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Measurement of flow rate, friction Factor, and velocity Profile in Pipe Flow

57:020 mechanics of Fluids and Transfer Processes

Experimental Laboratory #2

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Purpose

Measure Flow rate in a pipe (smooth)Friction factorVelocity profileSpecify the turbulent-flow Reynolds NumberCompare the results with benchmark dataUncertainty analysis for:

Friction factor Velocity profile



Test Design

The facility consists of:Closed pipe networkFanReservoir Instruments used:3 Venturi meters

Simple water ManometerDifferential Water manometerPitot ProbeDigital Micrometer (Accurate radial positioning)

Contraction Diameters (mm):

12.7 25.4 52.93

Flow Coefficient, K 0.915 0.937

0.935



Air Flow Pipe facility

Pressuretaps

M otorcontro lle r

F loor

6’-6

”

Res

ervo

ir

2.0” sm ooth

0.5” sm ooth2.0” rough

R elie fva lves

B low er

D = 2 .0” D = 1.0”D = 0.5”

tt

t

36’

Venturi m eter gate valvesTherm om eter

1 2 3 4

Valve m anifold

S im plem anom eter

P itot tubehousings

Valves

Differentia lm anom eter

Venturi m eters


Test Design (Continue)Reservoir:

To build up pressure and force the air to flow downstream through any of the three straight experiment pipes.

Digital Micrometer:Allow the measurement of the position

of the Pitot probe at different locations along the cross section of the pipe tested

Pitot Probe:Located in the glass-wall boxUsed to measure the Stagnation

pressure and calculate the velocity profile in pipe

Venturi meters:Located on each pipe typeUsed to measure flow rate Q along the

differential water manometer

Pressure Taps:Located along each pipe, they are

connected to the simple water manometer to evaluate the head measurement

They are used to calculate the friction factor

Manometers:To measure the head at each pressure

Tap along the pipe and to make the Pitot-tube measurements (simple Manometer)

To measure head drops across the venturi meters (differential Manometer) Admission.edhole.com

Pressure tap manifold and Pitot-tube housing

Pressure tap manifold Pitot-tube housing


Measurement Systems:

The equipment used in the experiment includes:Digital thermometer with a range of – 40 to 450 F and a smallest reading of 0.1 F for measurement of the environment temperature. Digital micrometer with least significant digit 0.01 mm for positioning the Pitot-tube inside the pipe. Simple water manometer with a range of 2.5 ft and a least scale division of 0.001 ft for measurement of the head at each pressure tap along the pipes and for measurement of velocities using the Pitot-tube arrangement . Differential water manometer with a range 3 ft and a least scale division of 0.001ft for measurement of the head drop across the Venturi meters.


Measurement Systems (continue)

For the flow rate and friction factor, the individual measurement are performed for:

Ambient air temperature (A.3) Pipe air temperature (A.5) Pipe pressure head Venturi meter pressure head drop

The experimental Results are: Manometer water density Air density Kinematic viscosity Flow rate Reynolds number Friction factor

Data reduction equations are: )( o

ww Tf)( o

airair Tf )( oairair Tf

air

wDMt ZgKAQ

2

aire D

QR

4

ji SMSM

air

w ZZLQDgf

2

52

8


Measurement Systems (continue)

For the velocity profile, the individual measurement systems are for:

the ambient temperature pipe air temperature pitot stagnation and static pressure heads.

