Determining Fluid Velocity Lab

UNIVERSITI TENAGA NASIONAL COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING

MESB333 ENGINEERING MEASUREMENT LAB SEMESTER 1, 2014/2015

TITLE : DETERMINING FLUID VELOCITY AND DISCHARGE COEFFICIENT

AUTHOR

: TUNKU ATIQAH BINTI TENGKU HAMNET

SECTION

: 3A

GROUP

:B

GROUP MEMBERS: FAIQAH BINTI MOHD FADZIL

ME089856

SOFEA BALQIS BINTI JUB,LI

ME090241

RUCGNES A/L APPARAO

ME090233

MOHAMAD AIMAN B. TALIT

ME088598

INSTRUCTOR

:

DATE PERFORMED : 23 JUNE 2014 DATE SUBMITTED : 30 JUNE 2014

1

TABLE OF CONTENT

EXPERIMENT I: DETERMINING FLUID VELOCITY Summary / Abstract

3

Objective

3

Theory

3-5

Equipment

6

Procedure

6-7

Data, Observation and Results

8-10

Analysis and Discussion

10

Conclusion

11

EXPERIMENT II: DETERMINATION OF DISCHARGE COEFFICIENT Summary / Abstract

12

Objective

12

Theory

12-13

Equipment

14

Procedure

14

Data, Observation and Results

15-18

Analysis and Discussion

19

Conclusion

20

2

SUMMARY/ABSTRACT SUMMARY/ABSTRACT It is extensively used to verify the airspeed of an airplane, water speed of a boat, and to measure liquid, air and gas velocities in industrial applications. The pitot tube is used to evaluate the local velocity at a given position in the flow stream and not the average velocity in the pipe or conduit. The Bernoulli equation is then practical to calculate the velocity from the pressure difference. or

(1)

When fluid flows through a immobile solid wall, the shear stress set up near to this boundary due to the relative motion between the fluid and the wall directs to the growth of a flow boundary layer. The boundary layer may be either laminar or turbulent in nature depending on the flow Reynolds number. The growth of this boundary layer can be discovered by examining the velocity profiles at selected cross-sections, the core region still outside the border layer showing up as an area of more or less consistent velocity. If velocity profiles for cross-sections different remoteness from the pipe opening are compared, the pace of growth of the boundary layer along the pipe length can be determined. Once the boundary layer has mature to the point where it fills the whole pipe cross-section this is termed "fully developed pipe flow".

OBJECTIVE 1) To learn the method of measuring airflow velocity using pitot tube. 2) To understand the working principle of pitot tube as well as the importance of Bernoulli equation in deriving and calculating the velocity.

THEORY A pitot tube is used to explore the developing boundary layer in the entry length of a pipe which has air drawn through it. With pitot tube, the velocity distribution profiles can be determined at a number of cross-sections at different locations along a pipe. With pitot tube, air flow velocities in the pipe can be obtained by first measuring the pressure difference of the moving air in the pipe at two points, where one of the points is at static

3

velocity. The Bernoulli equation is then applied to calculate the velocity from the pressure difference. v

2p



or

2gh'

(1)

 the pitot tube and the wall pressure tapping  p – The pressure difference between  measured using manometer bank provided (  g  x where x is the level of fluid used in



the manometer). h’ – the pressure difference expressed as a 'head' of the fluid being measured (air)  The air density at the atmospheric pressure and temperture of that day.(kg/m3) g gravitational acceleration constant (9.81 m/s2) When fluid flows past a stationary solid wall, the shear stress set up close to this boundary due to the relative motion between the fluid and the wall leads to the development of a flow boundary layer. The boundary layer may be either laminar or turbulent in nature depending on the flow Reynolds number. The growth of this boundary layer can be revealed by studying the velocity profiles at selected cross-sections, the core region still outside the boundary layer showing up as an area of more or less uniform velocity. If velocity profiles for cross-sections different distances from the pipe entrance are compared, the rate of growth of the boundary layer along the pipe length can be determined. Once the boundary layer has grown to the point where it fills the whole pipe cross-section this is termed "fully developed pipe flow".

