Hydraulics and Fluid Mechanics in ME
The diameter of the nozzle (d) for maximum transmission of power is given by (where D = Diameter of pipe, f = Darcy’s coefficient of friction for pipe, and l = Length of pipe)

d = (D⁵/8fl)1/2
d = (D⁵/8fl)1/4
d = (D⁵/8fl)1/3
d = (D⁵/8fl)1/5

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Hydraulics and Fluid Mechanics in ME
A compound pipe of diameter d1, d2 and d3 having lengths l1, l2 and l3 is to be replaced by an equivalent pipe of uniform diameter d and of the same length (l) as that of the compound pipe. The size of the equivalent pipe is given by

l/d³ = (l₁/d₁³) + (l₂/d₂³) + (l₃/d₃³)
l/d⁵ = (l₁/d₁⁵) + (l₂/d₂⁵) + (l₃/d₃⁵)
l/d⁴ = (l₁/d₁⁴) + (l₂/d₂⁴) + (l₃/d₃⁴)
l/d² = (l₁/d₁²) + (l₂/d₂²) + (l₃/d₃²)

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