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Fluid Mechanics
Mechanical Operations
GATE 2010
Hard

The diameter of a drop of liquid fuel changes with time, due to combustion, according to the relationship D=D0(1−t/tb). While burning, the drop falls at its terminal velocity under Stokes' flow regime. The distance it will travel before complete combustion, is given by

  • AD0²Δρtbg/(18μ)
  • BD0²Δρtbg/(36μ)
  • D0²Δρtbg/(54μ)
  • DD0²Δρtbg/(108μ)

Explanation

Vt=Δρ·g·D²/(18μ). Distance=∫₀^tb Vt dt=[Δρg D0²/(18μ)]∫₀^tb(1−t/tb)²dt. Substituting u=1−t/tb: the integral equals tb/3. Distance=Δρg D0²tb/(18μ×3)=D0²Δρtbg/(54μ).

Source: GATE CH 2010 (2010)

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