,

noting the corresponding pressure drops.

9. Change the liquid flow rate to 0.5 L/min and 0.8 L/min and repeat steps 6 through 8 for these

liquid flow rates.

Safety Issues: Before the experiment, check that all valves are connected to the tower properly. Gas

pressure should not exceed 3 bars throughout the experiment. At the end of the experiment, be sure

that all water and gas valves are closed and the compressor is turned off.


1. Compare the observed pressure drop values with those estimated by Ergun’s correlation for dry

columns and Leva correlation for wetted columns. Make error analysis for each observation.

2. Plot the effects of the gas and liquid flow rates on the pressure drop on graph.

3. Discuss your results and errors.

References

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

edition,

McGraw-Hill, 1967.

2. Ergun, S., Fluid Flow through Packed Columns, Chemical Engineering Progress, Vol. 48, No. 2,

1952.

3. Perry, R.H. and D. Green, Perry’s Chemical Engineer’s Handbook, 6th

edition, McGraw-Hill,

Japan, 1984.

Fluid Practical

Documents

fluid pressure

pressure loss

measurement of pressure

pipe bends

laminar flow

turbulent flow

diameter of pipe

length of pipe