A slender tubehas sidewall holes measure the stagnmay also be of thethe duct diameter,this investigation.

Instead of meatransducer, as in F

Pitot tubes aretotal pressure meapitot tube is equal higher than the strethe error due to lowAnd this is for pitotfor example, U = 1resolution of most

The accuracy ostatic pressure meFortunately, they cof attack of 30o.ME-EM 3220 ENERGY LABORATORY

Air Flow Measurements

Pitot Static Tube aligned with the flow can measure local velocity by means of pressure differences. Itto measure the static pressure ps in the moving stream and a hole in the front toation pressure po, where the stream is decelerated to zero velocity. The pitot static tubemodified ellipsoidal-nose type. The tube has a very small diameter compared to that ofbut the resultant error caused by the additional blockage effect is considered minimal for

suring po and ps separately, it is customary to measure their difference with, say, aigure 1.

Figure 1 Pitot Tube Configuration

affected by Reynolds number at low fluid velocities. The minimum Reynolds number forsurements is approximately 30. This is the point where the characteristic length of theto the diameter of the impact hole. Below this value, the indicated impact pressure isam impact pressure due to viscosity effects. For air at standard atmospheric conditions, Reynolds number is only apparent for air velocities less than 12 ft./sec. (3.66 m/sec.).tubes with impact hole diameters of 0.010 inches (0.2543 mm) or less. For low-velocity

ft./sec. in standard air, p0-p equal to only 0.001 lbf/ft2 (0.048 Pa). This is beyond the

pressure gages.f pitot tubes is also affected if the sensor head is not parallel to the fluid. The total and

asurement error due to yaw and pitch angles increase rapidly above angles of 5 o.ancel each other out so velocity pressure measurements are 2% accurate up to angles

Fluid flow

V po

ps

ps

ps

popopo1

The measurempresence of a pitotpassage which incpressure which is l

The speed of rwithin the probe, thmanometer determordinary manometerapidly for smaller having a 1/16 inchethe pressure sensotubes that have ve

The pitot staticthe stream Mach n

If ReD > 1000,Bernoullis relation

or

For an incomp

Assuming that

Here is the air de

is the static pretemperature in Kel

The velocity mis done as follows

where

p2 p1----------------- +

p1-----

12---V 1

2+

ps12---V+

V th2-=

ps

RT-------=

ps

V V=

f Re(=

ReD---=ents of static pressure is also sensitive to the presence of fluid boundaries. The tube in a pipe also affects the static pressure. The pitot tube partially blocks the flowreases the flow velocity in the vicinity of the device. This results in an indicated staticess than the actual static pressure.esponse of pitot tubes is also geometry dependent. The diameter of the air passagee diameter and length of the interconnecting tubes, and the displacement volume of theines the time constant. For tubes diameters greater than 1/8 inches (3.175 mm) andr connections, the time constant is very short. However the time constant increases

diameter tubes, with a response time of approximately 15 to 60 seconds for tubess (1.59 mm) diameter. Because of the slow response of the fluid-filled tubes leading tors, it is not useful for unsteady-flow measurements. One common problem with pitot

ry small diameters is that they tend to choke up easily if there is fine dirt in the fluid.tube is useful in liquids and gases; for gases a compressibility correction is necessary ifumber is high. where D is the probe diameter, the flow around the probe is nearly frictionless and applies with good accuracy.

[1]

[2]

ressible flow

[3]

the elevation pressure difference is negligible, this reduces to

[4]

nsity in kg/m3;

, [5]

ssure in Pascal, is the gas constant and the value is 287 m2/(s2.K), is the absolutevin.easured by the pitot tube needs to be corrected due to geometry and flow interactions. It

[6]

, and the Reynolds number,

[7]

12--- V 2

2 V 12

( ) g z2 z1( )+ 0=

gz1+p2-----

12---V 2

2 gz2+ + const= =

2 gzs+ p012--- 0( )

2 gz0+ +

g zs z0( )p0 ps( )------------------------

R T

th

D)VD---------2

Table below giv

Since V is not STEP 1: -

Hint: Start STEP 2: - STEP 4: - STEP 5: - STEP 6: - NOTE:

Different sensors wavailable use the tahave, you may also

For channel floevaluating the effec

where N is the num

ReD

Peff =es the range of as a function of Reynolds numbers.,

known, process is one which requires iteration, as described next;guess your values anywhere from 0.986 to 0.991from the lowest value.plug in the values and calculate VEvaluateLook up your guess values whether it matches with the calculated or notIf the assumed values is not in the calculated range, repeat Steps 1 - 5.

ill require a calibration data generated for that particular case. If such information is notble above as valid for the pitot tube you are using. Depending on the application you be advised to delete velocity correction altogether, = 1.

w where an average velocity is required, can also be determined bytive pressure (or average) for the channel after multiple measurements as follows:

[8]

ber of measurements.

0.986 0.988 0.990 0.991

3 104 1 105 3 105 1 106

ReD

ReD ReD

p0 ps( )

1N---- P j

0.5

j 1=

j N=

23

CaThe volumetric

that a fluid of veloc

Denoting the csection of the duct

For a flow whic(centerline) as it isdependency otherw

What follows is

and the infinitesima

where r is the radiaproduct can be simthe tube. Thus

where u is the magtube is given by

Knowing the veSince the data set integral. We can, hnumerical estimateunderneath a curve

The curve in F, etc.

by the shaded rect

Q A=

u u r( )=

dA 2=

u r( ) n

Qr 0=

r R=

=

u2 u r2( )=lculating the Flow Rate from the Velocity Profile airflow rate can be directly determined from the velocity profile across the duct. Recallity passing across an infinitesimal area dA with outward unit normal vector .

Figure 2 Velocity Profile

ross sectional area of the duct as A, the volume flow rate through any given cross can be found from integration

[9]

h is axisymmetric, the velocity is only a function of radial distance from the tube axis in the case of circular cross-section but it will have also have an azimuthal angle

ise. a discussion for a channel of circular cross-section area only. In this instance,

[10]l area element

[11]l distance from centerline, which varies from r=0 to r=R (the tube wall). The vector dot-plified by recognizing the flow velocity is always perpendicular to the cross section of

[12]nitude of the velocity. With these simplifications, the volumetric flow-rate in the circular

[13]

locity profile u(r) then allows us to calculate the volumetric flow rate by integration.is usually limited to a finite number of values u(r), we cannot perform the exact analyticowever, use a numerical estimate to approximately evaluate the flow rate. Thisis best understood by recognizing that integration is the process of calculating the area.

igure 3 represents the true function u(r), for which the discrete values ,are available. We can approximate the integration by summing the areas representedangles. In this case, the flow rate can be estimated from

u n

u

n

dA

u n( ) Ad

rdr

u r( )=

2u r( )r rd

u1 u r1( )=4

Figur

Mass flow rate

An analysis sim

Q 2n =

6

Q 2 u(

m Q=e 3 Approximating an Analytic Integral With Discrete Numeric Values

[14]

[15]

can be evaluated as

[16]

ilar to above can be performed for rectangular cross-sections as well.

r1

u1 u2u(r)

r2 r3 r4 r5 r6=R

dr1 dr2

unrndrn1

1r1dr1 u2r2dr2 u3r3dr3 u4r4dr4 u5r5dr5 u6r6dr6+ + + + + )5

Consider the g

Figure 4 Ve

The energy gra

The hydraulic g

where the height c

h0 z +=

V 2

2g------Air Flow Measurements

Bernoulli Obstruction Theoryeneralized flow obstruction shown in Figure 4.

locity and Pressure Change through a Generalized Bernoulli ObstructionMeter

de line (EGL) shows the height of the total Bernoulli constant

[17]

rade line (HGL) shows

[18]

orresponding to elevation and pressure head

p---

V 2

2g------+6

that is, the EGL mitube attached to th

The flow in theparameter of the d

After leaving thD2 < d, as shown.to estimate the pre

Continuity:

Bernoulli

Eliminating

But this is surely invery important. NoEquation 23. We a

where subscript t daccounts for the diexpect

where

The geometric

One can also g

zp---+

dD----=

Q 4---D=

p0 p1=

V 1QA2------ V 2=

Q AtV=

Cd f (=

ReD---=

E 1 (=

CdE=[19]

nus the velocity head. The HGL is the height to which liquid would rise in a piezometere flow. In an open-channel flow the HGL is identical to the free surface of the water.basic duct of diameter D is forced through an obstruction of diameter d; the is a key

evice,

[20]

e obstruction, the flow may neck down even more through a vena contracta of diameterApply the continuity and Bernoulli equations for incompressible steady frictionless flowssure change:

[21]

[22]

, we solve these for or Q in terms of the pressure change :

[23]

accurate because we neglected friction in a duct flow, where we know friction will ber do we want to get into the business of measuring vena contracta ratios D2/d for use inssume that and then calibrate the device to fit the relation.

