where ε is the roughness height and Re is the Reynolds number. The
Reynolds number is defined as VD2/n, where V is the flow velocity.
Note that whenQis known,f andCL are functions ofD2 only. Solving
for D2 in the above relation of ðCLÞopt=ðA2
2Þ gives D2 ¼ 0.3968 m. In
practice, a penstock with an internal diameter equal or slightly
larger than 0.3968 m (397 mm) would be selected. Assuming that a
schedule 80 steel pipe is required due to structural considerations,
a 18 in outside diameter pipe would be selected. For this pipe, the
wall thickness is 0.938 in, and hence the internal diameter is 16.124
in (409.5 mm). For this pipe diameter, the value of CL is 25.35. This
value can be used to determine the dimensionless head loss as
follows (e.g., second and first terms in Eq. (6), respectively).
where ε is the roughness height and Re is the Reynolds number. The
Reynolds number is defined as VD2/n, where V is the flow velocity.
Note that whenQis known,f andCL are functions ofD2 only. Solving
for D2 in the above relation of ðCLÞopt=ðA2
2Þ gives D2 ¼ 0.3968 m. In
practice, a penstock with an internal diameter equal or slightly
larger than 0.3968 m (397 mm) would be selected. Assuming that a
schedule 80 steel pipe is required due to structural considerations,
a 18 in outside diameter pipe would be selected. For this pipe, the
wall thickness is 0.938 in, and hence the internal diameter is 16.124
in (409.5 mm). For this pipe diameter, the value of CL is 25.35. This
value can be used to determine the dimensionless head loss as
follows (e.g., second and first terms in Eq. (6), respectively).
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