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7.0 Results 7.1 Demonstration of the operation and characteristic of three different basic types of flowmeter. 7.1.1 Venturi Meter Experiment
Manometer Reading (mm)
A
B
C
D
E
Volume (L)
Time (min)
Flowrate, Q (L/min)
Flowrate calculated using Bernoulli’s equation, Q (L/min)
F
1
310 308 298 303 304 305
3
0.738
4.0690
6.200
2
398 391 353 376 381 386
3
0.340
8.8530
12.010
3
425 412 339 285 396 405
3
0.239
12.568
16.600
4
426 405 285 361 378 393
3
0.160
18.752
21.350
7.1.2 Orifice Meter Experiment
Manometer
Volume
Time
Flowrate, Q
Flowrate
Reading
(L)
(min)
(L/min)
calculated
(mm)
using Bernoulli’s equation, Q (L/min)
G
H
1
307
281
3
0.738
4.0690
5.87
2
385
294
3
0.340
8.8530
10.97
3
403
224
3
0.239
12.568
15.39
4
396
86
3
0.160
18.752
20.26
7.1.3 Rotameter Experiment
Volume
Time
Flowrate, Q
Rotameter, Q
(L)
(min)
(L/min )
(L/min)
1
3
0.738
4.0690
5
2
3
0.340
8.8530
10
3
3
0.239
12.568
15
4
3
0.160
18.752
20
7.2 Determination Of Loss Coefficient When Fluid Flows Through A 90 Degree Elbow. Differential Pieometer, ∆ℎ′ (mm) 1
V (m/s)
V2/2g (mm)
0.1277
0.83116
326
3
0.2780
3.9390
295
290
5
0.3946
7.9362
210
202
8
0.5886
17.658
Volume (L)
Time (min)
Flowrate, Q (L/min)
3
0.738
4.0690
Manometer Reading I J 291 290
3
0.340
8.8530
329
3
0.239
12.568
3
0.160
18.752
Piezometric Head (mm)
Piezometric Head Versus Velocity Head 9 8 7 6 5 4 3 2 1 0
y = 0.4022x + 1.1972 R² = 0.9704
0
5
Velocity Head (mm)
10
15
20
8.0 Calculations 8.1 Sample calculation for actual flow rate, Q.
𝑽𝒐𝒍𝒖𝒎𝒆 (𝑳)
Flow rate, Q (L/min) = 𝑻𝒊𝒎𝒆 (𝒎𝒊𝒏)
1.
2.
Q (L/min) =
3𝐿 0.7377 𝑚𝑖𝑛
= 4.0690 L/min
3.
Q (L/min) =
3𝐿 0.34 𝑚𝑖𝑛
= 8.8530 L/min
4. 3𝐿
3𝐿
Q (L/min) = 0.2387 𝑚𝑖𝑛 = 12.568 L/min
Q (L/min) = 0.16 𝑚𝑖𝑛 = 18.752 L/min
8.2 Sample Calculation for cross-section area.
A=
𝝅 (𝑫)𝟐 𝟒
A = Cross section area (m2) D = Diameter of the cross section (m)
Cross – Section A
Cross-Section Area AA =
𝜋 (0.0260 𝑚)2 4
= 2.011 x 10-4 m2
C
AC =
𝜋 (0.0160 𝑚)2 4
= 5.309 x 10-4 m2
The cross-section area of G and H are equal to A and C, since the diameter of the crosssection are the same.
