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 90o elbow, and to estimate pressure drops or losses for the above-mentioned devices.
Table 1: Raw Data Sheet
Diameters Trial
No.
Manometer Reading Rotameter
Reading Weight (kg) Time (s) A B C D E F G H I DA = DC = 26 1 5.0 15.26 DB = 16 323 195 299 306 313 166 193 162 51 159 10.0 30.41 DD = DE = DG = 51 2 5.0 17.14 DH = DI = 26 302 200 281 287 292 177 198 173 64 139 10.0 34.24 3 5.0 19.98 Areas 280 205 264 269 271 186 202 185 79 119 10.0 39.86
AC = 531 4 5.0 23.08 AB = 201 265 207 251 255 257 194 205 192 90 99 10.0 45.83 AD = AG = 2040 5 5.0 27.76 AF = 314 250 211 240 242 244 200 209 200 98 78 10.0 55.75 AH = 531 6 5.0 33.84 239 213 231 234 234 207 211 205 104 58 10.0 68.89
Table 2: Processed Data Sheet 1
Trial No. Rotameter Reading (mm) QA (mm3/s) QT Venturi (mm3/s) ' QT Orifice (mm3/s) Venturi Loss HV (mm) Orifice Loss HO (mm) Diffuser Loss HD (mm) Elbow Loss HE (mm) Rotameter Loss HR (mm) 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
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 Q A (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 Rem arks 1 3.28 × 105 1.63 × 103 3.22 × 104 6.18 × 102 1.98 × 104 1.04 × 103 2.56 × 104 6.18 × 102 1.98 × 104 1.77 × 10-1 1.68 5.70 × 10-1 5.70 6.63 × 10-1 2 2.92 × 105 1.45 × 103 2.86 × 104 5.50 × 102 1.76 × 104 9.30 × 102 2.29 × 104 5.50 × 102 1.76 × 104 1.96 × 10-1 1.63 5.27 × 10-1 7.07 6.88 × 10-1 3 2.51 × 105 1.25 × 103 2.47 × 104 4.73 × 102 1.52 × 104 7.99 × 102 1.97 × 104 4.73 × 102 1.52 × 104 2.01 × 10-1 1.63 4.93 × 10-1 9.30 5.59 × 10-1 4 2.17 × 105 1.08 × 103 2.13 × 104 4.09 × 102 1.31 × 104 6.91 × 102 1.70 × 104 4.09 × 102 1.31 × 104 2.35 × 10-1 1.61 4.62 × 10-1 1.20 × 101 5.93 × 10-1 5 1.80 × 105 8.96 × 102 1.77 × 104 3.39 × 102 1.09 × 104 5.73 × 102 1.41 × 104 3.39 × 102 1.09 × 104 2.44 × 10-1 1.65 3.91 × 10-1 1.74 × 101 6.04 × 10-1
6 1.46 × 105 7.26 × 102 1.43 × 104 2.75 × 102 8.82 × 103 4.65 × 102 1.15 × 104 2.75 × 102 8.82 × 103 2.98 × 10-1 1.47 1.54 × 10-1 2.62 × 101 1.54 × 10-1
Temperature of water = 29.5°c Reynolds No. NR VD
Question 2 Cd = 0.9641 Question 3 y = 0.9641x - 0.039 0 0.5 1 1.5 2 2.5 3 3.5 0 1 2 3 4 QT × 10 5 (mm 3 /s) QA × 105 (mm3/s)
Graph of Q
Tvs Q
A Graph of Q_A vs Q_T Linear (Graph of Q_A vs Q_T)y = 0.5958x + 0.0668 0 0.5 1 1.5 2 2.5 3 3.5 0 1 2 3 4 5 6 Q'T × 10 5 (mm 3 /s) QA × 105 (mm3/s)
Graph of Q'
Tvs Q
A Graph of Q_A vs Q'_T Linear (Graph of Q_A vs Q'_T)C=0.5958 Cd= 0.600 ( using equation 5) Question 4 Question 5 y = 0.0183x + 0.7344 0 0.5 1 1.5 2 2.5 3 3.5 0 50 100 150 QA × 10 5 (m m 3/s L (mm) Graph of Q_A vs L Linear (Graph of Q_A vs L)
y = 9.0046x - 5.7209 (H_V) y = 41.475x - 47.592 (H_O) y = 5.394x - 7.1982 (H_D) y = 5.8854x - 7.055 (H_E) y = 5.8764x + 91.318 (H_R) 0 20 40 60 80 100 120 0 0.5 1 1.5 2 2.5 3 3.5 HV HO HD HE HR ( mm) QA × 105 (mm3/s) H_V H_O H_D H_E H_R Linear (H_V) Linear (H_V) Linear (H_D) Linear (H_E) Linear (H_E) Linear (H_R)
Question 6
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 2 1 2 B A * B * A A T 1 ) /A (A ) h g(h 2 A Q = (531)[2(9.81x103)(323-195)/(531/201)2-1)]0.5 = 3.44 x 105 mm3s-1 C = QA/ Q’T = 3.28 x 105 / 5.40 x 105 = 6.07 x 10-1 2 1 2 E O * F * E O T ) /A (A 1 ) h g(h 2 A Q
'
= (314)[2(9.81x103)(313-166)/(1-(314/2040)2]0.5 = 5.40 x 105 mm3s-1 * C * A V h h H = 323 – 299 = 24 mm
*
2
F * E O h h 1 C H = (313 – 166 )(1- 6.07 x 10-1) = 9.28 x 101 mm
2 D 2 C 2 A * D * C D A 1 A 1 g 2 Q h h H = (299-306) + [(3.28 x 10-1)2/2(9.81x103)](1/5312 – 1/20402) = 1.11 x 101 mm 0 5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 3 3.5 Loss Fact o r Reynold Number × 104 K_V vs N_RB K_O vs N_RO K_D vs N_RC K_R vs N_RH K_E vs N_RC Linear (K_V vs N_RB) Linear (K_O vs N_RO) Linear (K_D vs N_RC) Linear (K_R vs N_RH) Linear (K_E vs N_RC) 2 H 2 G 2 A * H * G E A 1 A 1 2g Q ) h h ( H = (193-162) + [(3.28 x 10-1 )2/2(9.81x103)](1/20402 – 1/5312) = 1.29 x 101mm * I * H R h h H = 162 – 51 = 1.11 x 102mm B A B A Q V = 3.28 x 105/201 = 1.63 x 103 mms-1 B B RB D V N = (3.28 x 105)(16)/8.11x10-1) = 3.22 x 104 C A C A Q V = 3.28 x 105/531 = 6.18 x 102 mms-1 C C RC D V N = (6.18 x 102)(26)/(8.11x10-1) = 1.98 x 104 O A O A Q V = .28 x 105/314 = 1.04 x 102 mms-1 O O RO D V N = (1.04 x 102)(20)/(8.11x10-1) = 2.56 x 104 H A H A Q V = .28 x 105/531 = 6.18 x 102 mms-1 H H RH D V N = = (6.18 x 102)(26)/(8.11x10-1) = 1.98 x 104 ) g 2 / (V H K 2 B V V = 24/ [(1.63 x 103)2/ 2(9.81x103)] ) g 2 / (V H K 2 O O O = 9.28 x 101/ [(1.04 x 102)2/ 2(9.81x103)] ) g 2 / (V H K 2 C D D = 1.11 x 101/ [(6.18 x 102)2/ 2(9.81x103)] ) g 2 / (V H K 2 H R R = 1.11 x 102/ [(6.18 x 102)2/ 2(9.81x103)] ) g 2 / (V H K 2 C E E = 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.
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:
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.