Objectives

Name: Hia Jing Matric Number: A0087309X Group: 2H2

Objectives This experiment is prepared for students taking ME2134 - Fluid Mechanics I with the following objectives: a)

To become familiar with several types of flow measuring devices, such as the Venturi meter, orifice meter and rotameter.

b)

To determine the coefficient of discharge, Cd, for the Venturi meter and orifice meter, and to calibrate the rotameter.

c)

To determine the energy losses in the Venturi meter, orifice meter, rotameter, as well as the wide angle diffuser and the 90 o elbow, and to estimate pressure drops or losses for the above-mentioned devices.

Table 1: Raw Data Sheet Diameters DA = DC = 26

Trial No.

B

C

G

H

I

Rotameter Reading

1

DB = 16 DD = DE = DG = 51

A

Manometer Reading D E F

323

195

299

306

313

166

193

162

51

159

2

DH = DI = 26

302

200

281

287

292

177

198

173

64

139

3 Areas

280

205

264

269

271

186

202

185

79

119

Weight (kg)

Time (s)

5.0

15.26

10.0

30.41

5.0

17.14

10.0

34.24

5.0

19.98

10.0

39.86

AC = 531

4

AB = 201

265

AD = AG = 2040

207

251

255

257

194

205

192

90

99

5

AF = 314

250

AH = 531

211

240

242

244

200

209

200

98

78

6 239

213

231

234

234

207

211

205

104

58

5.0

23.08

10.0

45.83

5.0

27.76

10.0

55.75

5.0

33.84

10.0

68.89

Table 2: Processed Data Sheet 1 Venturi Loss HV (mm)

Orifice Loss HO (mm)

Diffuser Loss HD (mm)

Elbow Loss HE (mm)

Rotameter Loss HR (mm)

Trial No.

1

159

3.28 × 105 3.44 × 105 5.40 × 105

24

9.28 × 101

1.11 × 101

1.29 × 101

1.11 × 102

2

139

2.92 × 105 3.07 × 105 4.77 × 105

21

7.19 × 101

8.37

1.06 × 101

1.09 × 102

3

119

2.51 × 105 2.63 × 105 4.10 × 105

16

5.32 × 101

5.62

6.38

1.06 × 102

4

99

2.17 × 105 2.32 × 105 3.53 × 105

14

3.92 × 101

3.94

5.06

1.02 × 102

QA (mm3/s)

QT Venturi (mm3/s)

Q'T Orifice (mm3/s)

Rotameter Reading (mm)

5

78

1.80 × 105 1.90 × 105 2.95 × 105

10

2.76 × 101

3.46

3.54

1.02 × 102

6

58

1.46 × 105 1.55 × 105 2.31 × 105

8

1.62 × 101

5.92 × 10-1

2.41

1.01 × 102

Table 3: Processed data sheet 2 (See SUMMARY OF EQUATIONS on Page 17) Estimation of loss factors Trial No

Actual flow QA (mm3/s)

Veloc ity VB (mm/ s)

Reynolds No NRB

Velocit y VC (mm/s)

Reynol ds No NRC

Velocity VO (mm/s)

Reynold s No NRO

Velocity VH (mm/s)

