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Fluid Mechanics
Bernoulli's Equation & Flow
GATE 2015
Medium

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of

  • A4
  • B16
  • C32
  • 64

Explanation

h_f = fLV²/(2gD). With ṁ, ρ, f constant, V=ṁ/(ρA)∝1/D², so halving D quadruples V, i.e. V² increases 16×. h_f ∝ L·V²/D: doubling L (×2), V² increasing 16× (×16), and D halving means dividing by D contributes another ×2. Total factor = 2×16×2 = 64.

Source: GATE ME 2015 (Session 1) (2015)

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