Fluid MechanicsEasy

Question

A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the
sphere attains its terminal velocity, is proportional to :-

Options

A.

r3

B.

r2

C.

r5

D.

r4

Solution

Rate of heat produced
dQdt=Fv×VT      ∴VT=2r29η(ρ-σ)g=6πηrVT × VT      ∴ VT α r2
dQdt=∝rVT2     ∴ VT  α  r2dQdt∝r5

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