Reynold s No NRH

Loss Factor KV

Loss Factor KO

Loss Factor KD

Loss Factor KR

Loss Factor KE

1

3.28 105

× 1.63 × 103

3.22 × 104

6.18 × 1.98 × 1.04 102 104 103

× 2.56 104

× 6.18 102

×

1.98 104

× 1.77 × 1.68 10-1

5.70 × 5.70 10-1

6.63 × 10-1

2

2.92 105

× 1.45 × 103

2.86 × 104

5.50 × 1.76 × 9.30 102 104 102

× 2.29 104

× 5.50 102

× 1.76 104

× 1.96 × 1.63 10-1

5.27 × 7.07 10-1

6.88 × 10-1

3

2.51 105

× 1.25 × 103

2.47 × 104

4.73 × 1.52 × 7.99 102 104 102

× 1.97 104

× 4.73 102

× 1.52 104

× 2.01 × 1.63 10-1

4.93 × 9.30 10-1

5.59 × 10-1

4

2.17 105

× 1.08 × 103

2.13 × 104

4.09 × 1.31 × 6.91 102 104 102

× 1.70 104

× 4.09 102

× 1.31 104

× 2.35 × 1.61 10-1

4.62 × 1.20 × 5.93 × 10-1 10-1 101

5

1.80 105

× 8.96 × 102

1.77 × 104

3.39 × 1.09 × 5.73 102 104 102

× 1.41 104

× 3.39 102

× 1.09 104

× 2.44 × 1.65 10-1

3.91 × 1.74 × 6.04 × 10-1 10-1 101

Rem arks

6

1.46 105

× 7.26 × 102

1.43 × 104

2.75 × 8.82 × 4.65 102 103 102

Temperature of water = 29.5°c Kinematic Viscosity of water  = 8.11 × 10-1 mm2/s

× 1.15 104

× 2.75 102

× 8.82 103

Reynolds No. N R 

VD



× 2.98 × 1.47 10-1

1.54 × 2.62 × 1.54 × 10-1 10-1 101

Question 2

Graph of QT vs QA 3.5 y = 0.9641x - 0.039

QT × 105 (mm3/s)

3 2.5 2 Graph of Q_A vs Q_T

1.5

Linear (Graph of Q_A vs Q_T) 1 0.5 0 0

1

2

QA ×

3

4

105 (mm3/s)

Cd = 0.9641 Question 3

Graph of Q'T vs QA 3.5 y = 0.5958x + 0.0668

Q'T × 105 (mm3/s)

3 2.5 2 Graph of Q_A vs Q'_T

1.5

Linear (Graph of Q_A vs Q'_T) 1 0.5 0 0

1

2

QA ×

3

4

105 (mm3/s)

5

6

C=0.5958 Cd= 0.600 ( using equation 5) Question 4 3.5 y = 0.0183x + 0.7344 3

QA × 105 (mm3/s

2.5 2 Graph of Q_A vs L

1.5

Linear (Graph of Q_A vs L) 1 0.5 0 0

50

100

150

L (mm)

Question 5 120 y = 5.8764x + 91.318 (H_R)

HV HO HD HE HR (mm)

100

H_V H_O

80

H_D

y = 41.475x - 47.592 (H_O)

H_E 60

H_R Linear (H_V)

40

Linear (H_V) Linear (H_D)

y = 9.0046x - 5.7209 (H_V) 20

Linear (H_E)

y = 5.8854x - 7.055 (H_E)

Linear (H_E)

y = 5.394x - 7.1982 (H_D)

0 0

0.5

1

1.5

2

QA × 105 (mm3/s)

2.5

3

3.5

Linear (H_R)

Question 6 30

25 K_V vs N_RB K_O vs N_RO

Loss Factor

20

K_D vs N_RC K_R vs N_RH

15

K_E vs N_RC Linear (K_V vs N_RB)

10

Linear (K_O vs N_RO) Linear (K_D vs N_RC)

5

Linear (K_R vs N_RH) Linear (K_E vs N_RC)

0 0

0.5

1

1.5

2

Reynold Number ×

2.5

3

3.5

104

Question 7 Sample Calculation for Trial 1: Average Mass Rate = ṁ = ( m1 /t1 + m2/t2) /2 = (5/15.26 + 10/30.41)/2 = 3.28 x 10-1 kg-1s QA = ṁv = 3.28 x 10-1 x (1 x 106) = 3.28 x 105 mm3s-1 1

 2g(h *A h *B)  2 3 2 0.5 5 3 -1 Q T A A   = (531)[2(9.81x10 )(323-195)/(531/201) -1)] = 3.44 x 10 mm s 2  (A A /A B) 1 C = QA/ Q’T = 3.28 x 105 / 5.40 x 105 = 6.07 x 10-1 1

 2g(h *E h *F)  2 Q'T A O  = (314)[2(9.81x103)(313-166)/(1-(314/2040)2]0.5 = 5.40 x 105 mm3s-1 2 1(A O /A E )  H V  h *A  h *C = 323 – 299 = 24 mm H O  h *E  h *F 1  C 2  = (313 – 166 )(1- 6.07 x 10-1) = 9.28 x 101 mm

Q2A  1 1   2  2  = (299-306) + [(3.28 x 10-1)2/2(9.81x103)](1/5312 – 1/20402) H D  h  h   2g  A C A D  1 = 1.11 x 10 mm * C

