For what velocity of flow of water in a new, clean, 6-in Schedule 40 steel pipe would an energy loss of 20 ft of head occur over a length of 1000 ft? Compute the volume flow rate at that velocity. Then refigure the velocity using the design value of C_h for steel pipe.

Question

For what velocity of flow of water in a new, clean, 6-in Schedule 40 steel pipe would an energy loss of 20 ft of head occur over a length of 1000 ft? Compute the volume flow rate at that velocity. Then refigure the velocity using the design value of [latex] C_h [/latex]for steel pipe.

Accepted Answer

We can use Eq. (8–8). Write

[latex] v =1.32C_h R^{0.63}s^{0.54} [/latex] (8–8)

[latex] s = h_L/L = \left(20ft\right)/\left(1000ft\right)=0.02 [/latex]

[latex]R = D/4 = \left(0.5054ft\right)/4 = 0.126ft [/latex]

[latex] C_h = 130[/latex]

Then,

[latex] v =1.32C_h R^{0.63}s^{0.54} [/latex]

[latex] v = \left(1.32\right)\left(130\right) \left(0.126\right)^{0.63} \left(0.02\right)^{0.54} = 5.64 ft/s [/latex]

[latex]Q = Av = \left(0.2006ft^2\right)\left(5.64ft/s\right) =1.13 ft^3/s [/latex]

Now we can adjust the result for the design value of [latex] C_h [/latex].

Note that the velocity and volume flow rate are both directly proportional to the value of [latex] C_h [/latex]. If the pipe degrades after use so the design value of [latex] C_h =100[/latex], the allowable volume flow rate to limit the energy loss to the same value of 20 ft per 1000 ft of pipe length would be

[latex]v = \left(5.64ft/s\right) \left(100/130\right) =4.34 ft/s[/latex]

[latex]Q = \left(1.13 ft^3/s\right) \left(100/130\right) =0.869 ft^3/s[/latex]

Question 8.11: For what velocity of flow of water in a new, clean, 6-in Sch...

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