Compute the resulting pressure in kPa after a "real" diffuser in which the energy loss due to sudden enlargement is considered for the flow of water at 25°C from a 36 mm OD x 2.0 mm wall copper tube to an 85 mm OD x 2.5 mm wall copper tube, the pipes are the same elevation. The volume flow rate is 150 L/min and the pressure before the enlargement is 500.062 kPa. NB: OD = Outside Diameter, Wall refers to the pipe’s thickness (t)Hints:Obtain the specific weight of water for the given temperature from Appendix A (Table A.1).Obtain the resistance coefficient (K) for sudden enlargement from Table 10.3B in chapter 10.Instructions: Only express the areas in scientific notation to three decimal places but round off to three decimal places in normal number format where necessary throughout your calculations leading to the final answer and including the final answer for all other computations excluding the area. TABLE A.1 SI units [101 kPa (abs)]SpecificWeightDynamicViscosityKinematicDensityViscosityTemperature(°C)P(kN/m?)(kg/m)(Pa-s)(m²/s)1.75 x 109.8110001.75 x 10-39.8110001.52 x 1031.52 x 106109.8110001.30 x 10-31.30 x 10159.8110001.15 x 10-31.15 х 10-6209.799981.02 x 101.02 x 10-6259.789978.91 x 10-48.94 x 10-7309.779968.00 x 10-48.03 x 10-7359.759947.18 x 107.22 х 10409.739926.51 x 10-46.56 x 107459.719905.94 х 10-46.00 x 10-7509.699885.41 x 10-45.48 х 107559.679864.98 x 10-45.05 x 107609.659844.60 x 10-44.67 x 10-7659.629814.31 x 10-44.39 x 107709.599784.02 x 10-44.11 x 107759.569753.73 x 10-43.83 х 10 7809.539713.50 x 10-43.60 х 107859.509683.30 x 10-43.41 x 107909.479653.11 x 1043.22 x 107959.449622.92 x 10-43.04 x 1071009.409582.82 x 10-42.94 x 10-7 TABLE 10.3B Resistance coefficient-sudden contraction-Metric dataVelocity v2, m/sD1/D20.51.02.03.04.05.06.07.08.09.010.01.10.030.040.040.040.040.040.050.050.050.050.051.20.070.070.070.080.080.080.090.090.100.100.101.40.170.170.170.180.180.180.180.190.190.190.191.60.260.260.260.260.260.260.250.250.250.250.241.80.340.340.340.330.320.310.310.300.290.290.282.00.380.380.370.360.350.340.330.330.320.310.302.20.400.400.390.380.370.360.350.350.340.330.322.50.420.420.410.400.390.380.370.360.350.340.333.00.440.440.430.420.410.400.390.380.370.360.354.00.470.460.450.440.430.420.410.400.380.370.365.00.480.480.460.450.450.440.420.410.390.380.3710.00.490.480.470.460.460.440.430.420.410.400.390.490.490.470.470.460.450.440.430.420.410.40D /Dz-ratio of diameter of larger pipe to diameter of smaller pipe; vz-velocity in smaller pipe.Source: Brater, Ernest F, Horace W. King, James E. Lindell, and C. Y. Wei. 1996. Handbook of Hydraulics, 7th ed. New York: McGraw-Hill, Table 6-7.

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Answered: Compute the resulting pressure in kPa…

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Compute the resulting pressure in kPa after a "real" diffuser in which the energy loss due to sudden enlargement is considered for the flow of water at 25°C from a 36 mm OD x 2.0 mm wall copper tube to an 85 mm OD x 2.5 mm wall copper tube, the pipes are the same elevation. The volume flow rate is 150 L/min and the pressure before the enlargement is 500.062 kPa.

NB: OD = Outside Diameter, Wall refers to the pipe’s thickness (t)

Hints:

Obtain the specific weight of water for the given temperature from Appendix A (Table A.1).
Obtain the resistance coefficient (K) for sudden enlargement from Table 10.3B in chapter 10.

