flow apparatus

7/27/2019 flow apparatus

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Introduction:

Throughout the experiment, the three apparatus being studied are the Venturi, Orifice and

Rotameter. The venturi meter (Diagram 2) through using differential pressure, which is the

pressure difference between the pressure entering the meter and the pressure at the neck of the

meter. After the constricted area, the fluid is passes through a pressure recovery exit section,

where up to 80% of the differential pressure generated at the constricted area, is recovered. The

Venturi meter is generally preferred because it has less head loss than the other methods due to

its streamlined design.

The Orifice meter functions similarly to the Venturi meter. As the fluid approaches the orifice

the pressure increases slightly and then drops suddenly as the orifice is passed. It continues to

drop until the vena contracta is reached and then gradually increases until at approximately 5to 8 diameters downstream a maximum pressure point is reached that will be lower than the

pressure upstream of the orifice. The decrease in pressure as the fluid passes thru the orifice is a

result of the increased velocity of the gas passing thru the reduced area of the orifice. When the

velocity decreases as the fluid leaves the orifice the pressure increases and tends to return to its

original level. All of the pressure loss is not recovered because of friction and turbulence losses

in the stream. The pressure drop across the orifice (Diagram 1) increases when the rate of flow

increases. When there is no flow there is no differential. The differential pressure is proportional

to the square of the velocity.

The rotameter's (Diagram3) operation is based on the variable area principle: fluid flow raises a

float in a tapered tube, increasing the area for passage of the fluid. The greater the flow, the

higher the float is raised. The height of the float is directly proportional to the flowrate. With

liquids, the float is raised by a combination of the buoyancy of the liquid and the velocity head of

the fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone.

The float moves up or down in the tube in proportion to the fluid flowrate and the annular areabetween the float and the tube wall. The float reaches a stable position in the tube when the

upward force exerted by the flowing fluid equals the downward gravitational force exerted by the

weight of the float. A change in flowrate upsets this balance of forces. The float then moves up

or down, changing the annular area until it again reaches a position where the forces are in

equilibrium. To satisfy the force equation, the rotameter float assumes a distinct position for


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every constant flowrate. However, it is important to note that because the float position is gravity

dependent, rotameters must be vertically oriented and mounted.

In a nozzle or other constriction, the coefficient of discharge is the ratio of the mass flow rate at

the discharge end of the nozzle to that of an ideal nozzle which expands an identical working

fluid from the same initial conditions to the same exit pressure.

Whenever the fluid speed is sufficiently subsonic (V< mach 0.3),

the incompressibleBernoulli's equation describes the flow. Applying this equation to a streamline

travelling down the axis of the horizontal tube gives,

From continuity, the throat velocity Vb can be substituted out of the above equation to give,

Solving for the upstream velocity Va and multiplying by the cross-sectional areaAa gives the

volumetric flow rate Q,

Ideal, inviscid fluids would obey the above equation. The small amounts of energy converted

into heat within viscous boundary layers tend to lower the actual velocity of real fluids

somewhat. A discharge coefficient Cis typically introduced to account for the viscosity of fluids,
http://www.efunda.com/formulae/fluids/glossary.cfm?ref=incomp#incomphttp://www.efunda.com/formulae/fluids/navier_stokes.cfm#continuityhttp://www.efunda.com/formulae/fluids/glossary.cfm?ref=invis#invishttp://www.efunda.com/formulae/fluids/glossary.cfm?ref=invis#invishttp://www.efunda.com/formulae/fluids/navier_stokes.cfm#continuityhttp://www.efunda.com/formulae/fluids/glossary.cfm?ref=incomp#incomphttp://www.efunda.com/formulae/fluids/glossary.cfm?ref=incomp#incomp


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Cis found to depend on the Reynolds Numberof the flow, and usually lies between 0.90 and

0.98 for smoothly tapering venturis.

The mass flow rate can be found by multiplying Q with the fluid density,
http://www.efunda.com/formulae/fluids/overview.cfm#reynoldshttp://www.efunda.com/formulae/fluids/overview.cfm#reynolds


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Objectives:

a. To compare flow measurements by Venturi meter, Orifice meter and Rotameterb. To determine the coefficients of discharge for the Venturi and Orifice meters, and to

calibrate the Rota meter.

c. To compare the pressure drops across each device and also across a gradual enlargementand a sharp bend.

