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ME495—Thermo Fluids Laboratory ~~~~~~~~~~~~~~

PIPE FLOW CHARACTERISTICS

AND PRESSURE TRANSDUCER

CALIBRATION ~~~~~~~~~~~~~~

PREPARED BY: GROUP LEADER’S NAME

LAB PARTNERS: NAME

NAME

NAME

TIME/DATE OF EXPERIMENT: TIME , DATE ~~~~~~~~~~~~~~

OBJECTIVE— The objectives of this experiment are to: a) observe the characteristics of flow in a pipe,

b) evaluate the flow rate in a pipe using velocity

and pressure difference measurements, and c)

perform the calibration of a pressure transducer.

Upon completing this experiment you should have

learned (i) how to measure the flow rate and average

velocity in a pipe using a Pitot tube and/or a resistance

flow meter, and (ii) how to classify the general

characteristics of a pipe flow.

Nomenclature

a = speed of sound, m/s

A = area, m 2

C = discharge coefficient, dimensionless

d = pipe diameter, m

d0 = orifice diameter, m

E = velocity approach factor, dimensionless

f = Darcy friction factor, dimensionless K0 = flow coefficient, dimensionless

k = ratio of specific heats (cp/cv), dimensionless

L = length of pipe, m

M = Mach number, dimensionless

p = pressure, Pa

p0 = stagnation pressure, Pa

p1, p2 = pressure at two axial locations along a

pipe, Pa

Q = volumetric flow rate, m 3 /s

R = specific gas constant, J·kg/K

Re = Reynolds number, dimensionless

T = temperature, K

V = local velocity, m/s

V = average velocity, m/s Y = adiabatic expansion factor, dimensionless

 = ratio of orifice diameter to pipe diameter, dimensionless

p = pressure drop across an orifice meter, Pa

 = dynamic viscosity, Pa·s  = air density, kg/m3

INTRODUCTION— The flow of a fluid (liquid or

gas) through pipes or ducts is a common part of many

engineering systems. Household applications include

the flow of water in copper pipes, the flow of natural

gas in steel pipes, and the flow of heated air through

metal ducts of rectangular cross-section in a forced-air

furnace system. Industrial applications range from the

flow of liquid plastics in a manufacturing plant, to the

flow of yogurt in a food-processing plant. Because the

purpose of a piping system is to transport a desired

quantity of fluid, it is important to understand the

various methods of measuring the flow rate.

In order to work with a fluid system, and certainly to

design a fluid system that will deliver a prescribed

flow, it is necessary to understand certain fundamental

aspects of the fluid flow. For this, one should be able

to answer questions like: Are compressibility effects

important? Is the flow laminar or turbulent? Is the

viscosity of the fluid important or not? Is the flow

steady or varying with time? What are the primary

forces of importance? For internal flows in pipes or

ducts, the dominant forces are usually due to viscosity

and pressure. The velocity profile within the pipe is an

important factor since the viscous forces depend upon

the shear rate and hence on the velocity gradient at the

wall of a pipe. Being able to answer the above

questions and to understand their implications on the

flow through a pipe is crucial in being able to

successfully design and operate a pipe flow system.

In this lab you will study the flow of air in a 4-inch

diameter pipe. The flow measurements will be made

using a special type of Pitot tube, a “Kiel probe”

and/or using an orifice meter. The Pitot tube will

allow you to determine the shape of the velocity

profile at the exit of the pipe while the other devices

will allow you to determine the flow rate and average

velocity in the pipe.

THEORY

Compressible vs. Incompressible

Flow in a pipe (internal flow) can be classified as

incompressible or compressible. An incompressible

flow is one in which density variations are negligible.

Most liquid flows are considered incompressible since

it takes a tremendous amount of applied pressure to

increase the fluid density by a measurable amount.

For instance, it takes about 3200 psi (over 200 atm) of

applied pressure to change the density of water by 1%.

Gases, on the other hand, are very compressible. The

ideal gas law,

RTp 

shows that the density of a gas is directly proportional

to its pressure. A guideline used to decide if

compressibility plays a significant role in the flow of a

gas is the value of the Mach number,

aVM /

where V is the speed of the object relative to the

medium, and a is the speed of sound for an ideal gas.

