Assignment Document

Pelton Wheel Turbine

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  • "Ans. First we derive the equation for the work done by the shaft in rotation, so needto consider the flow of water to the turbine is cyclic and uniform in nature. Taking thepressure of gage at the outelequal to zero. The density of water is-1 1 kgl ..

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  • "Ans. First we derive the equation for the work done by the shaft in rotation, so needto consider the flow of water to the turbine is cyclic and uniform in nature. Taking thepressure of gage at the outelequal to zero. The density of water is-1 1 kgl .Compute the relation between linear and angular velocity,vr ? ?Here v is the linear velocity and r is the radius and?is takenas the angular velocity,Now, the relative velocity velocity of jet tobucket ,v?? v vr J bucket Now, for the control volume of Pelton wheel has the initial velocity is v and itsr component is taken as, v cos ? ,r Compute the equation for anguler momentum,?? M?? rmv rmv? ? ? outer inner The direction of moments in the anticlockwise are?? ve, andinclockwise are ve. Consider the angular momentumequationabout the axis of rotationis,?? ?M ?rmv cos ? ?rmvshaft r r Put the values of relative velocity in the above equation,?? M ?rmV (1 ? cos ?) ?rm(v ?r ?)(1 ? cos ?) Shaft r JNow, ? ? W?? 2?? nM M shaft shaft shaft ? m?? ? ? Here m is the mass flow rate,SO,Consider the power output of a pelton turbine,? W ? ? ?r ?(v ? ?r)(1 ? cos ?) shaft J Hence Proved. "

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