GATE Papers >> Mechanical >> 2016 >> Question No 28

Question No. 28 Mechanical | GATE 2016

Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio $\left(N_1/N_2\right)$ of the two turbines is 2, then the respective power ratio $\left(P_1/P_2\right)$ is _____________


Answer : 0.24 : 0.26


Solution of Question No 28 of GATE 2016 Mechanical Paper

Specific speed of a turbine,

$ {\mathrm N}_\mathrm s=\frac{\mathrm N\sqrt{\mathrm P}}{\mathrm H^{\displaystyle\frac54}}........(1) $

Given for 2 turbine 1 and 2

$ \begin{array}{l}{\mathrm N}_{\mathrm s1}={\mathrm N}_{\mathrm s2}\\{\mathrm H}_1={\mathrm H}_2\;\;\;\;\&\;\;\;\;\frac{{\mathrm N}_1}{{\mathrm N}_2}=2\end{array} $

Equation (1) can be written as:

$ \begin{array}{l}\mathrm N\sqrt{\mathrm P}={\mathrm N}_\mathrm s\mathrm H^\frac54\\\therefore{\mathrm N}_1\sqrt{{\mathrm P}_1}={\mathrm N}_2\sqrt{{\mathrm P}_2}\\\mathrm N_1^2\times{\mathrm P}_1=\mathrm N_2^2\times{\mathrm P}_2\\\frac{{\mathrm P}_1}{{\mathrm P}_2}=\left(\frac{{\mathrm N}_2}{{\mathrm N}_1}\right)^2=\left(\frac12\right)^2=\frac14\\\therefore\mathrm{Power}\;\mathrm{ratio}=\frac14=0.25\end{array} $

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