 Friends, I am Professor S.P. Mankani, Assistant Professor, Department of Mechanical Engineering, Vulture Institute of Technology, Solaapur. So today we are going to study numerical on Pelton turbine. At the end of this lecture, students will be able to solve numerical and design of Pelton turbine. So here, a Pelton wheel has a mean bucket speed of 10 meters per second with a jet of water flowing at the rate of 700 liters per second under a head of 30 meters. The bucket deflects the jet through an angle of 160 degree, calculate the power given by water to the runner and the hydraulic efficiency of the turbine. Assume coefficient of velocity as 0.98. Before going with actually the problems should understand the velocity diagram. So here in this particular problem, so as far as velocity diagram the inlet is going to be taken place here and here the V1 and Vw1 is equal and because of that V1 is given in the problem we can understand the Vw1 is V1 is equal to Vw1. So as we know the V1 value, so we can calculate the value of Vr1. We can calculate the value of Vr1 as V1 minus U1, we can get the Vr1. So as far as inlet triangle and outlet triangle is concerned, Vr1 is equal to Vr2. So as far as Pelton turbines are concerned. So here next to this one we supposed to be calculating Vw2. So as we required as a Vw1 and Vw2. So for getting these two values, so Vw1 we can get it from V1 and for Vw2 we are going to for the outlet velocity triangle. So here for calculating the Vw2 we are going to be referring the value of phi here. So as angle of deflection in the problem is given. So with the reference of this angle of deflection we can calculate this angle as a phi 180 degree minus this angle is given as a 160 degree in the problem. So this angle we can calculate as 180 degree minus 160 we can get the phi angle. By using this as a phi angle we can calculate Vw2. Vw2 we are going to be calculating as Vr2 cos phi minus U2 as U1 is equal to U2. So based on that one you can calculate the value of Vw2. So by knowing this Vw1 and Vw2 as well as V1 value and U1 is equal to U2 value. So based on this value also we can calculate. So by knowing these values so we can calculate the rest of the values. So as the Cv value is given as 0.98 so by using this value we can calculate the value of V1. V1 is equal to Cv under root of 2gs. So this value phi you have calculated. So V1 you can calculate based on this equation as Cv under root of 2gs. Cv is given in the problem as 0.98. So based on this value we can calculate Vr1. So Vr1 is this value as we have discussed in the previous diagram. So this is Vr1 this value as a Vr1. So this one we can calculate Vr1 is equal to V1 minus U1 that is V1 minus U1 that you are going to be calculating the value of Vr1. So as V1 is equal to Vw1 that value we can get it this as already V1 is calculated here. So based on that one you can get the value of Vw1 because Vw1 and Vw2 required for the calculation of hydraulic efficiency is considered. So from outlet triangle so this part we are going to be as a outlet triangle. So based on the outlet triangle we are going to be calculating as the value of Vw2. So Vr2 and Vr1 both the values are equal as far as the Pelton turbines are considered. So Vr2 is equal to Vr1 as Vr1 already calculated the value as 13.77 we can carry the same value. So Vw2 is equal to Vr2 cos phi minus this U2 value. So that you can get the value of this Vw2. So by knowing these two values work done by the jet per second on the runner is given as rho Q into bracket Vw1 plus Vw2 bracket complete that is U value. So this value we can calculate as a work done. So this value are going to be getting it as a work done. Here it is in terms of watts. So divided by 1000 we are going to get this as a kilo watts the value as kilo watts. So this value as a kilo watts. So now we are going with the hydraulic efficiency of the turbine is given by nu H is equal to 2 into bracket Vw1 plus Vw2 divided by V1 square into U value. So Vw1 we have calculated as it is V1 is equal to Vw2 V1 is equal to Vw1 and Vw2 just now we have calculated the values Vw2 here Vr2 cos phi. So then U value already you know that is a U is equal to U1 is equal to 10 meter per second is given in the problem okay. So based on that one we are going to be calculating as a hydraulic efficiency. So once you know this hydraulic efficiency you can go for a further all values are related with this particular problems are considered. So in continuation with this one problem we are going with the next one as how to design the Pelton turbine how to design the Pelton turbine. A Pelton wheel is to be designed for the following specification. So they are given as a