flow measurement lab procedures - university of...

ME 4600:483 – Lab Notes Revised 11/16/2015

Flow Measurement of 18

Flow Measurement

Table of Contents

Flow Measurement ......................................................................................................................... 1

I. Objective ................................................................................................................................. 1

II. Apparatus ............................................................................................................................... 1

III. Principles and Background .................................................................................................. 1

Pitot-Static Tubes .................................................................................................................... 2

Orifice Plates and Unrecoverable Losses ................................................................................ 4

Flow Development .................................................................................................................. 5

Environmental Effects ............................................................................................................. 5

IV. Procedure .............................................................................................................................. 6

Velocity Traverse and Differential Pressure Measurement ..................................................... 6

Recoverable and Non-Recoverable Pressure Drop Measurement ........................................... 9

V. Required Data Analysis ....................................................................................................... 10

VI. References ..................................................................................................................... 11

I. Objective

The object of this experiment is to study the performance of an orifice plate flow measurement

device mounted in a circular duct. In the first part, of the lab experiment, the orifice plate will be

used to determine the volumetric flow through the duct. A series of measurements will also be

taken using Pitot-static probes. In the second part of the lab experiment, the recoverable and the

non-recoverable pressure drop through the duct will be examined.

II. Apparatus

1. a 6 5/8 inch inside diameter clear plastic air duct with fan, orifice flanges, and air

straightener;

2. Dwyer 1/8 th inch diameter Pitot-static probes mounted in a quill with a 12 inch

Starret scale;

3. Several capacitance-based pressure gauges with digital readouts;

4. an orifice plate with a 3.033 inch diameter bore ( = d/D = 3.033/6.625 = 0.458);

5. a twelve inch ruler;

6. a protractor

7. a relative humidity gauge, an aneroid barometer and thermometer to measure ambient

conditions.

III. Principles and Background

Flow measurements must be made in chemical plants, refineries, power plants, and any other

place where the quality of the product or performance of the plant depends on having a precise

flow rate. Flow measurements also enter into our everyday lives in the metering of water and

natural gas into our homes and gasoline into our cars.

In this experiment we will measure the flow of air in a duct. An orifice plate, shown in Figures

1a and 1b, will be used to directly measure the volumetric flow rate. We will also measure the

flow velocity field using a Pitot-static probe, also shown in Figures 1a and 1b. Velocity readings



will be taken across the pipe at different radii, and the volumetric flow rate will be calculated

from integrating these readings over the pipe cross-sectional area.

The flow of fluid in a duct is governed by the conservation equations: conservation of mass,

conservation of momentum and conservation of energy. Because the flow in our duct is

effectively isothermal, we'll neglect the energy equation for now. Conservation of mass for a

control volume with steady-state flow says that mass flow in equals mass flow out.

] A v [ = ] A v [OUT IN

where is the fluid density, v is the average velocity and A is the duct cross-sectional area. For

the isothermal case with nearly constant density (only very small pressure changes allowed, or

will change according to the ideal gas law), the volumetric flow rate Q = vA must be constant

along the duct.

The momentum equation tells us what happens to pressure along the duct. For the case of steady-

state, inviscid (no wall friction) flow along a continuous streamline in a constant density medium,

the Bernoulli equation conserves momentum.

constant = h g + 2

v +

P = h g +

2

v +

P2

222

1

211

where P is the pressure, g is gravity and h is the fluid elevation at arbitrary points 1,2 along the

flow streamline. The difference in pressure between the points is called the recoverable pressure

difference because we can get the original pressure back by simply restoring the original velocity

and elevation. Any viscous losses, like friction, cannot be predicted with the Bernoulli equation -

these are unrecoverable, irreversible losses.

Pitot-Static Tubes

Recoverable pressure differences can be used to measure fluid velocity. The measurement of

velocity by a Pitot-static probe is based on the stagnation of the momentum of fluid in the moving

stream to a zero-velocity pressure force at the Pitot-static probeinlet, a relationship that can be

derived from the Bernoulli equation when v1 = v and v2 (at the probe entrance) goes to zero:

2

2vppp fluiddynamicstaticstagnation

where Pstagnation is the total pressure at the forward facing inlet to the Pitot-static probe where the

velocity becomes zero, Pstatic is the static pressure along the sides of the Pitot-static probe where

the velocity is unchanged from the upstream duct velocity v. The pressure difference, P, is

called the dynamic pressure because it is related to the change in fluid velocity. We can calculate

the duct velocity from the dynamic pressure as,

air

P 2 = v

Note that this expression is only accurate if the P-S tube points directly into v1 such that all of v1

is stagnated. If the P-S tube is misaligned, the measured velocity will be too low.