8.3 Sample Calculation of Actual Flow Rates for Venturi Meter (Calculated Using Bernoulli’s And Continuity Equation).
𝑨
Q = 𝑪𝒅 𝑨𝒄 [𝟏 – ( 𝑪 )𝟐 ] 𝑨𝑨
−𝟏⁄ 𝟐
[𝟐𝒈(𝒉𝑨 − 𝒉𝑪 )]
𝟏⁄ 𝟐
Where, Cd = Coefficient of discharge (0.98) AC = Area of cross section at C (m2) AA = Area of cross section at A (m2) HA = Manometer reading at A (m) HC = Manometer reading at C (m) g = 9.81 m/s2
Experiment 1 2.011 𝑥 10−4 2 −1⁄ ( ) ] 2 5.309 𝑥 10−4
Q = (0.98)(2.011 𝑥 10−4 ) [1 – = 1.0333 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.310 − 0.298)]
1⁄ 2
)
= 6.200 L/min Experiment 2
Q = (0.98)(2.011 𝑥 10−4 ) [1 – ( = 2.0009 𝑥 10−4 = 12.010
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.398 − 0.353)]
1⁄ 2
)
L/min Experiment 3
Q = (0.98)(2.011 𝑥 10−4 ) [1 – ( = 2.7661 𝑥 10−4 = 16.600
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4 60 𝑠
1 𝑚𝑖𝑛
)
L/min Experiment 4
[2(9.81)(0.425 − 0.339)]
1⁄ 2
Q = (0.98)(2.011 𝑥 10−4 ) [1 – ( = 3.5418 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.426 − 0.285)]
1⁄ 2
)
= 21.250 L/min 8.4 Sample Calculation of Actual Flow Rates for Orifice Meter (Calculated Using Bernoulli’s And Continuity Equation)
𝑨
Q = 𝑪𝒅 𝑨𝑮 [𝟏 – ( 𝑮 )𝟐 ] 𝑨𝑯
−𝟏⁄ 𝟐
[𝟐𝒈(𝒉𝑮 − 𝒉𝑯 )]
𝟏⁄ 𝟐
Where, Cd = Coefficient of discharge (0.63) AH = Area of cross section at H (m2) AG = Area of cross section at G (m2) HG = Manometer reading at G (m) HH = Manometer reading at H (m) g = 9.81 m/s2
Experiment 1
Q = (0.63)(2.011 𝑥 10−4 ) [1 – ( = 9.7771 𝑥 10−5 =
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.307 − 0.281)]
1⁄ 2
)
5.87 L/min Experiment 2
Q = (0.63)(2.011 𝑥 10−4 ) [1 – = 1.8291 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ( ) ] 2 5.309 𝑥 10−4 60 𝑠 1 𝑚𝑖𝑛
)
= 10.97 L/min Experiment 3
[2(9.81)(0.385 − 0.294)]
1⁄ 2
Q = (0.63)(2.011 𝑥 10−4 ) [1 – ( = 2.5654 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.403 − 0.224)]
1⁄ 2
)
= 15.39 L/min Experiment 4 2.011 𝑥 10−4 2 −1⁄ ( ) ] 2 5.309 𝑥 10−4
Q =(0.63) (2.011 𝑥 10−4 ) [1 – = 3.3760 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.396 − 0.086)]
)
= 20.26 L/min 8.5 Sample Calculation For The Velocity Of Water Flowing Through The 90⁰ Elbow
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 (𝑚/𝑠) =
𝑚3 ) 𝑠
𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒,𝑄 (
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 𝑐𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖𝑜𝑛 (𝑚2 )
Area of the pipe cross-section, 𝑨 = 𝝅𝒓𝟐 Diameter of the pipe = 26 mm
1.
2. V=
4.069 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 10−3 )2 4
(
𝑚3 1000 𝐿
)(
𝑚𝑖𝑛 60 𝑠
)
V=
= 0.1277 𝑚/𝑠
8.853 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 4
10−3 )
( 2
𝑚3 1000 𝐿
𝑚𝑖𝑛
)(
60 𝑠
)
= 0.2780 𝑚/𝑠
3.
4. V =
12.568 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 4
10−3 )2
= 0.3946 𝑚/𝑠
(
𝑚3 1000 𝐿
)(
𝑚𝑖𝑛 60 𝑠
)
V =
18.752 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 4
( 2
10−3 )
= 0.5886 𝑚/𝑠
𝑚3
1000 𝐿
)(
𝑚𝑖𝑛 60 𝑠
)
1⁄ 2
𝑽𝟐
8.6 Sample Calculation For Velocity Head, 𝟐𝒈 1.
2. 𝑉2 2𝑔
=
0.1277 𝑚/𝑠 2 𝑥 9.81
(
𝑚𝑚 10−3 𝑚
𝑉2
)
2𝑔
= 0.83116 mm
=
0.2780 𝑚/𝑠 2 𝑥 9.81
(
𝑚𝑚 10−3 𝑚
)
= 3.9390 mm
3.
