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Fluid Mechanics
Bernoulli's Equation & Flow
GATE 2007
Medium

In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by v=u₀(1+3x/L)i, where x is the distance along the axis of the nozzle from its inlet plane and L is the length of the nozzle. The time required for a fluid particle on the axis to travel from the inlet to the exit plane of the nozzle is

  • AL/u₀
  • (L/3u₀)ln4
  • CL/4u₀
  • DL/2.5u₀

Explanation

dx/dt=u₀(1+3x/L). Separating and integrating from x=0 to L: t=(L/3u₀)[ln(1+3x/L)]₀ᴸ=(L/3u₀)ln4.

Source: GATE ME 2007 (2007)

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