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Fluid Mechanics
Bernoulli's Equation & Flow
GATE 2008
Hard

Water (density 1000 kg/m³) issues from a nozzle at 10 m/s and strikes a bucket mounted on a Pelton wheel rotating at 10 rad/s. The mean wheel diameter is 1 m. The jet splits into two equal streams, each deflected by 120° (measured from the incoming jet direction). Neglecting friction, the magnitude of the torque exerted on the wheel per unit mass flow rate of the incoming jet is

  • A0 (N.m)/(kg/s)
  • B1.25 (N.m)/(kg/s)
  • C2.5 (N.m)/(kg/s)
  • 3.75 (N.m)/(kg/s)

Explanation

Bucket (blade) speed u=ωr=10×0.5=5 m/s. Relative velocity Vr1=V-u=10-5=5 m/s. Force per unit mass flow = Vr1(1-cosθ)=5(1-cos120°)=5×1.5=7.5 (m/s). Torque per unit mass flow = 7.5×r=7.5×0.5=3.75 N·m per kg/s.

Source: GATE ME 2008 (2008)

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