* D

Q2A H E  (h  h )  2g * G

* H

 1 1   2  2  = (193-162) + [(3.28 x 10-1)2/2(9.81x103)](1/20402 – 1/5312)  AG A H 

= 1.29 x 101mm H R  h *H  h *I = 162 – 51 = 1.11 x 102mm Q VB  A = 3.28 x 105/201 = 1.63 x 103 mms-1 AB V D N RB  B B = (3.28 x 105)(16)/8.11x10-1) = 3.22 x 104



Q VC  A = 3.28 x 105/531 = 6.18 x 102 mms-1 AC N RC 

VC DC



= (6.18 x 102)(26)/ (8.11x10-1) = 1.98 x 104

Q VO  A = .28 x 105/314 = 1.04 x 102 mms-1 AO V D N RO  O O = (1.04 x 102)(20)/(8.11x10-1) = 2.56 x 104



VH 

N RH

QA = .28 x 105/531 = 6.18 x 102 mms-1 AH V D  H H = = (6.18 x 102)(26)/(8.11x10-1) = 1.98 x 104



H V (VB2 / 2g) H  KO  2 O (VO / 2g) H  KD  2 D (VC / 2g) H  KR  2 R (VH / 2g) H  KE  2 E (VC / 2g)  KV 

= 24/ [(1.63 x 103)2/ 2(9.81x103)] = 9.28 x 101/ [(1.04 x 102)2/ 2(9.81x103)] = 1.11 x 101/ [(6.18 x 102)2/ 2(9.81x103)] = 1.11 x 102/ [(6.18 x 102)2/ 2(9.81x103)] = 1.29 x 101/ [(6.18 x 102)/ 2(9.81x103)]

Discussion Question 1: Comment on the relative advantages and disadvantages of Venturi meter, orifice platemeter and rotameter as flow measuring devices. Venturi Meter

Advantages: It has a wide range of flow and has better accuracy than the other devices as more pressure can be sustained. Disadvantages: It is expensive and difficult to maintain as it is rather heavy. It is also bulky so it can be quite inconvenient. Orifice Meter Advantages: It has a wide range of flow and it is easy to maintain to maintain due to it’s small size. Disadvantages: It is not very accurate as pressure is not sustained. Rotameter Advantages: It is accurate as pressure is sustained and it is also cheap. Disadvantages: It needs to be calibrated according to different fluids. Also, it has a limited usage as it must be aligned vertically with the fluids at all times. Therefore, some energy is lost, resulting in a high loss factor. Question 2: Comment on the head losses associated with all the flow meters studied in this experiment, emphasizing the relationship between mechanism of loss generation and its magnitude. Rotameter The rotameter has the largest head loss of all the flow meters. This is due to the fluid consuming energy by moving against gravity. Also, energy is lost through friction between the fluid and the walls of the rotameter. The head loss of the rotameter is relatively stable, given by the low gradient of the HR against QA graph. Orifice Meter The head loss of the orifice meter is relatively high, although lower than the head loss for the rotameter. However, the head loss increases with the flow rate, as shown in the high gradient of the HO against QA graph. This shows that the energy loss increases with the flow rate. Venturi Meter The head loss of the venturi meter is low. Also, the gradient of the Hv against QA is low. This is because the meter does not cause much deviation to the flow rate. Question 3: Explain with the aid of simple sketches what is the vena contractor of an orifice meter?

As the fluid flows through the meter, the fluid diameter contracts. The vena contractor is the point where the fluid flow diameter is the smallest due to the orifice meter. Before the flow diameter expands in it’s stream again. Question 7: Comment on the limitations and major sources of error in this experiment. Limitations:  

High flow rates cannot be measured in this experiment as it would result in large head losses in the rotameter and the orifice meter Fluids with high viscosity cannot be used as friction between the fluids and the tubes will result in large head losses in the meters

Sources of errors:     

Parallax error from reading off the manometer and the rotameter The meniscus is not very visible due to the clear form of the fluid Fluctuations of the fluid causes it to be difficult to read off the manometer Human reaction error may occur when taking timings for the water to be collected Changes in the motor that powers the pump may affect the readings on the manometer and rotameter

Conclusion This experiment familiarizes us to the workings of the flow measuring devices and to determine the head loss of each device. Through the head loss, it allows us to determine the advantages and disadvantages of the devices. It also allows us to develop a better understanding of the devices to determine whether they are appropriate to measure different kinds of fluids.