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

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Hydraulics and Fluid Mechanics in ME
The discharge through a wholly drowned orifice is given by (where H1 = Height of water (on the upstream side) above the top of the orifice, H2 = Height of water (on the downstream side) above the bottom of the orifice, and H = Difference between two water levels on either side of the orifice)

Q = Cd × bH × √(2gh)
Q = Cd × bH₁ × √(2gh)
Q = Cd × b (H2 - H1) × √(2gh)
Q = Cd × bH2 × √(2gh)

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Hydraulics and Fluid Mechanics in ME
Two dimensional flows occurs when

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

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