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GATE 2017 CE (CE2) – Question 17

Hydraulics · Dimensional analysis and hydraulic similitude · 1 mark · Multiple choice

A centrifugal pump has impeller speed N rpm, discharge Q m³/s and total head H m. Its specific speed is ______.

  1. $NQ^{0.5}/H^{0.5}$
  2. $NQ^{0.5}/H$
  3. $NQ^{0.5}/H^{0.75}$
  4. $NQ/H^{0.75}$

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Correct answer: (C) $NQ^{0.5}/H^{0.75}$

Explanation

For similar pumps, $Q\propto ND^3$ and $H\propto N^2D^2$. Eliminating diameter for the unit-discharge, unit-head reference gives $N_s=N\sqrt Q/H^{3/4}$ (C). The numerical conventional specific speed depends on the specified units.