Question Solved1 Answer Problem (Francis) A 75 mm free water jet moving with a velocity of 25 m/s strikes a single vane moving in the same direction as the jet with a velocity of 12 m/s. The friction losses cause the relative velocity at exit to be 92 % of the relative velocity at the inlet. The relative velocity at the exit has a total deflection angle of 165° with respect to the relative velocity at inlet. (a) calculate the force exerted by the jet on the vane. (b) if the vane forms a part of a series of such vanes, calculate (i) the power extracted out of the je, and (ii) power lost in friction.

K64ALA The Asker · Mechanical Engineering

Transcribed Image Text: Problem (Francis) A 75 mm free water jet moving with a velocity of 25 m/s strikes a single vane moving in the same direction as the jet with a velocity of 12 m/s. The friction losses cause the relative velocity at exit to be 92 % of the relative velocity at the inlet. The relative velocity at the exit has a total deflection angle of 165° with respect to the relative velocity at inlet. (a) calculate the force exerted by the jet on the vane. (b) if the vane forms a part of a series of such vanes, calculate (i) the power extracted out of the je, and (ii) power lost in friction.
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Transcribed Image Text: Problem (Francis) A 75 mm free water jet moving with a velocity of 25 m/s strikes a single vane moving in the same direction as the jet with a velocity of 12 m/s. The friction losses cause the relative velocity at exit to be 92 % of the relative velocity at the inlet. The relative velocity at the exit has a total deflection angle of 165° with respect to the relative velocity at inlet. (a) calculate the force exerted by the jet on the vane. (b) if the vane forms a part of a series of such vanes, calculate (i) the power extracted out of the je, and (ii) power lost in friction.
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rarr Given data,P. no. -1{:[d=75mm],[v_(1)=25m//s],[u_(1)=u_(2)=12m//s],[v_(r_(l))=0.92Vr","quad(V_(r)=:}" relative velocit-y) "],[theta=165^(@)],[F_("jet ")=?","P_("jet ")=?","Delta P=?]:}rarr Draw the velocily dia of francis furbine.rarr from diagram{:[V_(1)=V_(omega_(1))=25m//s],[V_(r_(1))=V_(1)-u_(1)=13m//s],[V_(r_(2))=0.92V_(r_(1))=11.96m//s],[V_(r_(2))cos phi=u_(2)+v_(omega_(2))]:}{:[11.96 cos phi=12+V_(omega_(2))],[V_(omega_(2))=-0.45*m//s],[=>PART-A]:}rarr force exerted by jet on vane{:[F=m^(˙)(v_(w_(1))+v_(w_(2)))],[=rho av_(2)","(v_(w_(1))+v_(w_(2)))],[=1000 xx(pi)/(4)(0.073)^(2)xx13(25-0.45)],[F=1409.96N],[F=1.41kN]:}#) PART-Bi) if vane forms a part of series. then Pjet =?{:[F=m^(˙)(V ... See the full answer