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If 3.0M , then the gas density varies by less than 5%

and the flow can be considered incompressible.

Laminar vs. Turbulent

The second major classification for an internal flow

concerns the “smoothness” of the flow. A laminar

flow is one in which the flow tends to stay in separate,

smooth layers. That is, a given fluid particle will tend

to stay at a single radial position in a circular pipe and

not mix with adjacent layers of fluid. Turbulent flows,

on the other hand, are characterized by significant

mixing of flow between various layers of a fluid. The

Reynolds number, as defined below, is used to specify

whether or not a pipe flow is laminar or turbulent:



 dV Re

It is generally accepted that flow in a pipe is laminar if

the Reynolds number is less than 2,300, in transition

from laminar to turbulent if 2,300 < Re < 4,000, and

turbulent if Re > 4,000. These numbers, though

widely accepted, are guidelines based upon

experimental observations and should not be

considered absolute. For instance, in a well controlled

flow experiment, laminar pipe flow has been observed

at Reynolds numbers well in excess of 2,300 (up to

values on the order of 100,000).

There are many significant differences between

laminar and turbulent pipe flows. At a similar flow

rate, in a turbulent flow the velocity gradient near the

pipe wall is steeper than in a laminar flow, with the

result that a turbulent flow exerts a larger shear stress

on the pipe wall and more energy is dissipated through

friction. Furthermore, in a turbulent flow, the pipe

roughness affects the energy dissipation whereas

roughness typically does not affect a laminar flow in

this way.

Steady vs. Unsteady

A steady flow is one that does not vary in time. If an

observer observes any arbitrary point in a flow field

and notes that the velocity at that point does not vary

over time (except for small, random fluctuations), then

the flow is called “steady.” On the other hand, if the

velocity does vary over time the flow is “unsteady.”

Whether or not a flow is steady or unsteady has

implications on the type of flow measurement system

one might select or design. If the flow is unsteady,

care must be taken to ensure the flow measurement

system responds quickly to changes in the flow rate

such that the measurements are accurate.

Velocity and Flow Rate Measurement

Pitot Tube. A common method of measuring the

velocity of a fluid is to use a Pitot tube (see Fig. 1a).

When directed into an incoming flow, a Pitot tube will

measure the stagnation (total) pressure of the flow. If

the flow is incompressible and inviscid, Bernoulli’s

equation can be applied as follows to determine the

local flow speed [1]:



)(2 0 ppV 

 (1)

A Kiel probe will be used in the lab to make

measurements of the stagnation pressure (see Fig. 1b).

A Kiel probe is less sensitive to errors in misalignment

with the flow direction due to the “shroud”

surrounding the pressure port.

Due to the “no-slip” condition, the fluid in contact

with a boundary has the same speed as the boundary.

Since the pipe is stationary, the air in contact with the

pipe will have zero speed. Thus a significant increase

in the flow velocity will occur between the wall and

the centerline of the pipe where the flow velocity is

maximum. In order to calculate a flow rate using

measurements made with a Pitot tube, it is necessary

Figure 1: (a) Pitot tube inserted in a pipe with associated static pressure tap; (b) Kiel probe showing

the “shroud” around the pressure port.

(a) (b)

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to measure the flow speed at several radial locations at

a given pipe cross-section. Recall that volumetric flow

rate is defined as

AVdAVQ

A

  (2)

If stagnation pressure measurements are made at the

radial locations shown in Figure 2, then the flow rate

can be computed by approximating the integral in Eq.

2 with a sum:

 



N

i

ii AVQ

1

(3)

where iV and iA are the local velocity and area of

each of the N slices of pipe cross-sectional area,

respectively.

Orifice Plate Flow Meter. Restriction flow meters

such as the Venturi tube, flow nozzle, and orifice plate

are commonly used to measure flow rate. These

devices restrict the flow and thereby cause a pressure

drop to occur. The pressure drop can then measured

and related to the flow rate. A diagram of an orifice

meter is shown in Fig. 3.