To obtain an estimate of the volumetric flow in the duct from a series of pitot-static tube velocity

measurements, one must integrate the velocity over the duct area.

dA v = A v = QA

AVG

There are a number of different methods for approximating the above integral. The simplest

method is to divide the duct cross-section into a number of equal area sectors, and measure the

"average" velocity at the center of each sectors. We can then estimate the velocity by calculating

the sum:

avgpipe

Numsectors

i

ipipe

Numsectors

i

ii vANumsectors

vAAv = Q **

11

The above method only works if the positions of the velocity measurements are carefully chosen.

Figure 4 shows how to split the pipe into 6, 12 or 24 equal area sectors. The specific radial

positions are given in the figure.

The dynamic pressure, P, can be measured using capacitance-based differential pressure (DP)

cells or manometers. A manometer relates the pressure difference to the difference in height of

two columns of liquid supported by the respective pressures. The equations of hydrostatics tell us

that if a manometer is connected to a Pitot-static tube the dynamic pressure will be given by P =

g h, where is the manometer fluid density and h is the difference in height of the fluid

columns. The DP cells convert pressure force acting over the surface area of a plate to a

movement of the plate to a varying electrical capacitance, which may be displayed or digitally

acquired. The gages are calibrated in "inches-of-water", an antiquated but common pressure unit

which corresponds to the pressure exerted by a one-inch vertical displacement of water at

standard conditions. It is easy to imagine how experimenters, using water-filled manometers,

chose this as a unit of pressure measurement. We can convert units of "inches-of-water" to

Pascals by the following conversion:

kPa = 4.019 "Inches-of-water"

The dimensions of the Pitot-static probe can be important in assuring that the probe gives an

accurate measure of the velocity. The diameter of the Dwyer Pitot-static probe is 1/8th of an

inch. To minimize the blockage effects of the Pitot-static probe on the measured flow, the

manufacturer recommends that this tube be used in ducts with an inside diameter of three inches

or more. This ensures that the blockage of the probe does not significantly change the duct

velocity at the probe static ports, causing an error in static pressure measurement. The length of

the axial tip of the Pitot-static probe is also critical. In this tube the side ports used to sense the

static pressure in the flowing air are five probe diameters from the end of the tube. This requires

a smooth end design to prevent disturbances from this leading edge from altering the static

pressure to be measured by the side ports. In most Pitot-static probe designs, a minimum distance

of eight diameters is recommended to remove this effect. The bend in the tube is also a minimum

distance from these side ports so that minimal interference will occur. In this tube, the bend is

eight diameters behind the side ports. A shorter distance could produce a higher static pressure

reading than is present in the stream.



Textbook descriptions of Pitot-static probes usually describe their use in a laminar flow. What

happens when Pitot-static probes are used in time-varying turbulent flows? The pressure

difference associated with the fluctuation velocity must move a mass in the pressure sensor to

measure the pressure change associated with a given velocity change. The measurement devices

are thus second-order mechanical systems with their own natural frequency and damping ratio. If

the frequency of the velocity fluctuation is much faster than the natural frequency of the

measuring system, then it will display the average value of the fluctuating signal. This will only

hold true for moderately turbulent flows (less than 10% turbulence intensity) because the velocity

vector must remain approximately parallel to the Pitot-static probe. Duct flows typically have

low enough turbulence intensities that the effect of turbulence can be neglected, but disturbed

regions of flow near sharp edges or area changes can prevent good readings.

Orifice Plates and Unrecoverable Losses

Unlike the pitot tube, which uses local recoverable pressure to find velocity at points in the duct,

many processes apply obstruction flow meters to measure volumetric flow rate for the entire duct.