Reynolds Number The Reynolds number is a measure of the way in which a moving fluid encounters an obstacle. It's proportional to the fluid's density, the size of the obstacle, and the fluid's speed, and inversely proportional to the fluid's viscosity (viscosity is the measure of a fluid's "thickness"--for example, honey has a much larger viscosity than water does). Re 

vd 

 : fluid density v : fluid velocity 





d : obstacle size

 : coefficient of fluid dynamic viscosity 4

A small Reynolds number refers to a flow in which the fluid has a low density so that it responds easily to forces, encounters a small obstacle, moves slowly, or has a large viscosity to keep it organized. In such a situation, the fluid is able to get around the obstacle smoothly in what is known as "laminar flow." You can describe such laminar flow as dominated by the fluid's viscosity--it's tendency to move smoothly together as a cohesive material. A large Reynolds number refers to a flow in which the fluid has a large density so that it doesn't respond easily to forces, encounters a large obstacle, moves rapidly, or has too small a viscosity to keep it organized. In such a situation, the fluid can't get around the obstacle without breaking up into turbulent swirls and eddies. You can describe such turbulent flow as dominated by the fluid's inertia--the tendency of each portion of fluid to follow a path determined by its own momentum. The transition from laminar to turbulent flow, critcal flow, occurs at a particular range of Reynolds number (usually around 2500). Below this range, the flow is normally laminar; above it, the flow is normally turbulent.

Calculation of Airflow Velocity The manometer tube liquid levels must be used to calculate pressure differences, Dh and pressure heads in all these experiments. Starting with the basic equation of hydrostatics: p =  gh (2) we can follow this procedure through using the following definitions: Example:



Manometer tubes

1(static ‘pressure’*)

2(stagnation ‘pressure’)

Liquid surface readings

X1

X2

(mm) Angle of inclination,  =0

equivalent vertical separation of liquid levels in manometer tubes,  h = (x1 - x2)cos 

If rk is the density of the kerosene in the manometer, the equivalent pressure difference  p is:   p =  k g  h =  k g(x1 - x2) cos  (4)

  

(3)









5

The value for kerosene is rk = 787 kg/m3 and g = 9.81 m/s2. If x1 and x2 are read in mm, then:  p = 7.72(x1 - x2)cos  [N/m2] (5) The  p obtained is then used in second equation (1) to obtain the velocity. To use the first  equation (1), convert this into a 'head' of air, h’. Assuming a value of 1.2

 

kg/m3 for this gives:

h' 



k (x1  x2) cos air 1000

[N/m2]

(6)

APPARATUS

Figure 1: Experiment Apparatus

6

PROCEDURE a) Five mounting positions are provided for the pitot tube assembly. These are: 54 mm, 294 mm, 774 mm, 1574 mm and 2534 mm from the pipe inlet b) Ensure that the standard inlet nozzle is fitted for this experiment and that the orifice plate is removed from the pipe break line. c) Set the manometer such that the inclined position is at 00. d) Mount the pitot tube assembly at position 1 (at 54mm, nearest to the pipe inlet). Note that the connecting tube, the pressure tapping at the outer end of the assembly, is connected to a convenient manometer tube. Make sure that the tip, the L-shape metal tube of the pitot tube is facing the incoming flow. e) Note that there is a pipe wall static pressure tapping near to the position where the pitot tube assembly is placed. The static pressure tapping is connected to a manometer tube. f) Position the pitot tube with the traverse poisition of 0mm. Start the fan with the outlet throttle opened. g) Starting with the traverse position at 0mm, where the tip is touching the bottom of the pipe, read and record both manometer tube levels of the wall static and the pitot tube until the traveverse position touching the top of the pipe. h) Repeat the velocity traverse for the same air flow value at the next positon with the pitot tube assembly. Make sure that the blanking plugs is placed at the holes that are not in use.

7

DATA, OBSERVATION AND RESULTS Data Sheet for Velocity Measurement Using Pitot Tube Pitot Tube at 54 mm Static ‘Pressure’ Reading 117 mm

Traverse Position (mm)

p (N/m2)

Pitot Tube at 294 mm Static ‘Pressure’ Reading 120 mm

Stagnation ‘Pressure’ Reading (mm) 

x (mm)

0

100

17

131.24

14.79

100

20

154.4

16.05

10

98

19

146.68

15.64

99

21

162.12

16.45

20

97

20

154.4

16.05

98

22

169.84

16.83

30

96

21

162.12

16.45

97

23

177.56

17.21

40

95

22

169.84

16.83

96

24

185.28

17.58

50

95

22

169.84

16.83

96

24

185.28

17.58

60

95

22

169.84

16.83

97.5

22.5

173.7

17.02

70

95

22

169.84

16.83

102

18

138.96

15.23



Velocity Stagnation (m/s) ‘Pressure’ Reading (mm) 

