Calculations:
Part I: Variation of the Piezometric Head along the Venturi Meter.
Flow Rate Q:
𝑄=
𝐸𝑛𝑑 𝑉𝑜𝑙𝑢𝑚𝑒 − 𝑆𝑡𝑎𝑟𝑡 𝑉𝑜𝑙𝑢𝑚𝑒
𝑇𝑖𝑚𝑒
𝑄=
10𝐿 − 0𝐿
= 0.16722 𝐿/𝑠
59.8𝑠
𝑄 = 0.16722 𝐿/𝑠 ×
1𝑚3
= 0.00016722𝑚3 /𝑠
1000𝐿
Converting Piezometric Head:
Piezometric Table No. 1
Piezometric Table No.2
1𝑚
1𝑚
ℎ = 275 𝑚𝑚 × 1000𝑚𝑚 = 0.275𝑚
ℎ = 215 𝑚𝑚 × 1000𝑚𝑚 = 0.215𝑚
Piezometric Table No. 3
Piezometric Table No.4
ℎ = 142 𝑚𝑚 ×
1𝑚
1000𝑚𝑚
= 0.142𝑚
ℎ = 65 𝑚𝑚 ×
Piezometric Table No. 5
ℎ = 5𝑚𝑚 ×
1𝑚
1000𝑚𝑚
1𝑚
1000𝑚𝑚
= 0.065𝑚
Piezometric Table No.6
= 0.005𝑚
ℎ = 153𝑚𝑚 ×
1𝑚
1000𝑚𝑚
= 0.153𝑚
Area of the Tube:
Piezometric Table No. 1
𝑎=
𝜋(24.5𝑚𝑚×
2
1𝑚
)
1000𝑚𝑚
4
Piezometric Table No.2
= 0.0004714𝑚
2
Piezometric Table No. 3
𝑎=
𝜋(11.6𝑚𝑚×
2
1𝑚
)
1000𝑚𝑚
4
Piezometric Table No. 1
𝑎=
𝜋(13.6𝑚𝑚×
2
1𝑚
)
1000𝑚𝑚
4
= 0.0001452𝑚2
Piezometric Table No.4
= 0.0001057𝑚
2
𝑎=
𝜋(10.5𝑚𝑚×
2
1𝑚
)
1000𝑚𝑚
4
Piezometric Table No.2
= 0.0000866𝑚2
𝑎=
𝜋(9.8𝑚𝑚×
2
1𝑚
)
1000𝑚𝑚
4
= 0.0000754𝑚
2
𝑎=
𝜋(24.5𝑚𝑚×
2
1𝑚
)
1000𝑚𝑚
4
= 0.0004714𝑚2
Velocity:
Piezometric Table No. 1
𝑉=
0.00016722𝑚3 /𝑠
0.0004714𝑚2
= 0.354713 𝑚/𝑠
Piezometric Table No. 3
𝑉=
0.00016722𝑚3 /𝑠
0.0001057𝑚2
= 1.58232 𝑚/𝑠
Piezometric Table No. 5
𝑉=
0.00016722𝑚3 /𝑠
0.0000754𝑚2
= 2.21696 𝑚/𝑠
Piezometric Table No.2
𝑉=
0.00016722𝑚3 /𝑠
0.0001452𝑚2
= 1.15115 𝑚/𝑠
Piezometric Table No.4
𝑉=
0.00016722𝑚3 /𝑠
0.0000866𝑚2
= 1.93121 𝑚/𝑠
Piezometric Table No.6
𝑉=
0.00016722𝑚3 /𝑠
0.0004714𝑚2
= 0.35471 𝑚/𝑠
Velocity Head:
Piezometric Table No. 1
Piezometric Table No.2
0.354713 𝑚/𝑠
1.15115 𝑚/𝑠
9.81𝑚
2( 2 )
𝑠
= 0.00685 𝑚
2(
9.81𝑚
)
𝑠2
= 0.07218 𝑚
Piezometric Table No. 3
Piezometric Table No.4
1.58232 𝑚/𝑠
1.93121 𝑚/𝑠
2(
9.81𝑚
)
𝑠2
= 0.13637 𝑚
2(
9.81𝑚
)
𝑠2
= 0.20314 𝑚
Piezometric Table No. 5
