Question

Niagara Falls is capable of producing a total power output of 2.575 MW at steady-state during the night when flow over the falls is diverted through a hydroelectric turbine. This is done at night so as not to detract from tourism during the daytime. Changes in temperature and pressure of the flow through the turbine are negligible. The intake to the turbine is located at the top of Niagara River and exits at the bottom of the falls, 22 m below. The velocity of the water in the penstock upstream of the turbine is, on average, 0.6 m/s and exits the turbine, operating adiabatically, at 0.9 m/s. - What is the mass flow rate of water through the turbine at night, in kg/s?

Answer 1

Step-by-step explanation:

This is the question based on First Law of Thermodynamics with Steady Flow Energy Equation for Turbine.

The total energy entering the turbine control volume is equal to the total energy leaving the turbine control volume.

The calculation is attached

Answer 2

m= 11953.67 kg/s

Step-by-step explanation:

Given : power output P = 2.575 MW

Head available H = 22 m

Inlet velocity V1 = 0.6 m/s

Outlet velocity V2 = 0.9 m/s

Solution:

Here the hydraulic energy available at the inlet of turbine is given by,

Eh= mgH

Where m is mass flow rate in kg/s

g is acceleration due to gravity

H is head available.

Part of this energy is converted in to electrical energy of 2575000 W and remaining is at outlet of Turbine in the form of kinetic energy i.e. (see attachment)

KE =\frac{mv^{2}}{2}

So we can write energy balance equation as, (see attachment)

mgH =\frac{mv^{2}}{2} + 2575000

m(gH -\frac{v^{2}}{2}) = 2575000

m(9.81*22 -\frac{0.9^{2}}{2}) = 2575000

m= 2575000/215.415

m= 11953.67 kg/s