Apparatus:

TecQuipment Flow Measuring Apparatus, TecQuipment Hydraulic Bench, stopwatch

Important dimensions:

Inlet and outlet diameters of the venture tube = 25.4mm

Throat diameter of the venturi tube = 15.9mm

Change of diameters at gradual enlargement = 25.4 to 50.8mm

Included angle of gradual enlargement = 53

Diameter of orifice = 22.2mm

Change of diameter in sharp bend = 50.8 to 38.1mm


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Diagram 1 showing an Orifice meter

Diagram 2 showing a Venturi meter


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Diagram 3 showing a Rotameter


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Diagram 4 Showing the positioning of each meter in the experiment apparatus


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Procedure:

The flow measuring apparatus was mounted on top of the Hydraulics Bench facing the weight

hanger. The end of the supply hose from the pump was put unto the inlet pipe. The end of the

discharge hose was positioned so as to lead the discharge to the weight tank.

It was ensured that the supply valve was closed. The outlet gate valve at the top of the unit was

fully opened. The brass valve in the vent line tube to the right of the manometer panel was

closed, before the pump was switched on. The bench supply valve was opened slowly/gradually.

All air bubbles were allowed to leave the flow passages and manometer tubes to help in this

process the tubes were gently tapped to allow the bubbles to leave. The bench supply valve was

adjusted to give a high reading of about 250mm on the Rotameter scale. A pencil was then used

to gently depress the air valve at the left end of the manifold, at the top of the manometer panel,

to release air and bring the level of h1 up to about 350mm. Alternatively, the brass valve in the

vent line at the right of the manometer panel was cracked open to achieve the same effect. All 8

manometric readings were recorded. A stopwatch was used to time the collection of about

13.6kg of water. This procedure was repeated, gradually reducing the flow rate down to a low

reading of about 40mm on the Rotameter to obtain a total of at least 6 sets of readings.

The pump was switched off, the brass valve in the vent line opened and the water allowed to

drain off the unit back to the sump. The bench supply valve and the brass valves were then

closed.


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RESULTS

Table 1 showing the results obtained from the Venturi, Orifice and Rota meters in the experiment

Table Showing Readings for The Venturi Meter

m Flow Rate (Q) m /s

0.276 0.525 0.00048

0.212 0.46 0.000428

0.136 0.369 0.00038

0.106 0.326 0.000299

0.082 0.286 0.000264

0.048 0.219 0.000196

0.047 0.217 0.000114

Table 2 showing some readings obtained from the Venturi meter.

ROTAMETER

(mm) MASS kg TIME (s) kg/s h1 h2 h h3 h4 h h5 h6 h h7 h8 h

250 13.636 28.39 0.48031 35 7.4 27.6 30.5 31 -0.5 32.8 12 20.8 16.2 10 6.2

220 13.636 31.89 0.427595 31.2 10 21.2 27.8 28 -0.2 29.4 13.4 16 16.6 11.8 4.8170 13.636 40.38 0.337692 26 12.4 13.6 23.6 24 -0.4 25 14.8 10.2 17 14 3

150 13.636 45.57 0.299232 24.1 13.5 10.6 22.3 22.4 -0.1 23.4 15.4 8 17 14.6 2.4

130 13.636 51.7 0.263752 22.6 14.4 8.2 21.2 21.6 -0.4 22.1 15.8 6.3 17 15.2 1.8

90 13.636 69.64 0.195807 20.2 15.4 4.8 19.2 19.2 0 19.6 16.4 3.2 17 16 1

40 13.636 119.15 0.114444 18.2 13.5 4.7 17.8 17.8 0 18 16.8 1.2 17.1 16.7 0.4

MEASURED FLOW VENTURIMETER ENLARGEMENT ORFICE METER 90 BEND


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Readings Obtained from the Orifice meter