Pitot Tube at 774 mm Static ‘Pressure’ Reading 126 mm

Traverse Position (mm)

p (N/m2)

x (mm)

p Velocity (N/m2) (m/s)



Pitot Tube at 1574 mm Static ‘Pressure’ Reading 130 mm

Stagnation ‘Pressure’ Reading (mm) 

x (mm)

0

102

24

185.28

17.58

116

14

108.08

13.43

10

104

22

169.84

16.83

114

16

123.52

14.36

20

98

28

216.16

18.99

112

18

138.96

15.23

30

97

29

223.88

19.33

110

20

154.4

16.05

40

96

30

231.6

19.66

100

30

231.6

19.66

50

98

28

216.16

18.99

99

31

239.32

19.98

60

100

26

200.72

18.29

98

32

247.64

20.30

70

106

20

154.4

16.05

110

20

154.4

16.05



Velocity Stagnation (m/s) ‘Pressure’ Reading (mm) 

x (mm)

p Velocity 2 (N/m ) (m/s)



8

Pitot Tube at 2534 mm Static ‘Pressure’ Reading 136 mm x p Stagnation ‘Pressure’ (mm) (N/m2) Reading (mm)   121 15 115.8

Traverse Position (mm) 0

Velocity (m/s)

13.89

10

112

24

185.28

17.58

20

110

26

200.72

18.29

30

108

28

216.16

18.99

40

110

26

200.72

18.29

50

106

30

231.6

19.66

60

108

28

216.16

18.99

70

116

20

154.4

16.05

Sample Calculation Taking :Pitot tube = 54mm Static pressure reading = 117mm At transverse position = 0m Stagnation pressure reading is 100mm ∆x = static pressure, x1 - stagnation pressure, x2 = 117mm - 100mm = 17mm ∆p = 7.72 (∆x) cos

where

= 0o, cos 0o = 1

= 7.72 (17mm) = 131.24 N/m2 Velocity, V =



2p / P √

=

2(131 .24) /1.2 = 14.79 m/s



9

Velocity against Traverse Position 25

Velocity (m/s)

20 15

54mm 294mm 774mm

10

1574mm 2534mm

5 0 0

20

40 Traverse Position (mm)

60

80

Graph 1: Velocity against Traverse Position

ANALYSIS AND DISCUSSION 1. From the data collected, we have plotted the graph of velocity against transverse position. The velocity of the Pitot Tube can be expressed as sinusoidal position or look like the Simple Harmonic Motion (SHM) of its corresponding transverse position. Pitot tube of 2534 mm have the best symmetrical sinusoidal shape where as pitot tube of 54 mm have unsymmetrical sinusoidal shape. 2. While conduction this experiment, there are lots of possible errors that has resulted in the inaccuracy of the results obtained. Among the sources of error is parallax error during the process of taking the value of manometer. The manometer level fluctuates at a very high and inconsistent rate making it hard to collect the accurate reading. This error can be said as the main source of error as the value of manometer that taken influences the results of the experiment.

CONCLUSION The objective of the experiment is achieved. The principle fluid (air) velocity measurement is explored and understood. The understanding on how to compute parameters such as ∆x, ∆p and the velocity with the help from the data obtained from the experiment is enhanced.

10

SUMMARY/ABSTRACT An orifice plate meter shapes a precise and economical device for measuring the discharge for the flow of liquids or gases through a pipe. The orifice presented can be put into the suction pipe at the flanged joint about half way along its length. The multitube manometer given is used to determine the pressure fall across the orifice and this is associated to the discharge determined independently.

In this experiment, we are going to find out the discharge coefficient by conducting an experiment for an orifice plate in an airflow pipe. Also using the static pressure tapings given, we are determining the pressure distribution along the pipe downstream of the orifice plate. From the obtained CD of the orifice plate, we will determine the CD of a small nozzle.

OBJECTIVE This experiment will ask student to determine the discharge coefficients, CD for orifice plate and the small nozzle.