The experimental results are for: manometer water density (A.3) Air density (A.5) Velocity profile (below)

Data reduction equation: (using the Bernoulli equation along the manometer equation)

staticstag SMSMa

w ZrZgru )(2)(


Flow rate, Friction factor and velocity profile measurement systems

Block diagram of the experimental determination of the Friction

Block diagram of the Velocity measurement

EXPERIMENTALRESULTS

EXPERIMENTAL ERROR SOURCES

INDIVIDUALMEASUREMENT

SYSTEMS

MEASUREMENTOF INDIVIDUAL

VARIABLES

DATA REDUCTIONEQUATIONS

TEMPERATUREWATER

TEMPERATUREAIR

fB , P

VENTURIPRESSURE

PIPEPRESSURE

f = F( , , z , Q = )a a

wg D

8LQ

Q = F( z )

w

w

T

TB T, Pz

zB , P

f f

SM

SMww

DM

SM

2

2

5

aT

TB T, Paa z SM

z

zB , PDM

DM z DM

= F(T )

( )

w

= F(T )a

zSM i

- zSM j

w

a

EXPERIMENTALRESULT

w

w

T

TB T, P

STAGNATIONPRESSURE

STATICPRESSURE

EXPERIMENTAL ERROR SOURCES

INDIVIDUALMEASUREMENT

SYSTEMS

MEASUREMENTOF INDIVIDUAL

VARIABLES

DATA REDUCTIONEQUATIONS

z

B , PSM

B , Pu u

u

= F(T )

u = F( , , z , z ) 2( ) g

½=

TEMPERATUREWATER

TEMPERATUREAIR

w

a stag

a

T

TB T, Pa z

w

ww

SMstag

z SMstag

z

B , PSM stat

zSMstat

z SMstat

= F(T )a

aa SMstag SM stat

zSM stag

- zSM stat

w

a


Data Acquisition and reduction The procedures for data acquisition and reduction are described as follow:

1. Use the appropriate Venturi meter, (2” smooth pipe) measure the head drop

2. Take reading for ambient air (manometer water) and pipe air temperatures.

3. To obtain velocity data, measure in the appropriate Pitot-tube box, the ambient head and stagnation heads across the full diameter. Measure the stagnation heads at radial intervals. The recommended radial spacing for one half of the diameter is 0, 5, 10, 15, 20, 23, and 24 mm.

4. Maintaining the discharge, measure the head along the pipe by means of the simple water manometer connected to the pressure taps located along the pipe being studied (10 times for uncertainty analysis)

5. Repeat step 26. Execute data reduction for data analysis and uncertainty analysis using

equation above


Uncertainty AnalysisThe data reduction equation for the friction factor is:

However here we will only consider bias limits for ZSM i and ZSM j . The total uncertainty for the friction is:

The Bias Limit, Bf and the precision limit, Pf, for the result are given by:

),,,,,,,(ji SMSMaw ZZQLDgFf

222fff PBU

2222

1

222

jSMSMjiSMiSM ZZZZ

j

iiif BBBB

M

tSP ff


Uncertainty Analysis (continue)

Data Reduction equation for the velocity profile is as follow:

222uuu PBU

2222

1

222

statSMstatSMSMstagnstagnSM ZZZZ

j

iiiu BBBB

MtSP u

u

),,,,(staticstagnation SMSMaw ZZgFf


Moody Chart for pipe friction with smooth and rough walls

10 104

10 10 10 105 6 7 83

0 .0 080 .0 09

0 .0 15

0 .0 25

0 .0 20

0 .010

0 .0 30

0 .0 40

0 .0 50

0 .0 60

0 .0 70

0 .0 800 .0 90

0 .1 0

R eynolds Number, R e = VD

Fric

tion

Fact

or f

=h

f

(L/D

)V /

(2g)

2

0 .00001

0 .00005

0 .0001

0 .0002

0 .00040 .00060 .00080 .001

0 .050 .040 .03

0 .02

0 .01

0 .015

0 .0080 .0060 .004

0 .002

Rel

ativ

e R

ough

ness

, /D

Lam inarF low

Critica lZ one

T ra ns itionZ one

Laminar Flow

f = 64/Re

/D = 0 .0 00005

/D = 0 .000001

Com p le te T urbu lence , Hyd rau lica l ly Rou gh

Hyd rau lica lly S m oo th

k

k

k


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Admissions in india 2015