The square root of m Flow Rate (Q) m

0.000208 0.0144 0.00048

0.00016 0.0126 0.000428

0.000102 0.0101 0.00038

0.000008 0.00283 0.000299

0.000063 0.00794 0.000264

0.000032 0.00566 0.000196

0.000012 0.00346 0.000114

Table 3 Showing results obtained from the Orifice meter

Graph 1 showing the Discharge versus h^1/2 of the Venturi meter

y = 0.0011x - 6E-05

R = 0.9329

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0 0.1 0.2 0.3 0.4 0.5 0.6

Discharge(Q)m^1/2m^1/2

(h)^1/2 m^1/2

Discharge (Q) m3/s vs (h)^1/2 m^1/2

Flow Rate (Q) m3/s

Linear (Flow Rate (Q) m3/s)


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Graph 2 showing the Discharge versus h^1/2 of the Orifice meter

Discussion:

The results obtained were used to plot graphs of discharge versus h. For the graphs obtained

from the Venturi and Orifice meters, it was observed that there is a direct correlation between the

two entities. As a result a straight line graph was obtained for both meters. As the difference in

h increases thee is also an increase in the values of Q and vice versa. It was found that the

coefficient of discharge for a venturi meter should be at or around 0.98 and that of the orifice

meter should be at or around 0.64. From the calculations the experimental values found for the

respective meters were 0.97 and 0.47. The venturi meter fell in the range it was supposed to nut

the reading of the orifice meter fell short. The venture meter was off by just 0.01 while the

orifice meter was off by 0.17.

The head loss caused by venturi meter is much smaller than that of the orifice meter. This is

because the diameter of the neck of the venturi meter is smaller than that between the orifice

meter with the 90obend. The manometer readings for h6 and h7 should not be the same because

y = 0.0008x + 0.0001

R = 0.7417

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0 0.1 0.2 0.3 0.4 0.5

Discharge(Q)m^3/s

(h)^1/2 m1/2

Discharge (Q) m3/s vs (h)^1/2 m^1/2

Flow Rate (Q) m3/s

Linear (Flow Rate (Q)

m3/s)


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there is a difference in diameter between the two. The coefficient of the enlargement was

calculated to be very small because the head loss is also small and the coefficient of the 90o

bend

is 0 because there is no head loss.

Pressure losses for the orifice and flow nozzles are similar but quite significant,

However pressure losses were lower for the venturi meter.

To ensure that the readings were taken correctly, throughout the experiment the tubes should be

tapped slightly to ensure that there is no air bubbles that develop even though at the beginning it

was ensured that there were no bubbles in the system.

Conclusion

The objectives of this experiment were successful in that the flow measurement of venturi meter,

orifice meter, and rotameter were all compared with each other and all have shown to have

different flow rate.

The coefficients of discharge for the venturi and orifice meters were 0.97 and .046 respectively.

The pressure drops experienced across each device, the enlargement and the 90 bend were all

different due to the varying diameters that the fluid passes through.

References

American Society of Mechanical Engineers (ASME). 1971. Fluid meters: Their theory and

application. Edited by H. S. Bean. 6ed. Report of ASME Research Committee on Fluid Meters

wefunda.com/formulae/fluids/venturi_flowmeter.cfmww.

http://www.grc.nasa.gov/WWW/K-12/airplane/bern.html
http://www.grc.nasa.gov/WWW/K-12/airplane/bern.htmlhttp://www.grc.nasa.gov/WWW/K-12/airplane/bern.html


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Calculations

Measured Flow =39.28

636.13

t

mass

= 0.48031 kg/s

Volumetric Flow rate (Q) = Measured Flow/ (density)

Density of water is 1000 kg/m3

1000

48031.0

sm /1048031.0 33

Venturi Meter h = h1- h2

h = 350-74

= 276 cm

Enlargement h = h3 - h4

h = 305-310

= -5cm

Orifice Meter h = h5h6

h = 328-120

= 208mm

Bend h = h7h8

h = 162-100

= 62mm

Converting millimetres to meters


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1m = 1000mm

Therefore from venture meter calculations 276 mm = 276/1000

= 0.276 m

m

h

525.0

276.02/1

Venturi Meter

2122

1

2

AA

hgACQ d

The graph plotted yields a straight line thus the equation, y = mx + c where Q = y, x = h and m

