Project ForgeFluid Mechanics
Flow Through Pipes
GATE 2016
Hard
Water (ρ=1000, μ=10⁻³ Pa·s) flows turbulently at ū=1 m/s through a smooth pipe, f=0.005 (Fanning). At 0.05mm from the wall (viscous sub-layer, linear velocity profile), the velocity (m/s), rounded to 3 decimal places, is
0.125 m/s(± 0.005 accepted)
Explanation
τw=fρū²/2=2.5Pa. u*=√(τw/ρ)=0.05m/s. y+=yu*/ν=(5×10⁻⁵×0.05)/10⁻⁶=2.5. In the sublayer u+=y+, so u=2.5×0.05=0.125 m/s.
Source: GATE CH 2016 (2016)
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