By combining Bernoulli’s equation and conservation

of mass to a control volume surrounding the orifice

meter, and including empirical coefficients to account

for viscous and compressibility effects, the following

relation for volumetric flow rate results [3, 4, 5]:



)(2 0

p AYKQ

  (5)

Here 0K is an empirical flow coefficient, A is the

area of the orifice, Y is an empirical adiabatic

expansion factor and accounts for compressibility

effects, p is the pressure drop across the orifice, and

 is the fluid density. The flow coefficient is further

defined as

CEK 0 (6)

where

)1(

1

4 

E (7)

and

d

d0 (8)

Here,  is the ratio of orifice to pipe diameter, C is

an empirical discharge coefficient that is a function of

the Reynolds number and  , and E is the velocity

approach factor. Values of the flow coefficient and

adiabatic expansion factor are tabulated in Reference 4

(an excerpt of it is available in the lab).

Figure 2: Location of stagnation pressure measurements along a pipe cross-section.

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EXPERIMENTAL APPARATUS — An illustration

of the experimental apparatus is shown in Figure 4.

Table 1 shows the list of the apparatus components.

The setup consists of a 4-inch acrylic pipe, a Kiel

probe, a Dwyer micromanometer (for calibration of

the pressure transducer), a differential pressure

transducer, and an orifice plate flow meter.

Flow through the pipe is controlled by a butterfly

valve. The micromanometer provides a highly

accurate differential pressure measurement, and is

used as the laboratory standard in calibrating the

pressure transducer. Expect the output of the

differential pressure transducer’s calibration to be

highly linear. Transducers of this type are quite

versatile and are relatively accurate over a reasonably

large range of input pressures. Instructions for

operation of the pressure transducer are provided in

the Appendix A of this document. ASME data on

fluid meters for use with the orifice meter will be

supplied in the lab.

Table 1. Apparatus Components List

1 4” acrylic pipe

2 Kiel probe

3 Dwyer micromanometer

4 Validyne differential pressure transducers

5 Tape measure

6 Calipers

7 Ruler with centimeter scale

8 Duct tape

9 Various sizes of orifice plates

Figure 4: Illustration of the experimental set-up.

Orifice Plate (side view)

Orifice Plate (front view)

Figure 3: Orifice plate flow meter shown with various possible pressure tap arrangements.

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EXPERIMENTAL PROCEDURE

Consult with your teammates if there are any

atmospheric measurements that you should take

before beginning the experiment.

1. Prior to starting measurements, review and understand the definitions of gage pressure, vacuum

pressure, absolute pressure and differential pressure.

2. Familiarize with the experimental apparatus and objectives. Devise a plan for taking data. Be sure

to consider the elements of a data acquisition plan

as described in Ch. 1 of your textbook by Figliola

and Beasley.

3. Collect data for the pressure transducer calibration using the Kiel probe and the micromanometer. The

calibration should relate voltage to pressure at 4 to 6

values of pressure, capturing any hysteresis effects

that may be present.

4. Before beginning your measurements, ask the lab instructor for an orifice plate. Insert the orifice plate

into the pipe and seal the opening with duct tape.

5. Ensure that the control handle on the fan generating the air flow through the pipe is set appropriately.

Now you are ready to perform the flow

measurements using the orifice meter or the Kiel

probe.

6. Measure the pressure drop across the orifice plate.

7. Measure the velocity profile at the exit plane of the acrylic pipe. Consider where the largest velocity

gradients will be located when planning your

measurement increments.

Are there any atmospheric measurements you should

take at the conclusion of your experiment?

EXPERIMENTAL RESULTS and DISCUSSION

1. Determine volumetric flow rate and average velocity using the pressure drop across the orifice

plate and the provided ASME data on flow meters.

2. Plot the horizontal and vertical velocity profile, at the exit of the pipe.

3. Determine the flow rate through the pipe by numerically integrating the velocity profile.

4. Compute the maximum velocity and the average velocity in the pipe.

5. Compare and contrast each method of computing the flow rate and average velocity, and comment on

the strengths and weaknesses of each.