[24]

enotes the throat of the obstruction. The dimensionless discharge coefficient Cdscrepancies in the approximate analysis. By dimensional analysis for a given design we

[25]

[26]

factor involving in Equation 24 is called the velocity-of-approach factor

[27]

roup Cd and E in Equation 24 to form the dimensionless flow coefficient

[28]

2V 1 D22V 2=

12---V 1

2+ p 12---V 2

2+=

V 2 p1 p2( )2 p1 p2( )

1 D24 D4( )

-----------------------------------

1 2

D2 D

t Cd At2 p1 p2( ) 1 4( )--------------------------

1 2

ReD, )

V 1D------------

4) 1 2

Cd1 4( )1 2

---------------------------=7

Thus,

Obviously the

Occasionally o

Since the desigto the fluid-meterin

Figure 5 showsStandardization (IS

Q A=

f (=

ReD---=[29]

flow coefficient is correlated in the same manner:

[30]ne uses the throat Reynolds number instead of the approach Reynolds number

[31]

n parameters are assumed known, the correlation of or of is the desired solutiong problem. three basic devices recommended for use by the International Organization forO): the orifice, nozzle, and venturi tube.

Figure 5 Orifice, Nozzle, and Venturi Tube Configurations

t

2 p1 p2( )--------------------------

1 2

ReD, )

V td---------

ReD----------=

Cd8

An orifice platecauses an increaseexists. By measurinrate can be found u

where flow coefplate, Pa, dens

The values of65 mm orifi95 mm orifi

The value of

where = press

The flow nozzlcontracta and givefollowing expressio

The values of t

NA venturi is jus

must increase as thbe used to find the

The values of t

Q --=

u

0.42=

Pu

Q --=

0.9=

Q --=

0.9=Thin-Plate Orifice. is nothing but a flat plate with a hole in it. Once placed in the duct, it restricts flow andin velocity similar to a venturi. Directly behind the orifice plate an area of low pressureg the difference in pressure from this point to the-free flowing duct, the volumetric flowsing the following equation:

[32]

ficient, expansibility factor, diameter of orifice, m, pressure drop over orificeity upstream of the device (i.e. at atmospheric pressure) kg/m3.

for the orifice plates are as follows:ce: = 0.599ce: = 0.596 for an inlet orifice is given by the following expression

[33]

ure upstream of the device (atmospheric), Pa.

Nozzle.e, with its smooth rounded entrance convergence, practically eliminates the venas discharge coefficients near unity. The volumetric flow rate is determined from then;

[34]

he dimensionless compound coefficient is given by the expression

[35]

ozzle Inlet Venturi Flow-Rate Measuring Device.t a gradual constriction in the duct. Since the mass flow rate is constant, the velocitye area decreases. A change in static pressure occurs, and that change in pressure can

flow rate using the following formula and dimensions (same as the nozzle).

[36]

he dimensionless compound coefficient is given by the expression

[37]

d2

4-------2Pu

----------- m3

s

d P

PPu-------

d2

4-------2Pu

----------- m3

s

86 0.0055 10 3 P( )

dV2

4--------2Pu

----------- m3

s

86 0.0055 10 3 P( )9

CoThis device is m

the expressions

where

and

Note that conical instant diameter ducpressure measured

F

Q --=

1.0=

0.9=

Place theorice ornozzlehere

Off button

Start button

On/Off switcnical Inlet Venturi Flow-Rate Measuring Device.ounted on the inlet side of the fan ducting. The volume flow relationship is given by

