FlowMeasLab and Worksheet

7/29/2019 FlowMeasLab and Worksheet

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ME 4600:483 Lab Notes Revised 04/07/05

Flow Measurement

Table of Contents

Flow Measurement ......................................................................................................................... 1I. Objective................................................................................................................................. 1II. Apparatus............................................................................................................................... 1

III. Principles and Background.................................................................................................. 1Pitot-Static Tubes .................................................................................................................... 2Orifice Plates and Unrecoverable Losses................................................................................ 4

Flow Development .................................................................................................................. 5Environmental Effects............................................................................................................. 5

IV. Procedure.............................................................................................................................. 6Velocity Traverse and Differential Pressure Measurement..................................................... 6Recoverable and Non-Recoverable Pressure Drop Measurement........................................... 8

V. Required Data Analysis......................................................................................................... 9VI. References ..................................................................................................................... 10

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 beused to determine the volumetric flow through the duct. A series of measurements will also betaken using Pitot-static probes. In the second part of the lab experiment, the recoverable and thenon-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 airstraightener;

2. Dwyer 1/8 th inch diameter Pitot-static probes mounted in a quill with a 12 inchStarret 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 protractor7. a relative humidity gauge, an aneroid barometer and thermometer to measure ambient

conditions.

III. Principles and Background

Fl t t b d i h i l l t fi i l t d th


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will be taken across the pipe at different radii, and the volumetric flow rate will be calculatedfrom 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 iseffectively isothermal, we'll neglect the energy equation for now. Conservation of mass for acontrol volume with steady-state flow says that mass flow in equals mass flow out.

]Av[=]Av[ OUTIN

where is the fluid density, v is the average velocity andA is the duct cross-sectional area. Forthe isothermal case with nearly constant density (only very small pressure changes allowed, orwill change according to the ideal gas law), the volumetric flow rate Q = vA must be constantalong 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=hg+2

v+

P=hg+

2

v+

P2

222

1

211

wherePis the pressure,gis gravity and h is the fluid elevation at arbitrary points 1,2 along theflow streamline. The difference in pressure between the points is called the recoverable pressuredifference 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 ofvelocity 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 bederived from the Bernoulli equation when v1 = v and v2 (at the probe entrance) goes to zero:

2

2v

ppp fluiddynamicstaticstagnation ==

wherePstagnation is the total pressure at the forward facing inlet to the Pitot-static probe where thevelocity 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, iscalled the dynamic pressure because it is related to the change in fluid velocity. We can calculate

the duct velocity from the dynamic pressure as,


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To obtain an estimate of the volumetric flow in the duct from a series of pitot-static tube velocitymeasurements, one must integrate the velocity over the duct area.

dAv=Av=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:

( ) avgpipeNumsectors

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 oftwo 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, whereis the manometer fluid density and h is the difference in height of the fluidcolumns. 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 digitallyacquired. 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 atstandard 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 anaccurate 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, themanufacturer recommends that this tube be used in ducts with an inside diameter of three inchesor 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 ofthe 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 requiresth d d i t t di t b f thi l di d f lt i th t ti


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Textbook descriptions of Pitot-static probes usually describe their use in a laminar flow. Whathappens 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 tomeasure 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. Ifthe frequency of the velocity fluctuation is much faster than the natural frequency of themeasuring 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 velocityvector 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 disturbedregions 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 velocityand therefore a change in recoverable pressure according to the Bernoulli equation. Volumetricflow 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 throughan orifice is not inviscid and the pressure difference is only partially recoverable. Downstream ofthe orifice flow separation occurs, creating recirculating eddies that affect the downstream

pressure. We need a different equation to account for these unrecoverable losses. A generalequation for unrecoverable pressure drop is

)2

v(k+)2

v(D

Lf=P

2r

2

bleunrecovera

wherefis an empirical term called a friction factor that accounts for wall friction losses over aduct of lengthL and diameterD, and kis a term called a form loss coefficient that accounts forlosses 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 kandfdepend on a characteristic called the Reynolds number,

Dv=Re

whereis the fluid viscosity. Reynolds number is an important scaling parameter for fluidflows. It is often used to predict, whether flow is laminar, with Re less than about 5000, orturbulent when Re is greater than about 5000 The friction factor can be evaluated using a table


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air

oo

P2AK=Q

where Q is the volumetric flow rate of air,Ao is the orifice cross-sectional area andKo is theorifice flow coefficient. Note that this is nearly the inverse of the unrecoverable pressure drop

equation given before, andKo 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 Reynoldsnumber for flow in the duct. A graph of values forKo for different Reynolds numbers is shown inFigure 2a. This figure is for square-edged orifices with flange taps that are spaced one inch infront 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 forboth recoverable and unrecoverable effects.