4. 𝑉2 2𝑔
=
0.3946 𝑚/𝑠 2 𝑥 9.81
= 7.9362 mm
(
𝑚𝑚 10−3 𝑚
)
𝑉2 2𝑔
=
0.5886 𝑚/𝑠 2 𝑥 9.81
= 17.658 mm
(
𝑚𝑚 10−3 𝑚
)
Manometer Reading (mm)
A
B
C
D
E
Volume (L)
Time (min)
Flowrate, Q (L/min)
Flowrate calculated using Bernoulli’s equation, Q (L/min)
F
1
310 308 298 303 304 305
3
0.738
4.0690
6.200
2
398 391 353 376 381 386
3
0.340
8.8530
12.010
3
425 412 339 285 396 405
3
0.239
12.568
16.600
4
426 405 285 361 378 393
3
0.160
18.752
21.350
7.1.2 Orifice Meter Experiment
Manometer
Volume
Time
Flowrate, Q
Flowrate
Reading
(L)
(min)
(L/min)
calculated
(mm)
using Bernoulli’s equation, Q (L/min)
G
H
1
307
281
3
0.738
4.0690
5.87
2
385
294
3
0.340
8.8530
10.97
3
403
224
3
0.239
12.568
15.39
4
396
86
3
0.160
18.752
20.26
7.1.3 Rotameter Experiment
Volume
Time
Flowrate, Q
Rotameter, Q
(L)
(min)
(L/min )
(L/min)
1
3
0.738
4.0690
5
2
3
0.340
8.8530
10
3
3
0.239
12.568
15
4
3
0.160
18.752
20
7.2 Determination Of Loss Coefficient When Fluid Flows Through A 90 Degree Elbow. Differential Pieometer, ∆ℎ′ (mm) 1
V (m/s)
V2/2g (mm)
0.1277
0.83116
326
3
0.2780
3.9390
295
290
5
0.3946
7.9362
210
202
8
0.5886
17.658
Volume (L)
Time (min)
Flowrate, Q (L/min)
3
0.738
4.0690
Manometer Reading I J 291 290
3
0.340
8.8530
329
3
0.239
12.568
3
0.160
18.752
Piezometric Head (mm)
Piezometric Head Versus Velocity Head 9 8 7 6 5 4 3 2 1 0
y = 0.4022x + 1.1972 R² = 0.9704
0
5
Velocity Head (mm)
10
15
20
8.0 Calculations 8.1 Sample calculation for actual flow rate, Q.
𝑽𝒐𝒍𝒖𝒎𝒆 (𝑳)
Flow rate, Q (L/min) = 𝑻𝒊𝒎𝒆 (𝒎𝒊𝒏)
1.
2.
Q (L/min) =
3𝐿 0.7377 𝑚𝑖𝑛
= 4.0690 L/min
3.
Q (L/min) =
3𝐿 0.34 𝑚𝑖𝑛
= 8.8530 L/min
4. 3𝐿
3𝐿
Q (L/min) = 0.2387 𝑚𝑖𝑛 = 12.568 L/min
Q (L/min) = 0.16 𝑚𝑖𝑛 = 18.752 L/min
8.2 Sample Calculation for cross-section area.
A=
𝝅 (𝑫)𝟐 𝟒
A = Cross section area (m2) D = Diameter of the cross section (m)
Cross – Section A
Cross-Section Area AA =
𝜋 (0.0260 𝑚)2 4
= 2.011 x 10-4 m2
C
AC =
𝜋 (0.0160 𝑚)2 4
= 5.309 x 10-4 m2
The cross-section area of G and H are equal to A and C, since the diameter of the crosssection are the same.