this specification as shaft power shaft power is the power available at the shaft power is from the shaft we are going to be getting this as a shaft power 11772 kilo watts. So head is nothing but the water whatever the water is going to be hitting so this particular we are going to be considering it as a head from the total head of the level you are going to take it as the head. So this is given as 380 meters the speed is given as a 750 rpm this is a given condition as far as 750 rpm. So your overall efficiency new O value this value is nothing but a new overall efficiency 86 percentage. The jet diameter is not to exceed one sixth of the wheel diameter. So wheel diameter and jet diameter the comparison they are given as a one sixth. So you should not exceed as a one sixth this is nothing but a D upon capital D. So this value is given as a one upon six. So based on that one the shaft power is given as a 11772 kilo watts and head is given as h is equal to 380 meters kv1. So this value is nothing but a cv and kv1 is given in the problem as this is 0.45 that is a speed ratio and this value is given as a coefficient of velocity coefficient of velocity. So this value is given in this one. So based on these two values we are going to be calculating as the value of v1 v1 is cv under root of 2gh. So once you know the value of cv1 you can go for the further values as v1 is equal to vw1 you can apply the once again the same formula as v1 is equal to vw1 then vw if you know it so then you can calculate the value of vr1. Okay same equation you are going to be in the further step u is equal to u1 is equal to u2 that is the speed ratio already given in the problem as 0.45 head is given in the problem as then this is 380 meters and g is 9.81. So by substituting these values we are going to be getting it as a 38.85 meter per second this value are going to be getting as a value of u. So u is nothing but pi dn by 60, pi dn by 60 so based on this one so d is a diameter and this is n we are going to be given as a speed they are given as a n is speed and this is the value of u is already calculated here u is equal to u1 is equal to u2 divided by 60. So the extension is to get the diameter because diameter is required as a here d upon d is equal to 1 upon 6 they are given so based on that one you can calculate the value of d here. So d upon d is equal to 1 upon 6 we are going to be using and based on this u is equal to pi dn we are going to be calculating it as a d is equal to 0.8989 meter. So now we are going with the d upon d is equal to 1 upon 6 and d already you know the value of d is here so by using these two values we are going to calculate the value of diameter of the jet this is a small d is a diameter of the jet. So here by d is equal to 1 upon 6 capital D capital D already just now you are calculated by using this small d as a value we can calculate the discharge of 1 jet discharge of 1 jet q is equal to area of the jet multiplied by velocity of the jet. So based on this one you can calculate the q as a discharge of 1 jet so by knowing this discharge of 1 jet so here pi by 4 d square into v1 velocity of jet so you are going to be getting this as a value as 1.1818 meter cube per second. So by knowing this value you can calculate the overall efficiency so this value is given in the problem this value is given in the problem and sharp power already are calculated and rho g qh divided by 1000. So here on this basis we are going to be calculating the value of q so value of q you are going to be calculating it. By calculating the value of q you are going to be already calculated the value of jet from the single jet as a small q and this is a capital q. So ratio of this one we are going to be taken as a capital q divided by small q so that gives the number of jets so capital q divided by small q so this approximately you are going to be getting it as a 2 jets even if it is coming as a fraction we are going to be taking this as a next number as a 2 jets. So now just one small question as what is hydraulic efficiency of a designed pelton wheel? Here hydraulic efficiency is equal to 2 into bracket vw1 plus vw2 divided by v1 square and u so the hydraulic efficiency so this you can calculate it. So here approximately it has to come as around more than 90 percentage then you can consider that whatever the design you have made it so that design you are going to be considering it as a correct otherwise you go for a some correction factors related to the given values. So you can go for a further details fluid mechanics and fluid machinery by R.K. Bansal you will get a further details in this particular book for just for it is a reference purpose. Thank you.