[38]

when [39]

when [40]

let flow measurement should not be used when Red

Experimental s

ApparatusAir Flow Bench

Inlet cone, Venturi,

Procedure: (1. Couple t

using the toggle ca2. Attached3. Support 4. Ensure t

adapter housing5. Insert th

the counter sunk s6. Fit the p

(Blank off the pitot 7. Connect

manometer inlet) (8. Connect9. Set each10. Fully clo11. Set the o

(after disconnectinNote: The read

Experimental s

ApparatusStandard test sProcedure: (1. Install th2. Install a

section3. Connect

the appropriate ma4. Using th

locate the pitot tubNote: The lab i

Area of the ietups and Apparatus. (Cusson - For orifice plate)

, Manometers (small & large scale), Orifice (65 mm & 95 mm), Nozzle (95 mm), Conical Pitot tube

Emperiments I, and III)he 1 meter long ducting to the flow straightening section positioned at the inlet of the fantches the orifice inlet adapter housing to that 1 meter ductthe overhanging section of the assembly to a suitable height using the standhat the flow straightening honeycomb disc is positioned squarely within the orifice inlet

e 65 mm orifice plate into the inlet adaptor housing. (The orifice plate is positioned withide downstream from the inlet, i.e. facing into the housing)itot static tube and scale to the 1 meter ductwork at any of the three radial positions.static tube tappings if not in use) the pitot static tube to the smaller manometer (Total Pressure to the back of the smallStatic Pressure to the limb of the smaller adapter the orifice adapter housing tapping to the larger manometer limb. manometer limb in the upright position, level and zero the manometer

se the fan outlet valve and then switch on the fanrifice plate manometer limb to the most sensitive position possible and re-zero it again

g the pressure taping tube). Record the reading in kPaings should be multiplied with the multiplier written on that manometer.

etups and Apparatus. (Hampden)

ection, pitot-static probe, probe positioner, ManometersExperiment II)e standard test section in the wind tunnelpitot-static probe, in the probe positioner and through the duct access hole in the test

pressure tubing from the static and total pressure taps on the pitot-static tube to one ofnometerse variable frequency drive control to adjust fan speed and the pitot tube positioner toe vertical location in the duct, read and record velocity pressures at various locationsnstructor will show how to turn on/off the drive control and monitor the speed.nside duct (standard test section) is 0.444 ft2 (0.0413 m2) inside dimensions.11

Pitot-Tub

For air at 20oC

1. Traverseat each position anpossible, bearing in

2. Repeat ttion and record you

Assignments Complete Plot the ve Calculate

to Chapter 6 of you Discuss th

Trial # Pi

M=1 +

M=2 +

M=3 +

M=4 +

M=5 +

M=6 +

M=7 CE

Effective

AverageVelocityVolume FlowRateMass Flowrate

p

V

Q

mEXPERIMENT I

e Based Velocity Profile and Flow Rate Measurements

Cusson Wind Tunnel (D = 147 mm)

and 1 atm; = 1.20 kg/m3, = 1.8 E-5 kg/(m.s), = 1.51 E-5 m2/sec

the pitot static tube across the diameter of the ductwork, noting the manometer readingd record them in Data Sheet. (The manometer should be in the most sensitive position mind that the maximum values will be obtained at the central positions)

he experiments again by adjusting the fan outlet to the center and almost open posi-r data in Data Sheet.:the table above.locity across the diameter.the entrance length required to establish a fully developed boundary layer at inlet (referr text book).e velocity profile within the light of the entrance length.

tot Tube Locations

Valve Outlet PositionsAlmost closed Center Almost open

V V V

6 cm

5 cm

4 cm

3 cm

2 cm

1 cm

NTER: 0 cm

(Pascal)

(m/s)

(kg/s)

p p p

Peff Eq 8( )=

av

AV av=

Q=12

Pitot-Tub

Hampd

For air at 20oC

1. Traversereading at each poposition possible, b

2. Repeat ttion and record you

Assignments Complete Plot the ve Calculate

to Chapter 6 of you Discuss th

Trial # Pi

M=5 +

M=4 +

M=3 +

M=2 +

M=1 CE

Effective

AverageVelocityVolume FlowRateMass FlowRate

p

V

Q

mEXPERIMENT II

e Based Velocity Profile and Flow Rate Measurements

en Wind Tunnel (Test section Inside area 0.0413 m2)

and 1 atm; = 1.20 kg/m3, = 1.8 E-5 kg/(m.s), = 1.51 E-5 m2/sec

the pitot static tube across the cross section of the test chamber, noting the manometersition and record them in Data Sheet. (The manometer should be in the most sensitiveearing in mind that the maximum values will be obtained at the central positions)he experiments again by adjusting the fan outlet to the center and almost open posi-r data in Data Sheet.:the table above.locity across the plane.the entrance length required to establish a fully developed boundary layer at inlet (referr text book).e velocity profile within the light of the entrance length.