= 212

21

2

AA

gACd

The gradient m = 0.0011 from the graph

Cd =

gA

AAm

2

/1

2

2

12

4

2

11

dA

d1= 25.4 mm or 25.410-3

m

24

1

23

1

10067.5

4

104.25

mA

A


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4

2

22

dA

d2 = 15.9 mm or 15.910-3

m

973.0

10803.8

779.00011.0

784.921099.1

10067.5/1099.110011.0

4

4

44

d

d

d

C

C

C

Orifice Meter

hgACQ d 2

The graph plotted yield a straight line thus the equation y = mx + c, where y = Q and

x =

h and m gACm d 2

gA

mCd

20

The gradient m = 0.0008 from the graph

4

2

10

dA

Where d1= 22.210-3

m

24

1

23

0

1087.3

4

102.22

mA

A

24

2

23

2

10986.14

109.15

mA

A


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467.0

568.191087.3

0008.04

d

d

C

C

Venturi Meter

Head loss (hl) = h1h3

= 350305

= 45mm

Inlet velocity

A

Qv

vAQ

Where Q = 0.4810-3

m3/s and A = 1.9910

-4m

2

smv

v

/41.2

1099.1

1048.0

4

3

Velocity head (hv)g

v

2

2

mh

h

v

v

297.0

568.19

8081.5

Head loss/inlet velocity head ratio (hl/hv)

hl/hvm

m

297.0

040.0

= 0.135


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Orifice Meter

Head loss = h5h7

= 328-162

= 166mm

Inlet velocity head for orifice

A

Qv

vAQ

Where Q = .4810-3

m3/s and A = 3.8710

-4m

2

smv

v

/24.1

1087.3

1048.0

4

3

Head Velocity (hv)g

v

2

2

mh

h

v

v

21086.7

568.19

538.1

Head loss/inlet velocity head (hl/hv)

hl/hvm

m

0786.0

166.0

= 2.11

Enlargement


18/22

Bernoullis equationg

v

g

PZ

g

v

g

PZ

22

2

222

2

111

mmZZ 7021

g

v

g

v

g

P

g

PZZ

2)(

2

3

2

44321

d4 = 50.8mm

d3 = 25.4mm

4

2

44

dA

23

4

23

4

100268.2

4

108.50

mA

A

24

3

23

3

10067.5

4

104.25

mA

A

4

4A

Qv

vAQ

smv

v

/237.0

100268.2

1048.0

4

3

3

4

smv

v

/9473.0

10067.5

1048.0

3

4

3

3

gvvhh 2/232443


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568.19

9473.0237.0 22

43

hh

= -0.043m

he = h1- hm

Where h1= -0.043m and hm = 0.305-0.310 = -0.005

he = -0.043-(-0.005) = -0.038m

gVKh ee 2/2

1

1

1A

Qv

vAQ

Where A1= 5.067 10-4

m2

and Q = 0.48 10-3

m3/s

smv

v

/947.0

10067.5

1048.0

1

4

3

1

gvhK ee2

2

1

784.92947.0

038.02

eK

Ke = -0.829

Sharp Bend

d7 = 50.8mm

d8 = 38.1mm

4

2

7

7

dA


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4

)108.50(23

7

A

A7 = 2.0268 10-3

m2

4

)101.38( 23

8

A

A8 = 1.14 10-3

m2

7

7A

Qv

vAQ

smv

v

/2368.0

100268.2

1048.0

7

3

3

7

smv

v

/421.01014.1

1048.0

7

3

3

8

gvvhh 2/272887

568.19

2368.0421.0 22

87

hh

= 6.19 10-3

m

hs = h(7-8)-hm2

hm2 = 0.162-0.10 = 0.062

hs = 6.1910-3

- 0.062


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= -0.000384 m

gVKh ss 2/2

1

gvhK ss2

2

1

Where v = 0.974m/s

784.92237.0

000384.02

eK

= -0.134


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The University of Technology, Jamaica

Thermal Fluid Science Lab. 1

Flow Measuring Apparatus

Name: George Robinson

I.D. # 0907818

Lecturer: Mr Kavian Cook

flow apparatus

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