Obstruction flow meters effectively block part of the duct area, causing an increase in velocity

and therefore a change in recoverable pressure according to the Bernoulli equation. Volumetric

flow is evaluated by measuring the pressure difference between the upstream and downstream

sides of the obstruction, which is an orifice in our experiment.

If we try to use the Bernoulli equation here, however, we will be disappointed. The flow through

an orifice is not inviscid and the pressure difference is only partially recoverable. Downstream of

the orifice flow separation occurs, creating recirculating eddies that affect the downstream

pressure. We need a different equation to account for these unrecoverable losses. A general

equation for unrecoverable pressure drop is

)2

v ( k + )

2

v (

D

L f = P

2r

2

bleunrecovera

where f is an empirical term called a friction factor that accounts for wall friction losses over a

duct of length L and diameter D, and k is a term called a form loss coefficient that accounts for

losses caused by a change in duct configuration like the orifice plate. The velocity vr is calculated

at the smallest area where the form loss occurs, the orifice diameter in this case. Both k and f

depend on a characteristic called the Reynolds number,

D v = Re

where is the fluid viscosity. Reynolds number is an important scaling parameter for fluid

flows. It is often used to predict, whether flow is laminar, with Re less than about 5000, or

turbulent when Re is greater than about 5000. The friction factor can be evaluated using a table

like that shown in Figure 5 given Reynolds number. The form loss must be empirically

estimated for specific objects.

Because orifice plates are used often for flow measurement, engineers have, over time, developed

very detailed instructions, called standards, on how to make plates that give repeatable results.

If these instructions are followed, as they are for the orifice in this experiment, the volumetric

flow is given by the orifice flow equation,



air

oo

P 2 A K = Q

where Q is the volumetric flow rate of air, Ao is the orifice cross-sectional area and Ko is the

orifice flow coefficient. Note that this is nearly the inverse of the unrecoverable pressure drop

equation given before, and Ko is related to but not the same as k. The orifice flow coefficient is a

function of the ratio of the orifice diameter to the duct diameter, = d/D, and the Reynolds

number for flow in the duct. A graph of values for Ko for different Reynolds numbers is shown in

Figure 2a. This figure is for square-edged orifices with flange taps that are spaced one inch in

front of and one inch behind the orifice plate. The Reynolds number, Red1, is based on the duct

diameter. Unlike the earlier unrecoverable pressure drop equation, this equation accounts for

both recoverable and unrecoverable effects.

Alternatively, the following equation can be used for determining volumetric flow rate and

follows a more generalized form. Discharge coefficient can be determined from Figure 2b.

41

/2

air

od

pACQ

Flow Development

Whenever the velocity profile in a duct is perturbed, it will eventually recover to a steady profile

as it traverses the duct. This is called flow development.

When the duct flow goes through the orifice, it forms a high velocity jet downstream. The

pressure in this jet is lower than the upstream pressure, because of unrecoverable viscous effects

(recirculating eddies) and recoverable effects (increased velocity). The duct diameter is the same,

both upstream and downstream of the orifice, so we expect that the jet downstream of the orifice

will eventually expand. After some distance, the velocity profile in the duct will look just like the

upstream profile. At this point, the recoverable component of pressure drop will have recovered,

because velocity is restored. As the jet is expanding, the flow is called a developing flow. In this

region the profile is changing along the duct and there is a radial velocity component. It can be

difficult to take measurements in developing flows. Once the velocity profile has stabilized, and

no longer changes with distance along the duct, the flow is fully developed.

Environmental Effects

The accuracies of both the Pitot-static probe velocity measurement and the orifice flow

measurement are directly related to the accuracy with which the density of the fluid in the duct is

known. Since air can be treated as an ideal gas at atmospheric pressures, its density is directly

proportional to its pressure and inversely proportional to its temperature as defined by the ideal

gas law. The ideal gas law states that:

TRvporTRp

where p is the gas pressure; v is the gas specific volume, which is the reciprocal of the gas density

; R is the gas constant for air; and T is the gas temperature. Both the pressure and temperature

are required in absolute scales. Thus, the density of dry air is:



airair

air

airTR

p

The pressure of the air in the laboratory will be measured with a barometer, while temperature is

measured with a thermometer. We are also at a latitude of 41 degrees, so the acceleration due to

gravity in Akron is approximately 9.79 m/s2.

