Mean diameter or the pitch diameter (D) of the Pelton Wheel which rotates at N r.p.m. is given by

(where, Ku is the speed of rotation and H is the net head)

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BPSC AE Paper IV General Engineering 19 Dec 2024 Official Paper
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  1. \(\mathrm{D}=\frac{60\left(\mathrm{K}_{\mathrm{u}} \sqrt{2 \mathrm{gH}}\right)}{\pi \mathrm{N}}\)
  2. \(\rm D=60 K_u \sqrt{\frac{2 g H}{\pi N}}\)
  3. \(\mathrm{D}=\frac{\left(\sqrt{2 \mathrm{K}_{\mathrm{u}} \mathrm{gH}}\right)}{\pi \mathrm{N}}\)
  4. \(\mathrm{D}=\frac{60\left(\sqrt{2 \mathrm{K}_{\mathrm{u}} \mathrm{gH}}\right)}{\pi \mathrm{N}}\)

Answer (Detailed Solution Below)

Option 1 : \(\mathrm{D}=\frac{60\left(\mathrm{K}_{\mathrm{u}} \sqrt{2 \mathrm{gH}}\right)}{\pi \mathrm{N}}\)
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Detailed Solution

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Concept:

The pitch diameter of a Pelton wheel is calculated by equating the tangential velocity derived from geometry and speed ratio. The tangential velocity is:

and also

Equating both:

Final Answer:

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