Instructions: Only express the areas in scientific notation to three decimal places but round off to three decimal places in normal number format where necessary throughout your calculations leading to the final answer and including the final answer for all other computations excluding the area.

TABLE A.1 SI units [101 kPa (abs)]
Specific
Weight
Dynamic
Viscosity
Kinematic
Density
Viscosity
Temperature
(°C)
P
(kN/m?)
(kg/m)
(Pa-s)
(m²/s)
1.75 x 10
9.81
1000
1.75 x 10-3
9.81
1000
1.52 x 103
1.52 x 106
10
9.81
1000
1.30 x 10-3
1.30 x 10
15
9.81
1000
1.15 x 10-3
1.15 х 10-6
20
9.79
998
1.02 x 10
1.02 x 10-6
25
9.78
997
8.91 x 10-4
8.94 x 10-7
30
9.77
996
8.00 x 10-4
8.03 x 10-7
35
9.75
994
7.18 x 10
7.22 х 10
40
9.73
992
6.51 x 10-4
6.56 x 107
45
9.71
990
5.94 х 10-4
6.00 x 10-7
50
9.69
988
5.41 x 10-4
5.48 х 107
55
9.67
986
4.98 x 10-4
5.05 x 107
60
9.65
984
4.60 x 10-4
4.67 x 10-7
65
9.62
981
4.31 x 10-4
4.39 x 107
70
9.59
978
4.02 x 10-4
4.11 x 107
75
9.56
975
3.73 x 10-4
3.83 х 10 7
80
9.53
971
3.50 x 10-4
3.60 х 107
85
9.50
968
3.30 x 10-4
3.41 x 107
90
9.47
965
3.11 x 104
3.22 x 107
95
9.44
962
2.92 x 10-4
3.04 x 107
100
9.40
958
2.82 x 10-4
2.94 x 10-7

TABLE 10.3B Resistance coefficient-sudden contraction-Metric data
Velocity v2, m/s
D1/D2
0.5
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
1.1
0.03
0.04
0.04
0.04
0.04
0.04
0.05
0.05
0.05
0.05
0.05
1.2
0.07
0.07
0.07
0.08
0.08
0.08
0.09
0.09
0.10
0.10
0.10
1.4
0.17
0.17
0.17
0.18
0.18
0.18
0.18
0.19
0.19
0.19
0.19
1.6
0.26
0.26
0.26
0.26
0.26
0.26
0.25
0.25
0.25
0.25
0.24
1.8
0.34
0.34
0.34
0.33
0.32
0.31
0.31
0.30
0.29
0.29
0.28
2.0
0.38
0.38
0.37
0.36
0.35
0.34
0.33
0.33
0.32
0.31
0.30
2.2
0.40
0.40
0.39
0.38
0.37
0.36
0.35
0.35
0.34
0.33
0.32
2.5
0.42
0.42
0.41
0.40
0.39
0.38
0.37
0.36
0.35
0.34
0.33
3.0
0.44
0.44
0.43
0.42
0.41
0.40
0.39
0.38
0.37
0.36
0.35
4.0
0.47
0.46
0.45
0.44
0.43
0.42
0.41
0.40
0.38
0.37
0.36
5.0
0.48
0.48
0.46
0.45
0.45
0.44
0.42
0.41
0.39
0.38
0.37
10.0
0.49
0.48
0.47
0.46
0.46
0.44
0.43
0.42
0.41
0.40
0.39
0.49
0.49
0.47
0.47
0.46
0.45
0.44
0.43
0.42
0.41
0.40
D /Dz-ratio of diameter of larger pipe to diameter of smaller pipe; vz-velocity in smaller pipe.
Source: Brater, Ernest F, Horace W. King, James E. Lindell, and C. Y. Wei. 1996. Handbook of Hydraulics, 7th ed. New York: McGraw-Hill, Table 6-7.

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