8.3 Sample Calculation of Actual Flow Rates for Venturi Meter (Calculated Using Bernoulli’s And Continuity Equation).
𝑨
Q = 𝑪𝒅 𝑨𝒄 [𝟏 – ( 𝑪 )𝟐 ] 𝑨𝑨
−𝟏⁄ 𝟐
[𝟐𝒈(𝒉𝑨 − 𝒉𝑪 )]
𝟏⁄ 𝟐
Where, Cd = Coefficient of discharge (0.98) AC = Area of cross section at C (m2) AA = Area of cross section at A (m2) HA = Manometer reading at A (m) HC = Manometer reading at C (m) g = 9.81 m/s2
Experiment 1 2.011 𝑥 10−4 2 −1⁄ ( ) ] 2 5.309 𝑥 10−4
Q = (0.98)(2.011 𝑥 10−4 ) [1 – = 1.0333 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.310 − 0.298)]
1⁄ 2
)
= 6.200 L/min Experiment 2
Q = (0.98)(2.011 𝑥 10−4 ) [1 – ( = 2.0009 𝑥 10−4 = 12.010
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.398 − 0.353)]
1⁄ 2
)
L/min Experiment 3
Q = (0.98)(2.011 𝑥 10−4 ) [1 – ( = 2.7661 𝑥 10−4 = 16.600
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4 60 𝑠
1 𝑚𝑖𝑛
)
L/min Experiment 4
[2(9.81)(0.425 − 0.339)]
1⁄ 2
Q = (0.98)(2.011 𝑥 10−4 ) [1 – ( = 3.5418 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.426 − 0.285)]
1⁄ 2
)
= 21.250 L/min 8.4 Sample Calculation of Actual Flow Rates for Orifice Meter (Calculated Using Bernoulli’s And Continuity Equation)
𝑨
Q = 𝑪𝒅 𝑨𝑮 [𝟏 – ( 𝑮 )𝟐 ] 𝑨𝑯
−𝟏⁄ 𝟐
[𝟐𝒈(𝒉𝑮 − 𝒉𝑯 )]
𝟏⁄ 𝟐
Where, Cd = Coefficient of discharge (0.63) AH = Area of cross section at H (m2) AG = Area of cross section at G (m2) HG = Manometer reading at G (m) HH = Manometer reading at H (m) g = 9.81 m/s2
Experiment 1
Q = (0.63)(2.011 𝑥 10−4 ) [1 – ( = 9.7771 𝑥 10−5 =
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.307 − 0.281)]
1⁄ 2
)
5.87 L/min Experiment 2
Q = (0.63)(2.011 𝑥 10−4 ) [1 – = 1.8291 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ( ) ] 2 5.309 𝑥 10−4 60 𝑠 1 𝑚𝑖𝑛
)
= 10.97 L/min Experiment 3
[2(9.81)(0.385 − 0.294)]
1⁄ 2
Q = (0.63)(2.011 𝑥 10−4 ) [1 – ( = 2.5654 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
2.011 𝑥 10−4 2 −1⁄ ) ] 2 5.309 𝑥 10−4
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.403 − 0.224)]
1⁄ 2
)
= 15.39 L/min Experiment 4 2.011 𝑥 10−4 2 −1⁄ ( ) ] 2 5.309 𝑥 10−4
Q =(0.63) (2.011 𝑥 10−4 ) [1 – = 3.3760 𝑥 10−4
𝑚3 1000 𝐿 𝑠
(
1 𝑚3
)(
60 𝑠 1 𝑚𝑖𝑛
[2(9.81)(0.396 − 0.086)]
)
= 20.26 L/min 8.5 Sample Calculation For The Velocity Of Water Flowing Through The 90⁰ Elbow
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 (𝑚/𝑠) =
𝑚3 ) 𝑠
𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒,𝑄 (
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒 𝑐𝑟𝑜𝑠𝑠−𝑠𝑒𝑐𝑡𝑖𝑜𝑛 (𝑚2 )
Area of the pipe cross-section, 𝑨 = 𝝅𝒓𝟐 Diameter of the pipe = 26 mm
1.
2. V=
4.069 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 10−3 )2 4
(
𝑚3 1000 𝐿
)(
𝑚𝑖𝑛 60 𝑠
)
V=
= 0.1277 𝑚/𝑠
8.853 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 4
10−3 )
( 2
𝑚3 1000 𝐿
𝑚𝑖𝑛
)(
60 𝑠
)
= 0.2780 𝑚/𝑠
3.
4. V =
12.568 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 4
10−3 )2
= 0.3946 𝑚/𝑠
(
𝑚3 1000 𝐿
)(
𝑚𝑖𝑛 60 𝑠
)
V =
18.752 𝐿/𝑚𝑖𝑛 𝜋 (26 𝑥 4
( 2
10−3 )
= 0.5886 𝑚/𝑠
𝑚3
1000 𝐿
)(
𝑚𝑖𝑛 60 𝑠
)
1⁄ 2
𝑽𝟐
8.6 Sample Calculation For Velocity Head, 𝟐𝒈 1.
2. 𝑉2 2𝑔
=
0.1277 𝑚/𝑠 2 𝑥 9.81
(
𝑚𝑚 10−3 𝑚
𝑉2
)
2𝑔
= 0.83116 mm
=
0.2780 𝑚/𝑠 2 𝑥 9.81
(
𝑚𝑚 10−3 𝑚
)
= 3.9390 mm
3.
4. 𝑉2 2𝑔
=
0.3946 𝑚/𝑠 2 𝑥 9.81
= 7.9362 mm
(
𝑚𝑚 10−3 𝑚
)
𝑉2 2𝑔
=
0.5886 𝑚/𝑠 2 𝑥 9.81
= 17.658 mm
(
𝑚𝑚 10−3 𝑚
)
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