 Hello friends, my name is Saurabh Deshmukh. I am working as an assistant professor in department of mechanical engineering, Vulture Institute of Technology, Solapur. In this video, we are going to solve a problem on Pelton wheel turbine. The learning outcome. At the end of this session, the learner will be able to solve problem on Pelton wheel turbine. I will read the problem statement here. A Pelton wheel has a mean bucket speed of 10 m per second with a jet of water flowing at the rate of 700 liters per second under the head of 30 meters. The buckets deflect the jet through an angle of 160 degrees. Calculate the power given by water to the runner and the hydraulic efficiency of the turbine. Assume coefficient of viscosity as 0.98. So, first of all we will write the given data here. Now, they have given the speed of the bucket that is equals to u equals to it is also u1 equals to u2 is equals to 10 meter per second. And that bucket is heat by a jet of water flowing at the rate of 700 liters. So, the q is given here, q equals to 700 liter per second which is equals to 0.7 meter cube per second. Now, they have also given that the bucket deflects the jet through an angle of 160 degrees. So, it will be theta equals to 160 degrees. So, we will calculate phi from it, phi equals to 180 degree minus 160 degree equals to 20 degree. Also, now they have also given the coefficient of velocity. So, it is denoted by Cv equals to 0.98 and they have also given the head which is h equals to 30 meter. So, we need to calculate the power given by the water to the runner and the hydraulic efficiency of the turbine. So, first of all we will write the formulas here. So, it is power given by water to runner equals to it is rho a v1 into vw1 plus vw2 into u. And the hydraulic efficiency it is given by 2 into vw1 plus vw2 into u by v1 square. So, I will just draw a diagram here. So, what will strike here? So, this will be the point. This one will be u1, this one will be vr1 and this total velocity will be v1 or we will calculate we will consider it as a vw1 with no loss. So, now we will just this water will be deflected by 160 degree. So, we will just draw it here, this is beta, this is phi and this will be 160 degrees. So, this will be vr2, this will be v2, this will be vf2 and this will be u2 and this component will be vw2. So, first of all we need to calculate here v1 vw1 vw2. So, we need to calculate these values here. So, I will just write the formula for cv that is coefficient of velocity. So, what is the coefficient of velocity? It is cv equals to v1 by square root of 2gh. So, what will be v1 here? v1 equals to cv into square root of 2gh which is equals to 0.98 multiplied by 2 into 9.81 multiplied by 30. So, if you substitute these values in the calculator we will get the solution the value 23.77 meter per second. So, I will just change the phase here. So, now we will calculate vw1. So, we are considering v1 as vw1 with no loss. So, vw1 equals to v1 equals to we have calculated here v1 23.77. So, it will be 23.77 meter per second. Now, we will calculate vw2. So, we just need this diagram here. So, vw2 equals to what it will be? So, vw2. So, this component we need to calculate. So, it will be vR2 cos phi minus u2. So, let us consider vR2 equals to vR1. So, what will be vR1 here? vR1 equals to so, vR1 equals to it will be v1 minus u1. So, it will be 23.77 minus 10 equals to 13.77 meter per second. So, vR2 equals to vR1 equals to 13.77 meter per second. So, now we can calculate the vw2. So, vw2 equals to we will substitute the values of vR2 phi and u2. So, it will be 13.77 into cos it is 20 minus u2 is 10. So, by calculating in the calcium we will get the value 2.94 meter per second. Now, we will substitute all this given data into the formulae. So, power given by the water power given by the water to runner equals to rho A v1 into bracket vw1 plus vw2 into u. So, A into v1 is nothing but the area multiplied by velocity. So, it is water. So, the density of water will be 1000 multiplied by the discharge is 0.7 into vw1 is 23.77 plus vw2 is 2.94 multiplied by v1 or sorry u it is 10. So, after calculating this in the calcium we will get the answer here 19 sorry it is 186.970 Watt or it is 186.97 kilo Watt. So, for hydraulic efficiency the formulae is 2 into bracket vw1 plus vw2 into u by v1 square. So, we will substitute the values of all these entities. So, it will be 2 into 23.77 plus 2.94 into 10 upon v1 square it is 23.77 square. So, after calculating all this in the calcium we will get it as 0.9454 equals to 94.54 percent. So, the power of the turbine is 186.97 kilo Watt and the efficiency hydraulic efficiency of the turbine will be 94.54 percentage. These are the references. Thank you.