Hydraulics and Fluid Mechanics in ME
For similarity, in addition to models being geometrically similar to prototype, the following in both cases should also be equal

all the four ratios of inertial force to force due to viscosity, gravitation, surface tension, and elasticity
ratio of inertial force to force due to viscosity
ratio of inertial force to force due to surface tension
ratio of inertial force to force due to gravitation

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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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