THEORY The orifice plate meter forms a jet, which expands to fill the whole pipe, some diameter distance downstream. The pressure difference between the two sides of the plate is related to the jet velocity, and therefore the discharge, by the energy equation: Q = Ajvj = AoCcvj = AoCcCv 2gh where, Q – discharge (volume/time) _  Aj – jet cross-section area at minimun contraction (vena contracta) Ao – orifice cross-2/4: d = orifice size) vj – jet velocity at minimum contraction (vena contracta) Cc  coefficient of contraction of jet Cv  coefficient of velocity of jet g – gravitational acceleration (9.81 ms -2) h – pressure difference 'head' of air across orifice (refer to equation (6) of Exp. I)

11

These two coefficients are normally combined to give a single coefficient of discharge: CD = Cc.Cv Equation (1) now becomes Q = CDAO 2gh

(2)

If Q can be determined independently, then the discharge coefficient can be determined  as follows:CD =

Q Ao 2gh

(3)

Values of Qi can be determined if the standard nozzle is fitted at the pipe inlet.  Qi = C’DAi 2gh i (4) If hi = the drop in pressure head across the inlet, the discharge = (  k/  air )* (xbefore nozzle  –xafter nozzle): in which Ai = standard nozzle cross-section area (= pi*d2 /4) and C’D assumed to be   0.97. Values of hI are obtained from the manometer tube levels connected to the pipe inlet pressure tapping and open to the atmosphere.

Calculating the CD of orifice plate: From equation (4), with the Qi obtained from standard nozzle where CD of standard nozzle is assumed to be 0.97, we can calculate the CD of orifice plate. Assuming that Qi across standard nozzle and Qo across orifice plate is the same, apply equation (3) CD =

Qo Ao 2gho

(5)

where ho – (  k/  air)*( x across orifice) Ao – cross section area of orifice plate hole   

12

APPARATUS

PROCEDURE (a) Insert the orifice plate in position (taking care to observe the instructions as to) in which the surface should face the approaching airflow. (b) Connect all the static pressure tapping points to the manometer tubes ensuring that one manometer tube remains unconnected to record room air pressure and that one is attached to the first tapping point adjacent to the standard inlet nozzle which should be fitted. (c) Turn on fan with low airflow (damper plate closed) and read all manometer tubes, including any open to the air (reading should be taken after the fan is on). (d) Gradually increase air flow by increasing the damper opening to 100%, and take read at all opening. Measure the diameter of the orifice plate, and the pipe for computing the cross sectional area and Reynolds number.

13

DATA, OBSERVATION AND RESULTS Damper Openings (% Openings) 0%

25%

Points

50%

75%

100%

mm of kerosene

Room ‘Pressure’

96

94

94

94

94

After nozzle

101

103

104

105

104

54 mm

100

104

104

105

104

294 mm

100

104

105

106

105

774 mm

100

106

107

109

107

Before Orifice

100

107

108

110

108

After Orifice

113

180

200

205

208

1574 mm

110

160

176

182

184

2534 mm

107

148

160

164

165

Table 5.1 Static ‘Pressure’ Readings when using Standard Nozzle (80 mm)

Damper Openings (% Openings) 0%

25%

Points

50%

75%

100%

mm of kerosene

Room ‘Pressure’

95

92

90

90

89

After nozzle

104

130

136

138

140

54 mm

105

132

138

140

141

294 mm

101

116

120

121

122

774 mm

101

118

121

122

123

Before Orifice

102

119

122

124

124

After Orifice

114

178

193

199

202

1574 mm

110

164

177

181

182

2534 mm

108

152

163

167

168

Table 5.2 Static ‘Pressure’ when using Small Nozzle (50 mm)

14

Damper Openings (% Opening) Points

0%

25%

50%

75%

100%

Qi

0.039

0.053

0.055

0.058

0.055

Hi

3.279

5.903

6.558

7.214

6.558

Cd

0.599

0.344

0.318

0.330

0.305

Ho

8.526

47.88

60.34

62.30

65.58

Re

26599

36147

37511

39557

37511

Table 2.3: Data of mm (kerosene) for each damper opening (diameter of orifice = 80mm)

Damper Openings (% Opening) Points

0%

25%

50%

75%

100%

Qi

0.020

0.042

0.046

0.047

0.049

Hi

5.903

24.922

30.168

31.480

33.448

Cd

0.820

0.776

0.775

0.771

0.788

Ho

7.87

38.69

46.56

49.19

51.16

Re

34924

73342

80327

82073

85565

Table 2.4: Data of mm (kerosene) for each damper opening (diameter of orifice = 50mm) Sample Calculation Taking 0% damper openings with diameter 80mm: A0 = (3.142)(0.082) / 4 = 5.027 x 10-3 m2

ho = (Pk/Pair)(xafter orifice - xbefore orifice)/1000 = (787/1.2)(113-100)/1000 = 8.526 m h1 = (Pk/Pair)(xafter nozzle - xbefore nozzle)/1000 = (787/1.2)(101-96)/1000 = 3.279 m