Alternatively, the following equation can be used for determining volumetric flow rate andfollows a more generalized form. Discharge coefficient can be determined from Figure 2b.

41

/2

= airod

pACQ

Flow Development

Whenever the velocity profile in a duct is perturbed, it will eventually recover to a steady profileas it traverses the duct. This is called flow development.

When the duct flow goes through the orifice, it forms a high velocity jet downstream. Thepressure 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 theupstream 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 bedifficult 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 isknown. 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


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airair

airair

TR

p=

The pressure of the air in the laboratory will be measured with a barometer, while temperature ismeasured with a thermometer. We are also at a latitude of 41 degrees, so the acceleration due togravity in Akron is approximately 9.79 m/s

2.

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 theair and then correcting for the difference in the gas constant R, which is 0.4615 kJ/kg Kfor water

vapor compared to 0.2870kJ

/kg K for dry air as given by

]1.608+1

+1[=]

)R

R(+1

+1[=

airdry

air

vaporairdryairhumid

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 thepartially 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 bemade 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 portswith 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 thataccurate estimates of the density of the air in the duct may be made for the velocity calculations.

Velocity Traverse and Differential Pressure Measurement

1. Start the Labview Main DAQ GUI on the computers desktop.

2. a. Make sure that the fan and the duct sections are assembled together without gaps orleaks. The orifice plate should be installed with the sharp edge facing


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c. Connect the high-pressure hose of a 5" DP cell to the flange tap at the UPSTREAMside 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 tothe data acquisition board. Zero the DP cell readout with the TARE control.

3. Record the temperature, barometric pressure and relative humidity from the weatherstation 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 acquisitionsystem 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 willoscillate 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 thereading. Now sample the signal and record the mean value. Make sure that thetotal 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. Ifso, 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 ifthe 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 thatyou 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 theduct, far from the orifice plate or other obstruction. Now attach the two hosesfrom 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 centertube of the device and is the tap that rises axially from the quill. Connect thelow-pressure hose to the static pressure tap of the Pitot-static probe. This is thetap that comes out from the side of the tube. It is connected to the outer tube ofthe 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 positivepressure differences (thats why the ports are labeled high and low). Anegative 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.


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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 velocitymeasurement 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 themean 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 theP-S tube to face downstream and note in your notebook that the velocitycalculated 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 tubeoff-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 unrecoverablestatic 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 theatmosphere. Zero the DAQ system again by adjusting the bias (if necessary).

c. Turn the fan ON. Starting at the farthest upstream location, insert the static probe tothe 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 themean 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 DPcell isn't designed to read negative pressure so switch the hoses Remember that


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Connect the high-pressure hose of the 5-inch DP cell to the static pressure port ofthe UPSTREAM Pitot-static probe. Connect the low-pressure hose to the static

pressure port of the DOWNSTREAM Pitot-static probe. The DP cell will nowindicate the pressure difference between the probes.

b. Make sure to record two channels (the pressure drop across the orifice and thepressure 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 aswell 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 standarddeviations 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 thestatic 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 thenrepeat the two readings from step 2b. Repeat the measurements for five

flowrates with orifice DPs of approximately 2.8, 2.6, 2.2, 1.5 and 0.3 inches ofwater. You don't have to match these values, just use similar spacing betweenthem. Note that these values appear unevenly spaced because pressure drop

across the orifice plate, your reference measurement of duct flowrate, is related tothe square of the flowrate rather than linearly related.