Piezometric Table No.6
2.21696 𝑚/𝑠
0.35471 𝑚/𝑠
9.81𝑚
2( 2 )
𝑠
= 0.2677 𝑚
Total Head:
2(
9.81𝑚
)
𝑠2
= 0.00685 𝑚
Piezometric Table No. 1
0.275𝑚 +
0.354713 𝑚/𝑠
2(
9.81𝑚
)
𝑠2
Piezometric Table No.2
= 0.28185 𝑚
Piezometric Table No. 3
0.142𝑚 +
1.58232 𝑚/𝑠
2(
9.81𝑚
)
𝑠2
2.21696 𝑚/𝑠
2(
9.81𝑚
)
𝑠2
1.15115 𝑚/𝑠
9.81𝑚
)
𝑠2
2(
= 0.28718 𝑚
Piezometric Table No.4
= 0.27837 𝑚
Piezometric Table No. 5
0.005𝑚 +
0.215𝑚 +
0.065𝑚 +
1.93121 𝑚/𝑠
2(
9.81𝑚
)
𝑠2
= 0.26814 𝑚
Piezometric Table No.6
= 0.2727 𝑚
0.153𝑚 +
0.35471 𝑚/𝑠
2(
9.81𝑚
)
𝑠2
= 0.15985 𝑚
Part 2: Calibration of the Venturi Meter:
Flow Rate at Each Trial:
Trial 1:
𝑄=
10𝐿−0𝐿
59.8𝑠
Trial 2:
1𝑚3
× 1000𝐿 = 0.000167 𝑚3 /𝑠
Trial 3:
𝑄=
10𝐿−0𝐿
74.99𝑠
10𝐿−0𝐿
66.57𝑠
1𝑚3
× 1000𝐿 = 0.00015 𝑚3 /𝑠
Trial 4:
1𝑚3
× 1000𝐿 = 0.000133 𝑚3 /𝑠
Trial 5:
10𝐿−0𝐿
𝑄=
𝑄=
10𝐿−0𝐿
79.28𝑠
1𝑚3
× 1000𝐿 = 0.000126 𝑚3 /𝑠
Trial 6:
1𝑚3
𝑄 = 119.03𝑠 × 1000𝐿 = 0.000084 𝑚3 /𝑠
𝑄=
10𝐿−0𝐿
253.1𝑠
1𝑚3
× 1000𝐿 = 0.000040 𝑚3 /𝑠
Height Difference:
Trial 1:
Trial 2:
1𝑚
1𝑚
∆ℎ = (275𝑚𝑚 − 5𝑚𝑚) × 1000𝑚 = 0.27𝑚
∆h = (245𝑚𝑚 − 40𝑚𝑚) × 1000𝑚 = 0.205𝑚
Trial 3:
Trial 4:
∆ℎ = (220𝑚𝑚 − 50𝑚𝑚) ×
1𝑚
1000𝑚
= 0.17𝑚
Trial 5:
∆ℎ = (180𝑚𝑚 − 113𝑚𝑚) ×
1𝑚
1000𝑚
= 0.146𝑚
Trial 6:
1𝑚
∆ℎ = (180𝑚𝑚 − 113𝑚𝑚) × 1000𝑚 = 0.067𝑚
1𝑚
∆ℎ = (161𝑚𝑚 − 147𝑚𝑚) × 1000𝑚 = 0.014𝑚
Value of B:
Assuming trial 5 diameter as throat diameter and trial 1 diameter as pipe diameter
9.81𝑚
2( 2 )
𝑠
𝐵 = 0.000075𝑚 √
2
0.000075𝑚2
1−(
)
0.000471𝑚2
2𝑔
𝐵 = 𝑎5
√
𝑎 2
1 − (𝑎5 )
1
2
5
𝑚 ⁄2
𝐵 = 0.0003385
𝑠
Discharge Coefficient:
Trial 1:
𝐶=
Trial 2:
0.000167 𝑚3 /𝑠
5⁄
𝑚 2
0.0003385
√0.27𝑚
𝑠
= 0.95081
= 0.98022
Trial 4:
0.000133 𝑚3 /𝑠
5⁄
𝑚 2
0.0003385
√0.17𝑚
𝑠
= 0.95554
0.000126 𝑚3 /𝑠
𝐶=
5⁄
𝑚 2
√0.146𝑚
𝑠
= 0.9753
0.0003385
Trial 5:
𝐶=
5⁄
𝑚 2
√0.205𝑚
𝑠
0.0003385
Trial 3:
𝐶=
0.00015 𝑚3 /𝑠
𝐶=
Trial 6:
𝑚3
𝑠
0.000084
5⁄
𝑚 2
0.0003385
√0.067𝑚
𝑠
= 0.95892
Average Discharge Coefficient:
𝐶=
0.000040 𝑚3 /𝑠
5⁄
𝑚 2
0.0003385
√0.014𝑚
𝑠
= 0.98655
𝐶𝑎𝑣𝑔 =
0.95081+0.98022+0.95554+0.9753+0.95892+0.98655
6
=0.967890109
From the plot, Q vs. (h1-hT)1/2
y = 0.000326268x
Discharge Coefficient:
𝐶𝑝𝑙𝑜𝑡 =
0.000326268
𝐵
=
0.000326268
0.0003385
= 0.9638641064
Average of Cavg and Cplot:
𝐶𝑓𝑖𝑛𝑎𝑙 =
0.967890109+0.9638641064
2
=0.96591681
Reynolds Number:
 Assuming throat diameter is 0.0098m, area is 0.00007543m2
 Temperature is at 25℃
 ρ of water is 997.08 kg/m3
 μ of water is 0.8937×10-3 Pa-s
Trial 1:
𝑁𝑅𝑒 =
Trial 2:
𝑚3 997.08𝑘𝑔
0.0098𝑚(0.000167 )(
)
𝑠
𝑚3
0.00007543m2 (0.8937×10−3 𝑃𝑎∙𝑠)
𝑁𝑅𝑒 =
𝑚3 997.08𝑘𝑔
)(
)
𝑠
𝑚3
0.00007543m2 (0.8937×10−3 𝑃𝑎∙𝑠)
0.0098𝑚(0.00015
𝑁𝑅𝑒 =24239.35761
𝑁𝑅𝑒 =21774.2765
Trial 3:
Trial 4:
𝑁𝑅𝑒 =
𝑚3 997.08𝑘𝑔
0.0098𝑚(0.000133 )(
)
𝑠
𝑚3
0.00007543m2 (0.8937×10−3 𝑃𝑎∙𝑠)
𝑁𝑅𝑒 =
𝑚3 997.08𝑘𝑔
)(
)
𝑠
𝑚3
0.00007543m2 (0.8937×10−3 𝑃𝑎∙𝑠)
0.0098𝑚(0.000126
𝑁𝑅𝑒 =19329.42506
𝑁𝑅𝑒 =18283.47105
Trial 5:
Trial 6:
𝑁𝑅𝑒 =
𝑚3 997.08𝑘𝑔
0.0098𝑚(0.000084 )(
)
𝑠
𝑚3
0.00007543m2 (0.8937×10−3 𝑃𝑎∙𝑠)
𝑁𝑅𝑒 =12177.71642
𝑁𝑅𝑒 =
𝑚3 997.08𝑘𝑔
)(
)
𝑠
𝑚3
0.00007543m2 (0.8937×10−3 𝑃𝑎∙𝑠)
0.0098𝑚(0.000040
𝑁𝑅𝑒 =5727.039056
Pressure Drop:
Trial 1:
∆𝑃 = (997.08𝑘𝑔/𝑚3 )(9.81𝑚/𝑠 2 )(0.27𝑚)
Trial 2:
∆𝑃 = (997.08𝑘𝑔/𝑚3 )(9.81𝑚/𝑠 2 )(0.205𝑚)
∆𝑃 =2640.965796 Pa
∆𝑃 =2005.177734 Pa
Trial 3:
∆𝑃 = (997.08𝑘𝑔/𝑚3 )(9.81𝑚/𝑠 2 )(0.17𝑚)
Trial 4:
∆𝑃 = (997.08𝑘𝑔/𝑚3 )(9.81𝑚/𝑠 2 )(0.146𝑚)
∆𝑃 = 19329.42506 Pa
∆𝑃 = 18283.47105 Pa
Trial 1:
∆𝑃 = (997.08𝑘𝑔/𝑚3 )(9.81𝑚/𝑠 2 )(0.067𝑚)
Trial 2:
∆𝑃 = (997.08𝑘𝑔/𝑚3 )(9.81𝑚/𝑠 2 )(0.014𝑚)
∆𝑃 = 12177.71642 Pa
∆𝑃 = 5727.039056 Pa