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

57:020 mechanics of Fluids and Transfer ProcessesExperimental 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

P r e s s u r et a p s

M o t o rc o n t r o l l e r

F l o o r

6’-

6”

Re

serv

oir

2 . 0 ” s m o o t h

0 . 5 ” s m o o t h

2 . 0 ” r o u g h

R e l i e fv a l v e s

B l o w e r

D = 2 . 0 ”D = 1 . 0 ”

D = 0 . 5 ”

tt

t

3 6 ’

V e n t u r i m e t e r g a t e v a l v e s

T h e r m o m e t e r

1 2 3 4

V a l v e m a n i f o l d

S i m p l em a n o m e t e r

P i t o t t u b eh o u s i n g s

V a l v e s

D i f f e r e n t i a lm a n o m e t e r

V e n t u r i m e t e r s


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)


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 f low rate and frict ion 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:

)( oww Tf=ρ)( o

airair Tf=ρ )( oairair Tf=ν

air

wDMt ZgKAQ

ρρ∆= 2

aire D

QR

νπ4=

( )ji SMSM

air

w ZZLQ

Dgf −=

ρρπ

2

52

8


Measurement Systems (continue)

For the velocity profi le, 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 ZrZg

ru )(2

)(ρρ


Flow rate, Friction factor and velocity profile measurement systems

Block diagram of the experimental determination of the Friction

Block diagram of the Velocity measurement

E X P E R I M E N T A LR E S U L T S

E X P E R I M E N T A L E R R O R S O U R C E S

I N D I V I D U A LM E A S U R E M E N T

S Y S T E M S

M E A S U R E M E N TO F I N D I V I D U A L

V A R I A B L E S

D A T A R E D U C T I O NE Q U A T I O N S

T E M P E R A T U R EW A T E R

T E M P E R A T U R EA I R

fB , P

V E N T U R IP R E S S U R E

P I P EP R E S S U R E

f = F ( , , z , Q =ρ ρ )a

a

wg Dπ 8 L Q

ρρ

Q = F ( z )∆

w

w

T

TB T, P

z

zB , P

f f

S M

S Mww

D M

S M

2

2

5

aT

TB T, Paa

z S M

z

zB , PD M

D M z D M

= F ( T )ρ

ρ

( )

w

= F ( T )a

zS M i

- zS M j

w

a

E X P E R I M E N T A LR E S U L T

w

w

T

TB T, P

S T A G N A T I O NP R E S S U R E

S T A T I CP R E S S U R E

E X P E R I M E N T A L E R R O R S O U R C E S

I N D I V I D U A LM E A S U R E M E N T

S Y S T E M S

M E A S U R E M E N TO F I N D I V I D U A L

V A R I A B L E S

D A T A R E D U C T I O NE Q U A T I O N S

z

B , PS M

B , Pu u

u

= F ( T )ρ

ρ

u = F ( , , z , z )ρ ρ2 ( ) gρ

ρ

½

=

T E M P E R A T U R EW A T E R

T E M P E R A T U R EA I R

w

a s t a g

a

T

TB T, Pa

z

w

w

w

S Ms t a g

zS M

s t a g

z

B , PS M s t a t

zS M

s t a t

zS M

s t a t

= F ( T )a

aa S M

s t a gS M

s t a t

zS M s t a g

- zS M s t a t

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

drop2. 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 Analysis

The 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 ρρ=

222fff PBU +=

2222

1

222

jSMSMjiSMiSM ZZZZ

j

iiif BBBB θθθ +== ∑

=

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 θθθ +== ∑

=

M

tSP uu =

),,,,(staticstagnation SMSMaw ZZgFf ρρ=


Moody Chart for pipe friction with smooth and rough walls

1 0 1 04

1 0 1 0 1 0 1 05 6 7 83

0 . 0 0 8

0 . 0 0 9

0 . 0 1 5

0 . 0 2 5

0 . 0 2 0

0 . 0 1 0

0 . 0 3 0

0 . 0 4 0

0 . 0 5 0

0 . 0 6 0

0 . 0 7 0

0 . 0 8 0

0 . 0 9 0

0 . 1 0

R e y n o l d s N u m b e r , R e = V D

Fric

tion

Fac

tor

f =h

f

(L/D

)V /

(2g

)2

0 . 0 0 0 0 1

0 . 0 0 0 0 5

0 . 0 0 0 1

0 . 0 0 0 2

0 . 0 0 0 40 . 0 0 0 60 . 0 0 0 80 . 0 0 1

0 . 0 50 . 0 4

0 . 0 3

0 . 0 2

0 . 0 1

0 . 0 1 5

0 . 0 0 80 . 0 0 6

0 . 0 0 4

0 . 0 0 2

Re

lativ

e R

ough

ness

, /

D

L a m i n a rF l o w

C r i t i c a lZ o n e

T r a n s i t i o nZ o n e

L a mi n a r F l o w

f = 6 4 / Re

/ D = 0 . 0 0 0 0 0 5

/ D = 0 . 0 0 0 0 0 1

C o m p l e t e T u r b u l e n c e , H y d r a u l i c a l l y R o u g h

H y d r a u l i c a l l y S m o o t h

κ

ν

k

k


Education

Admission in india 2014