) The intake to a hydraulic turbine (not drawn to scale) installed in a dam is located at an elevation of 10 m above the turbine exit. Water enters at 20 degrees C with negligible velocity and exits from the turbine at 10 m/s. The water passes through the turbine with no significant changes in temperature or pressure between the inlet and exit, and heat transfer is negligible. The acceleration of gravity is constant at g = 9.81 m/s2. If the power output at steady state is 500 kW, what is the mass flow rate of water in kg/s?

5.1 kg/s

Explanation:

From the question, the following parameters are given:

Velocity V = 10 m/s

Height h = 10 m

Acceleration due to gravity g = 9.8m/s^2

Power = 500 Kw

From definition of power,

Power = WD / time

Where WD = force × distance

Substitute all the parameters into the formula

500 = (F × 10)/ t

But F = mg

500 = (mg × 10)/t

Rearrange the formula

500 = m/t × 9.8 × 10

Where m/t is the mass flow rate of water in kg/s

500 = m/t × 98

m/t = 500/98

m/t = 5.102 kg/s

Therefore, the mass flow rate of water is 5.1 kg/s

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