tot Tube Locations

Valve Outlet PositionsN = 800 rpm N = 1600 rpm N = 2400 rpm

V V V

8 cm

6 cm

4 cm

2 cm

NTER: 0 cm

(Pascal)

(m/s)

(kg/s)

p p p

Peff Eq 8( )=

av

AV av=

Q=13

Orifice Pla

Nozzle Fo

Conical In

Nozzle Inl

Valve Pos

Almost cl

Center

Almost O

Valve Pos

Almost cl

Center

Almost O

Valve Pos

Almost cl

Center

Almost O

Valve Pos

Almost cl

Center

Almost OEXPERIMENT III

Cusson Wind Tunnel (D = 147 mm)te For Flow Rate Measurements

r Flow Rate Measurements

let Venturi For Flow Rate Measurements

et Venturi For Flow Rate Measurements

itions) kPa

Q m3/sosed

pen

itions) kPa Q m3/s

osed

pen

itions) kPa Q m3/s

osed

pen

itions) kPa Q m3/s

osed

pen

P

P

P

P14

Ber

Background

Pressure MePressure meas

bluff body shown in

Assume that thare to be studied. Athe body. As the floPoint 2 is known asstreamline B, the vit follows thatconservation of maand between 3 and

However, beca

Hence, it followenergy per unit maisentropic manner

V 1 =

p1 V(+

p3 V(+

p2 pto=noulli Equation Demonstrator

asurements In Moving Fluidsurements in moving fluids deserve special considerations. Consider the flow over the Figure 1.

Figure 6 Streamlines over a bluff body

e upstream flow is uniform and steady. Points along the two streamlines labeled as Along streamline A, the flow moves with a velocity, , such as at point 1 upstream ofw approaches point 2 it must slow down and finally stop at the front end of the body. the stagnation point and streamline A the stagnation streamline for this flow. Along

elocity at point 3 will be and because the upstream flow is considered to be uniform. As the flow along B approaches the body, it is deflected around the body. From

ss principles, . Application of conservation of energy between points 1 and 2 4 yields

[41]

[42]

use point 2 is the stagnation point, , and

[43]

s that by an amount equal to , an amount equivalent to the kineticss of the flow as it moves along the streamline. If the flow is brought to rest in an(i.e., no energy lost through irreversible processes such as through a transfer of heat1),

V 1

V 3V 3

V 4 V 3>

12) 2g( ) p2 V 22( ) 2g( )+=

32) 2g( ) p4 V 42( ) 2g( )+=

V 2 0=

tal p0 p1 V 12( ) 2g( )+= =

p2 p1> V 22 2g15

this translational kipressure and will bpoint in an isentrop

The flow at 1, 3uniform,freestream pressurincreases such thapressure. The statvelocity as the loca

Background

Closely relatedin a frictionless flowwidely used, but onto some extent. tonearly frictionless.

For an incomp

where is the staThe total pressureequation for steady

A venturi tube

It is readily appto

Using the cons

V 1 V 3=

p2 p1( )----------------------

p1-----

V 12

2------+ +p1-----

V 12

2g------+ +

p---

p1-----

V 12

2g------+

V 1 A1 =netic energy will be transferred completely into p2 is known as the stagnation or totale noted as p0. The total pressure can be determined by bringing the flow to rest at aic manner., and 4 are known as the stream or static pressures2 of the flow. Because the flow is, so that . The static pressure and velocity at points 1 and 3 are known as the

e and freestream velocity. However, as the flow accelerates around the body its velocityt, from Eq (1), . The pressure, such as at point 4, is called a local staticic pressure is that pressure sensed by a fluid particle as it is moves with the samel flow.

