Water flows from a reservoir at the rate of 3000 kg / min, to a turbine 120 m below. If the ef

First, we need to calculate the potential energy of the water per minute. The formula for potent

Water flows from a reservoir at the rate of 3000 kg / min,...

Water flows from a reservoir at the rate of $3000 \mathrm{~kg} / \mathrm{min}$, to a turbine $120 \mathrm{~m}$ below. If the efficiency of the turbine is 80 percent, compute the power output of the turbine. Neglect friction in the pipe and the small KE of the water leaving the turbine. Don't forget that it's only 80 percent efficient.

Transcript

00:01 Hi there, so for this problem we are told that water flows from a reservoir at a rate that is given, and that rate is 3 ,000 kilograms per minute, to a turbine that is 120 meters below.

00:27 Now if the efficiency of the turbine is given and that efficiency is 80%, which is the same as 0 .8, we need to compute the power output of the turbine.

00:44 We are also told that nellet the friction in the pipe and the small kinetic energy of the water leaving the turbine.

00:53 So with that said, we know that the power is the word done every second and can be obtained by the work divided by the time.

01:09 So the work itself is a change in energy.

01:14 That occurs in objects.

01:17 So the work is going to be the change in the kinetic energy or also the change in the potential energy.

01:29 Now in this case we know that the change in the potential energy is equal to the mass times acceleration due to gravity times the difference in the heights 2 and 1.

01:42 Something similar for the change in the kinetic energy that is 1 divided by 2 times the mass, times the speed at the point 2 to the square minus the speed of the point 1 to the square.

01:56 Now in this case for this problem we are told that the water floats from a reservoir at a rate of 3 ,000 kilograms per minute to a turbine of 120 meters below and also an efficiency of 80%.

02:15 Then we are going to call this simply as m.

02:22 The flow, the mass flow rate is 3 ,000 kilograms per minute.

02:31 We can also transform this into kilograms per second by just knowing that one minute corresponds to 60 seconds.

02:41 So from this we obtain 50 kilograms per second.

02:50 And a height that we're gonna call age that is equal to 120 meters.

02:56 Now, the potential energy for, from water will be converted as an input energy for the turbine.

03:04 So the input power of the turbine, the input power, we're going to call this p -end, is equal to the change in the potential energy divided by the time.

03:16 So that will be the mass times the acceleration due to gravity, and this times the height, which is the difference in the height, and this divided by the time...

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