2612

VD = 3.83 X 0.4915 = 1.88 m's X m = 1.88 X 129.2 = 242 ft's X in

From Figure 33 From Figure 32 From Figure 31 Using Eq. 16,

In USCS units

FIGURE 33 Kinematic viscosity and Reynolds number. (Hydraulic Institute Engineering Data Book, Reference 5) [1 ft2/s = 0.0929 m2/s; 1 cSt = 1.0 X 10—6 m2/s; 1VD (m/s X m) = 129.2 VD" (ft/s X in); °F = (°C + 18) 1.8]

kinematic viscosity, ceimsroncs

FIGURE 33 Kinematic viscosity and Reynolds number. (Hydraulic Institute Engineering Data Book, Reference 5) [1 ft2/s = 0.0929 m2/s; 1 cSt = 1.0 X 10—6 m2/s; 1VD (m/s X m) = 129.2 VD" (ft/s X in); °F = (°C + 18) 1.8]

In SI units hf example 7 The flow in Example 6 is increased until complete turbulence results. Determine the friction factor f and flow.

From Figure 31, follow the relative roughness curve e/D = 0.00009 to the beginning of the zone marked "complete turbulence, rough pipes" and read f = 0.0119 at Re = 2 X 107

The problem may also be solved using Figure 32. Enter relative roughness e/D = 0.00009 and read directly across to f= 0.0119

An increase in Re from 3 X 106 to 2 X 107 would require an increase in flow to

2 X 107

3 X 106

2 X 107

3 X 106

example 8 The liquid in Example 6 is changed to water at 60°F (15.6°C). Determine Re, f, and the frictional head loss per 100 ft (100 m) of pipe.

Because the liquid is 60°F (15.6°C) water, enter Figure 31 and read directly downward from VD" to

Where the line VD" to Re crosses e/D = 0.00009 in Figure 31, read f = 0.013

Water at 60°F (15.6°C) is more viscous than 109°F (42.8°C) water, and this accounts for the fact that Re decreases and f increases. Using Eq. 16, it can be calculated that the frictional head loss increases to

TV2 100 12 532

m USCS unfts hf = fD - = °.°13 _ X 2X32117 = L97 11

T V2 100 3.832

m SI unfts hf = f D _ = 0.013 — X 2X9807 = L97 m example 9 A 102-in (259-cm) ID welded steel pipe is to be used to convey water at a velocity of 11.9 ft/s (3.63 m/s). Calculate the expected loss of head due to friction per 1000 ft and per 1000 m of pipe after 20 years. Use the empirical Hazen-Williams formula. From Table 2, C = 100.

In USCS units

In SI units f L Y = 0012 X 12.532 = 1 82 ft f d 2g = 0.012 1.61 X 2 X 32.17 = L82

SL Y2 A n,n 30.48 „ 3.832 . f D 2g = 0.012 0.4915 X 2 X 9.807 = Œ556 m

2.13 ft

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