A further complication is the slight effect of humidity on the density of air. Water vapor is less

dense than air, so humid air is less dense than dry air as represented by the ideal gas equation.

We can account for this by finding the mass ratio, , of water vapor mass to dry air mass in the

air and then correcting for the difference in the gas constant R, which is 0.4615 kJ

/kg K for water

vapor compared to 0.2870 kJ

/kg K for dry air as given by

] 1.608 + 1

+ 1[ =]

)R

R( + 1

+ 1[ =

airdry

air

vaporairdry air humid

One can determine the mass ratio, , from the psychrometric chart (Figure 3) as a function of the

temperature of the air and the relative humidity, , which is the ratio of the vapor pressure of the

partially saturated humid air to the vapor pressure of fully saturated air at the given temperature.

IV. Procedure

The experiment will be conducted in two parts. In the first part, flow rate measurements will be

made using both the orifice and Pitot-static probe traverses and the results will be compared.

Here we will see the development of the flow downstream of the orifice. In the second part, the

static pressure port of the Pitot-static probe will be used to study the recoverable and

unrecoverable components of static pressure drop across the orifice plate and along the duct.

Differential pressure readings are to be taken across the orifice taps and the pitot-static tube ports

with the DP cells. Using these pressure readings and the dimensions of the duct and orifice,

calculation of flow through the duct will be possible.

The room temperature, barometric pressure and relative humidity will be measured so that

accurate estimates of the density of the air in the duct may be made for the velocity calculations.

Velocity Traverse and Differential Pressure Measurement

1. Build a VI to measure two channels of data.

a. Set up the DAQ Assist to read two voltage channels, AI0 and AI1. Set voltage range to

-10 – 10 V and continuously collect 1000 samples at 1000 Hz.

b. Split the signal into the two channels using the “Split Signals” command.

Express – Sig Manip – Split Signals. Drag down on the icon to show both outputs.

c. Add a statistics command to both channels. Mathematics – Prob & Stat – S.D. &

Variance.

d. Add numeric indicators to show the mean and standard deviation of the signals.



2. a. Make sure that the fan and the duct sections are assembled together without gaps or

leaks. The orifice plate should be installed with the sharp edge facing

UPSTREAM and the chamfered edge facing DOWNSTREAM. Record the

orifice parameters from the tag on the plate. The flow straightener should be

installed at the fan end of the duct. Be sure that all access ports other than the

one to be used at the moment are sealed. Make sure that the duct is fully opened

by removing the plate at the end of the duct.

b. Measure the inside diameter of the duct -average several angles.

c. Connect the high-pressure hose of a 5" DP cell to the flange tap at the UPSTREAM

side of the orifice and the low-pressure hose to the flange tap on the

DOWNSTREAM side of the orifice. Verify that the DP cell is also connected to

the data acquisition board. Zero the DP cell readout with the TARE control.

3. Record the temperature, barometric pressure and relative humidity from the weather

station in the laboratory. These data will be used to determine the air densities

for the orifice flow calculation and the Pitot-static probe velocity calculations.

4 a. Calibrate the data acquisition system to be certain the DP cell and the data acquisition

system agree. With no flow in the duct, take 10000 samples at 1000 samples/sec.

Record the mean - it should be close to zero. If not, record the bias under no-

flow conditions.

b. Next, turn the fan on and read the pressure difference on the DP cell display. It will

oscillate in value. Note the time it takes to cycle and try to determine an average

reading by eyeballing. Pinching the hoses to the DP cell may help stabilize the

reading. Now sample the signal and record the mean value. Make sure that the

total sample time is long enough to average out any cyclical fluctuations in the

pressure. The data acquisition may give a reading different than the DP cell. If

so, divide the average DP cell reading by the DAQ system mean measurement



and then input this ratio as the gain for the DAQ system. Sample again to see if

the DP cell and DAQ measurements coincide. If not, keep trying.

c. Take a long sample - long enough to average long-term fluctuations of the DP cell that

you have observed. Record the mean value and standard deviation of the orifice

pressure drop and then turn the fan off.