6. Characterize the flow in the pipe as fully developed, laminar or turbulent, compressible or

incompressible, steady or unsteady. Cite at least two

observations or calculations that justify your

answer.

7. Compare the volumetric flow computed from integration of the exit velocity profile with that

determined using the orifice plate.

8. Comment on how does the presence of the orifice meter affect the velocity profile shape and why?

What were the Reynolds number and Mach number

for flow in the pipe?

9. Provide the pressure transducer calibration equation.

10. Comment on the uncertainty of the calibration equation and on the possible sources of error that

affected the calibration process.

Note: 1) Use SI units throughout your report.

2) When submitting the report, each team

member must also submit a peer

evaluation form. The form is in the

appendix of this handout.

REFERENCES

Fox, R. W., and McDonald, A. T., Introduction to

Fluid Mechanics, 4 th

ed., John Wiley & Sons, New

York, 1992, Chapter 6-3.3.

Figliola, R.S., and Beasley, D. E., Theory and Design

for Mechanical Measurements, 2 nd

ed., John Wiley &

Sons, New York, 1995, Chapter 10.4.

Fox, R. W., and McDonald, A. T., Introduction to

Fluid Mechanics, 4 th

ed., John Wiley & Sons, New

York, 1992, Chapter 10.

ASME Research Committee, Fluid Meters, 5 th

ed.,

The American Society of Mechanical Engineers, New

York, 1959.

Figliola, R.S., and Beasley, D. E., Theory and Design

for Mechanical Measurements, 2 nd

ed., John Wiley &

Sons, New York, 1995, Chapter 10.5.

Fox, R. W., and McDonald, A. T., Introduction to

Fluid Mechanics, 4 th

ed., John Wiley & Sons, New

York, 1992, Chapter 8.

Munson, B.R., Young, D.F., and Okiishi, T.H.,

Fundamentals of Fluid Mechanics, 3 rd

ed., John Wiley

& Sons, New York, 1998.

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APPENDIX

Validyne Engineering Corp.

Instructions for the DP45 Differential Pressure Transducers

1. Be sure the pressure transducers are properly wired to the back of the demodulator before turning the power on.

The transducers should be wired as follows:

IN: Black and Red wires twisted together

C1: Green wire

C2: White wire

OUT: + Output signal (Transducer not wired to this terminal)

COM: - Output signal (Transducer not wired to this terminal)

2. Be sure the power strip on the demodulator cart is plugged in and the power is on.

3. Press the power button on the front of the demodulator to turn it on.

4. Use the channel selector to select the appropriate channel (as indicated on the screw terminal on the back of the demodulator).

5. When pressures are measured, be sure the pressure transducer is in a vertical position.

6. Use the ZERO adjustment on the demodulator to zero the voltage reading when both ports on the transducer are at the same pressure. (The easiest way to be sure both ports are at the same pressure is to attach a short piece of Tygon tubing between the

ports.)

7. Only use the SPAN adjustment on the demodulator when the transducer is being calibrated.

8. The maximum pressure the DP45-16 pressure transducer will measure is 1.4 inH20 (differential).

9. The maximum voltage output of the demodulator is 10.0 Vdc.

10. Therefore, at 1.4 inH20 differential pressure, the voltage output should be 10.0 Vdc.

11. The output terminals on the back of the demodulator should output the same dc voltage as indicated on the LCD display on the front of the demodulator. (Note: the OUT and COM terminals on the far lower left of the screw panel will output the voltage

of which ever channel is selected).

Name: ME 495 Lab

Group #:

Peer Evaluation Grade your teammates – be honest: A – Work is exemplary, exciting, engaging. This student made a positive, active, and essential contribution to the team. Outstanding effort

B – Student was a willing participant. Contribution was positive and exactly what was expected. Very good effort and solid work.

C – Fair to average effort. Only worked on tasks when they were assigned. Not much volunteering.

D – Irresponsible and didn’t contribute to the team effort. Hurt team.

F – Who is this person? Were they on our team? Never heard of him/her….. Grade Name