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(Solved): (b) A vane pump is to have a volumetric displacement of $$115 \mathrm{~cm}^{3}$$ and volumetric ...

(b) A vane pump is to have a volumetric displacement of $$115 \mathrm{~cm}^{3}$$ and volumetric efficiency of $$90 \%$$. It has a rotor diameter of $$63.5 \mathrm{~mm}$$, a cam ring diameter of $$89.0 \mathrm{~mm}$$ and a vane width of $$50.8 \mathrm{~mm}$$. The pump delivers $$0.09315 \mathrm{~m}^{3} / \mathrm{min}$$ of flow rate at pressure of 70 bar and actual power delivered to the pump of $$12.7 \mathrm{~kW}$$. Determine: i) the eccentricity between the rotor and the cam ring, $$e(\mathrm{~mm})$$ ii) the pump speed, $$N$$ (rpm) iii) the prime mover actual input torque, $$T(\mathrm{Nm})$$ iv) the mechanical efficiency, $$\eta_{m}(\%)$$, and v) the overall efficiency, $$\eta_{0}(\%)$$.

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The vane pumps are of two types, 1) Unbalanced vane pumps: These are two types a) Unbalanced pump with fixed delivery. b) Unbalanced
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