Hydraulics and Fluid Mechanics in ME
Mach number is significant in

supersonics, as with projectiles and jet propulsion
full immersion or completely enclosed flow, as with pipes, aircraft wings, nozzles etc
all of fhe above
simultaneous motion through two fluids where there is a surface of dis-continuity, gravity force, and wave making effects, as with ship’s hulls

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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/d² = (l₁/d₁²) + (l₂/d₂²) + (l₃/d₃²)
l/d⁵ = (l₁/d₁⁵) + (l₂/d₂⁵) + (l₃/d₃⁵)
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 depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where IG = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface, and x = Depth of centre of gravity of the immersed surface from the liquid surface)

(Ax̅/IG) + x̅
(IG/Ax̅) - x̅
(IG/x̅) - Ax̅
(IG/Ax̅) + x̅

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