5. Insert the Pitot-static probe quill in the duct at a vertical location near the end of the

duct, far from the orifice plate or other obstruction. Now attach the two hoses

from a 5-inch DP cell to the Pitot-static probe. Be sure to connect the high-

pressure hose to the total pressure tap of the Pitot-static probe. This is the center

tube of the device and is the tap that rises axially from the quill. Connect the

low-pressure hose to the static pressure tap of the Pitot-static probe. This is the

tap that comes out from the side of the tube. It is connected to the outer tube of

the Pitot-static probe. Check that this DP cell is also connected to the data

acquisition system. NOTE: The DP cell is designed to record only positive

pressure differences (that’s why the ports are labeled high and low). A

negative pressure difference on the DP cell will produce a negative reading

but it is not accurate and therefore the hoses have to be switched in order to

measure a positive pressure difference. However, the recorded pressure

difference may be recorded with a negative sign in order to account for the

switching of the hoses.

6. Align the probe tip to point directly upstream toward the fan, which should be into the

flow. Maintain this alignment of the Pitot-static probe while taking all velocity

measurements. Bring the Pitot-static probe to the bottom of its stroke to make it

touch the inside of the duct wall. Record the location of a convenient marker on

the top of the Pitot-static probe (such as the bottom of the hose) that has a reading

greater than 6.6" on the displacement scale. This is your reference bottom

position in inches.

7 a. Calculate the scale readings for the 12 vertical positions indicated in Figure 4.

Remember that the P-S tube has a diameter of 1/8", so your initial velocity

measurement will be 1/16" away from the wall. Double-check your positions.

You must take readings at appropriate positions, or data analysis will be difficult.

b. Turn the fan on and sample the P-S tube DP cell output at each of the 12 positions

across the diameter of the duct. Be sure to sample long enough. Record the

mean value and standard deviation at each position.

8. Repeat steps 5 and 6 at a location just downstream of the orifice plate. If you are in the

developing flow region, you may get a reading that is negative. If so, rotate the

P-S tube to face downstream and note in your notebook that the velocity

calculated at that point will be negative (toward the fan) rather than positive

when integrating to find volumetric flow.

9. In order to evaluate potential error in the measurement caused by aligning the pitot tube

off-axis, the range of angles must be determined for the P-S tube. Using the

protractor, measure the alignment of the P-S tube to determine the maximum off-

angle at which measurements were taken. When performing the data analysis,



use Figure 6 to determine the uncertainty in the pressure measurement due to this

alignment error.

Recoverable and Non-Recoverable Pressure Drop Measurement

1. a. Use a simple static probe to measure the sum of the recoverable and unrecoverable

static pressure drop along the tube. First, measure the positions of each pressure

port along the length of the duct relative to the fan outlet.

b. Next, connect the high-pressure hose of the 5-inch DP cell to the static pressure port

of the Pitot-static probe. Leave the low-pressure port of the gauge open to the

atmosphere. Zero the DAQ system again by adjusting the bias (if necessary).

c. Turn the fan ON. Starting at the farthest upstream location (closest to the fan), insert

the static probe to the centerline of the duct, and align it with the flow. The

position is not critical but the alignment is. Sample the static pressure at this

location and record the mean value and standard deviation.

d. Move the static probe to the next downstream port and repeat the measurement.

Continue until you have readings for the entire length of the duct. Note: the

indicated pressure can become negative downstream of the orifice plate. The DP

cell isn't designed to read negative pressure, so switch the hoses. Remember that

a positive measurement now means a negative pressure, so be sure you record it

that way. Don't forget to switch the hoses back.

2 a. Measure the total duct non-recoverable pressure drop as a function of flow rate by

taking the difference between the static pressure readings of a far upstream

(near the fan) and a far downstream static probe. Position two Pitot-static

probes in the center of the pipe; one far upstream and one far downstream of the

orifice plate. Choose locations that are in regions of fully developed flow, away

from any obstructions. Connect the high-pressure hose of the 5-inch DP cell to

the static pressure port of the UPSTREAM Pitot-static probe. Connect the low-

pressure hose to the static pressure port of the DOWNSTREAM Pitot-static

probe. The DP cell will now indicate the pressure difference between the probes.