15

C’D = 0.97 Qi = (Ai)(C’d)√2ghi = (5.027 x 10-3)(0.97) √(2)(9.81)(3.279) = 0.039 Reynold's Number, Re = ud/ = (1.2)(0.039/5.027 x 10-3)0.05 /1.75e-5) = 26599 Cd = = 

Qo Ao 2gho 0.039 = 0.5998 0.005027 (2)(9.81)(8.526)



Discharge Coefficient, Cd

CD against Reynold Number for Standard Nozzle 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

10000

20000 30000 Reynolds Number, Re

40000

50000

Discharge Coefficient, Cd

CD against Reynolds Number for Small Nozzle 0.83 0.82 0.81 0.8 0.79 0.78 0.77 0.76 0

20000

40000 60000 Reynolds Number, Re

80000

100000

16

Longitudinal Pressure (mm kerosene) against Tapping Position for Standard Nozzle Longitudinal Pressure (mm)

250 200 0%

150

25% 100

50% 75%

50

100%

0 0

500

1000 1500 2000 Tapping Position (mm)

2500

3000

Longitudinal Pressure (mm kerosene) against Tapping Position for Small Nozzle Longitudinal Pressure (mm)

250 200 0%

150

25% 100

50% 75%

50

100%

0 0

500

1000 1500 2000 Tapping Position (mm)

2500

3000

17

ANALYSIS AND DISCUSSION 1. Based on the graphs plotted we can witness a sudden change in longitudinal pressure between 1000-1500 mm. This is expected because as the air flows, the orifice plate meter forms a jet that expands to fill up whole pipe, some diameter distance downstream. This will subsequently induce a significant pressure between the two sides of the plate. (Sudden increase in its longitudinal pressure or higher mm of kerosene). 2. CD obtained in the orifice has smaller value in comparison with CD obtained for small nozzle. The two main contributors for the drag coefficient are the skin friction and form drag. These values are calculated by using the same mathematical formula and method. However the CD orifice is acquired by considering the difference of pressure before and after the orifice. Whereas, CD for small nozzle is obtained by taking into consideration the pressure difference between before and after the nozzle. 3. The broader the damper opened, the higher the value of drag coefficient. The relationship between the opening damper and drag coefficient are directly proportional. 4. Based on the graph plotted, as the damper opening increases from 0% to 100% , the longitudinal pressure at each points of the pipe will also generally decrease. The longitudinal pressure achieves maximum value at 208 mm Kerosene for standard nozzle and 202 mm for small nozzle when the damper opening is 100%. The pressure only reaches 113 mm Kerosene and 114 mm Kerosene for standard nozzle and small nozzle respectively when the damper opening is completely closed or at 0%. The data tells us that as the damper opening enlarge, the manometer readings and also increase. The damper opening provide outlet for air inside the pipe. As the opening become larger, more air can pass through it. Therefore, pressure at the finish of the pipe is reduced. 5. The pressure in the pipe increases after the small opening of the orifice plate where the flow cross-section returns to its original value. The pressure downstream of the matter is lower that the upstream pressure because of the water resistance. The low pressure at the point of highest velocity creates the likelihood for the liquid to partially vaporize. It might remain partially vaporized after the sensor or return to a liquid state as the pressure increases after the lowest point 18

CONCLUSION In conclusions, since the objectives to determine the discharge coefficient, CD for orifice plate and the small nozzle is effectively done; this experiment can be considered as successful. Based on the data collected and the graph that we plot, we can wrap up that the pressure in the pipe increases after the small opening of the orifice plate where the flow crosses section return to its original value. Yet, because of the meter resistance, the pressure downstream of the meter is lower than the upstream pressure. The low pressure at the point of highest velocity builds the possibility for the liquid to partially vaporize and it might remain partially vaporized after the sensor or it may return to a liquid as the pressure increase after the lowest pressure point. As the damper opening increases from 0% to 100%, the longitudinal pressure at each points of the pipe will also reduce. In addition, this experiment enlighten the students’ understanding that as the damper opening enlarge from 0% to 50%, its corresponding CD is decreasing, before it rise up as the damper opening increase from 50% to 100%.

19