3. Repeat the room temperature, barometric pressure and humidity measurements for use inthe 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 dropmeasurement. You must iterate on the orifice coefficient K0 (from Figure 2) andRe for the duct (which is based on the duct diameter and velocity, not the orifice

parameters). Evaluate the volumetric flow rate, average velocity and Reynoldsnumber in the duct. Is the flow laminar or turbulent?

b. Evaluate the precision and bias uncertainty in the measured value based on thestandard deviation (precision) and manufacturer's uncertainty (bias) on the

pressure measurement, variations in the room conditions and the accuracy of theorifice coefficient lookup.

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


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3. Calculate the volumetric flow in the duct by integrating the velocities found from each ofthe two pitot traverses over the duct area. You will get two values ofQ.

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

4. Plot the duct mean static pressure as a function of distance from the fan outlet. Identifyin 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 dropexpected 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 theorifice 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. CheckRe 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).


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


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

Bernoulli obstruction metered orifice (White, 1979).


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

(White, 1979).


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


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Worksheet 1 for flow lab

Resolution

Air TemperatureAtm Pressure

Rel Humidity

Air Temperature

Atm Pressure Orifice Pressure Drop (4c)

Rel HumidityMean diff.

Pressure

std dev diff.

pressure

Resolution

Diameter

P-S

Diameter

[in] 0.125

Top Reference

Pos:

Top Reference

Pos:

Vertical

Position

Distance from

wall at top [in]

Offset from top

reference [in]

Reading on P-

S ruler

Mean diff.

Pressure

std dev diff.

pressure

Vertical

Position

Distance from

wall at top [in]

Offset from top

reference [in]

Reading on P-

S ruler

Mean diff.

Pressure

std dev diff.

pressure

1 0.14 0.08 1 0.14 0.08

2 0.45 0.39 2 0.45 0.39

3 0.79 0.73 3 0.79 0.73

4 1.18 1.12 4 1.18 1.12

5 1.68 1.62 5 1.68 1.626 2.63 2.57 6 2.63 2.57

Bot Reference

Pos:

Bot Reference

Pos:

Vertical

Position

Distance from

wall at bottom

bottom

reference

Reading on P-

S ruler

Mean diff.

Pressure

std dev diff.

pressure

Vertical

Position

Distance from

wall at bottom

bottom

reference

Reading on P-

S ruler

Mean diff.

Pressure

std dev diff.

pressure

7 2.63 2.57 7 2.63 2.57

8 1.68 1.62 8 1.68 1.62

9 1.18 1.12 9 1.18 1.12

10 0.79 0.73 10 0.79 0.73

11 0.45 0.39 11 0.45 0.39

12 0.14 0.08 12 0.14 0.08

START OF EXP.

END OF EXP.

VERT. PORT AT END OF DUCT VERTICAL PORT IMMEDIATELY DOWNSTREAM ORIFICE

DUCT

A1A2

A3

A6

A7

A12

Cross-section of duct with 12 equal area sections

P-S tube at bottom of duct

P-S tube at top of duct

NOTE: Use this worksheet to record your data. Record numeric values and their units.

The measured voltages in this experiment vary from 0.02V during some measurements to over 2V for others. If you change the voltage resolution of the

DAQ board with the software interface, dont forget to change it back, when the voltage exceeds your selected range. You can tell, that you have bad data,

when you don't see any noise on the display of your measurement data ( the board has saturated at the max. voltage)

Handle the P-S tubes with care, twist them to get them in and out of the duct ports. Don't yank or pull the P-S tubes straight up.


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Worksheet 2 for flow lab

Static pressure drop along the duct

Port 1 2 3 4 5 6 7 8 9

Distance between ports [in] 0

Distance from port 1 [in] 0Pressure diff: (Static Press. -

Atm Press.)

Std dev of pressure diff.

Total duct non-recoverable pressure drop versus flow rate

Orifice pressure drop

duct outlet obstructionMean diff.

Pressure

std dev diff.

pressure

Mean diff.

Pressure

std dev diff.

pressure

unobstructed flow

orifice press. drop about 2.8





OBTAIN FINAL AMBIENT CONDITIONS AND ADD TO WORKSHEET 1

Static pressure dropbetween port1 and

port9

Port1 Port2 Port3 Port4 Port5 Port6 Port7 Port8 Port9

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FlowMeasLab and Worksheet