b. Make sure to record two channels (the pressure drop across the orifice and the

pressure difference between the static pressure upstream and downstream). Turn

the fan ON and sample the output of the DP cell connected to the static probes as

well as the DP cell connected to the orifice meter. Make sure the static probes

are properly aligned with the flow. Record the mean values and standard

deviations for each DP cell by exporting the data to a file. From the data we can

compare the duct non-recoverable pressure drop (the difference between the

static probes) with the total duct flowrate measured by the orifice meter.

c. Obstruct the duct outlet, using the gate valve, to reduce the duct flowrate and then

repeat the two readings from step 2b. Repeat the measurements for five

flowrates with orifice DPs of approximately 2.2, 1.8, 1.5, 1.0, 0.7 and 0.3 inches

of water. You don't have to match these values, just use similar spacing

between them, and record the values. Note that these values appear unevenly

spaced because pressure drop across the orifice plate, your reference



measurement of duct flowrate, is related to the square of the flowrate rather than

linearly related.

3. Repeat the room temperature, barometric pressure and humidity measurements for use in

the error analysis. Clean up and leave the equipment in an orderly state.

V. Required Data Analysis

1 a. Find the volumetric flow in the duct using the mean orifice pressure drop

measurement. You must iterate on the orifice coefficient K0 (from Figure 2) and

Re for the duct (which is based on the duct diameter and velocity, not the orifice

parameters). Evaluate the volumetric flow rate, average velocity and Reynolds

number in the duct. Is the flow laminar or turbulent?

b. Evaluate the precision and bias uncertainty in the measured value based on the

standard deviation (precision) and manufacturer's uncertainty (bias) on the

pressure measurement, variations in the room conditions and the accuracy of the

orifice coefficient lookup.

2 a. Make two plots of the duct velocity as a function of duct diameter (using zero as the

center of the duct), calculated from the dynamic pressure measured with the

pitot-static tube during the two vertical traverses. Assume V=0 at the pipe wall.

Do the velocity profiles look symmetric about the center? Do the measured

profiles appear to be laminar or turbulent in nature? Can you determine if the

flow is fully developed at any of the traverses?

b. Estimate the uncertainty in the P-S tube velocity readings based on a the standard

deviations and manufacturer's bias in dynamic pressure measurement, reasonable

errors in tube position and angle (Figure 6), and variations in the room

conditions.

3. Calculate the volumetric flow in the duct by integrating the velocities found from each of

the two pitot traverses over the duct area. You will get two values of Q.

Compare the integration of each traverse with the volumetric flow found from the

orifice.

4. Plot the duct mean static pressure as a function of distance from the fan outlet. Identify

in detail the pressure features that relate to the recoverable orifice pressure drop,

the unrecoverable orifice pressure drop and the friction pressure drop.

5. Use Figure 5 and the duct Reynolds number to calculate the friction pressure drop

expected per unit length of the duct. How does this compare to the measured

change in duct mean static pressure observed downstream of the orifice.

6. Plot the duct non-recoverable static pressure drop, measured from the difference in the

static probe readings, against the duct volumetric flow rate obtained from the

orifice pressure drop measurements in Steps 2b,c. You'll need to calculate the

orifice flow from the orifice mean pressure drop at each of the flowrates. Check

Re for each flowrate to be sure the orifice coefficient is correct. Show that this

plot follows a line of the form (VAORF)2 = C(PN-R) and then evaluate C.



VI. References

1. Theory and Design for Mechanical Measurements. R.S. Figliola and D.E. Beasley, Wiley,

(1991).

2. Fluid Mechanics. F.M. White, McGraw Hill, (1979).

3. Fundamentals of Engineering Thermodynamics. M. J. Moran and H. N. Shapiro, Wiley,

(1988).

Figure 1a. Schematic of the installation of a Pitot-static probe and a metered orifice plate.



Figure 1b. Detail of the velocities, pressures, and flow patterns through a generalized

Bernoulli obstruction metered orifice (White, 1979).

Figure 2a. Graph showing the variation of Flow coefficient with Reynold's number.



Figure 2b. Graph showing the variation of discharge coefficient with Reynold's number

(White, 1979).



Figure 4. The 24 equal area sections of the experimental circular duct.

Figure 6. The effect of Pitot-Static tube yaw angle of measurements of stagnation and

static pressure (White, 1979).

flow measurement lab procedures - university of...

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