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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 \( 90 \% \).

(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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