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

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Hydraulics and Fluid Mechanics in ME
Two dimensional flows occurs when

The velocity of successive fluid particles, at any point, is the same at successive periods of time
The fluid particles move in plane or parallel planes and the streamline patterns are identical in each plane
The magnitude and direction of the velocity do not change from point to point in the fluid
The direction and magnitude of the velocity at all points are identical

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