to the steady-flow energy equation is relation between pressure, velocity, and elevation, now called the Bernoulli equation. The Bernoulli equation is very famous and verye should be wary of its restrictions - all fluids are viscous and thus all flows have friction

use the Bernoulli equation correctly, one must confine it to regions of the flow which are

ressible fluid, the Bernoulli equation is

[44]

[45]

[46]

tic pressure head; is the velocity pressure head; and is the potential energy head.head is equal to the sum of the static and velocity pressure heads. This is the Bernoulli frictionless incompressible flow along a streamline.can be used to demonstrate the Bernoulli equation as shown in Figure 3.

arent that the potential energy head is zero ( , the Bernoulli equation reduces

[47]

ervation of mass, the mass flow rate at points 1 and 2 must be the same, or

[48]

p3 p1=

p4 p3

12--- V 2

2 V 12

( ) g z2 z1( )+ + 0=

gz1p2-----

V 22

2------ gz2+ + const= =

z1p2-----

V 22

2g------ z2+ + const= =

V 2

2g------ z

Figure 3: Venturi

AIR FLOWDIRECTION

z1 z2=

p2-----

V 22

2g------+ const= =

V 2 A216

Objective

To investigateExperimenta3. Attached

4. Make sure that t

4. Install a probe head with th

5. Connectas shown in Figuremagnitude of the sconnectors are reqMEEM 3220 ENERGY LABORATORY

EXPERIMENT IV

(HAMPDEN WINDTUNNEL)

the Bernoulli equation as it relates to pressure and velocity of a fluid along a streamline.l Setupsthe venturi section with convergent and divergent sections oriented as shown in Figure

he fastening screws are tightened to provide a tight seal.

Figure 7 Schematic Diagram

pitot-static probe into the probe positioner and one access hole in the duct. Align thee center line of the convergent-divergent section.the total and static pressure taps of the pitot-static tube to the appropriate manometers 4. please note that the choice of which inclined manometer is used depends on thetatic pressure; and this changes along the length of the venturi tube. Two universal teeuired.17

Experimenta6. Turn ON

fan in forward for pSTEP 1STEP 2STEP 3STEP 4

STEP 5STEP 6

7. Measurealong the cross se

Equations:

where in aconstant (287

Conversions:

AssignmentsPlot and(Refer to Eq (3

Ptotal =

P Pt=

P gh=

Pst(

----------=

Pstaticm

2

V 2-----=

1cm2 =

1Pa 1=

1inH2O

1atm =

1inHg =

1mmHg

AVl Procedurethe fan and use the variable frequency drive control to adjust fan speed. Always run theroper air flow direction.

Press JOG button.Press LOCAL.Press FWD.Press ARROW BUTTON UP to increase the speed or Press ARROW BUTTONDOWN to decrease the speed.Press STOP to turn OFF the fanDirectly Press FWD to choose the same speed as chosen before.

and record the total, static, and velocity pressures (inches of H2O) at various pointsction of the venturi tube at each location.

[49]

; is also known as [50]

[51]

[52]

bsolute pressure (Pa or ) is the gas is the absolute temperature (K)

in m/s; where in Pascal or [53]

[54]

[55]

[56]

[57]

[58]

[59]

Bernoulli Constant along the venturi.) for Bernoulli Constant)

Pstatic Pdynamic+

otal Pstatic Pdynamic Pvelocity= = Pdynamic Pvelocity

static hstatic=

atic)absRT----------------

N m2 Pstatic( )abs Patm Pstatic( )gauge+= Rs

2 K( ) TP

------ P N m2

1 10 4 m2

N m2

249.1Pa=

101325Pa

3372.2Pa

133.32Pa=18

Fan = _____rp

Test (

# Types

1

PstaticPtotal

2

PstaticPtotal

3

PstaticPtotal

4

PstaticPtotal

5

PstaticPtotal

6

PstaticPtotal

7

PstaticPtotal

8

PstaticPtotal

9

PstaticPtotal

10

PstaticPtotal

P

P

P

P

P

P

P

P

P

PDATA SHEET IVm Patm = ___ inH2O = ____N/m2 T = ________ K = _______ kg/m3

Pressure)gauge A V AV P/ V2/2gBernoulliConstant

inH2O N/m2 m2 m/s kg/s meter meter meter

19