How Is the Average Force on Water by a Turbine Blade Calculated?

[copitlory8]

Homework Statement

A stream of water strikes a stationary turbine blade, as the drawing illustrates. The incident water stream has a velocity of +18.0 m/s, while the exiting water stream has a velocity of -18.0 m/s. The mass of water per second that strikes the blade is 75.0 kg/s. Find the magnitude of the average force exerted on the water by the blade.

Homework Equations

kinematics equations
(PEf - PE0)

The Attempt at a Solution

i have no idea where to start

 

[ehild]

Think of impulse and change of momentum.

ehild

 

[kerimek]

, can someone help me

To calculate the average force exerted on the water by the blade, we can use the formula F = Δp/Δt, where F is the force, Δp is the change in momentum, and Δt is the change in time. We can also use the equation F = ma, where m is the mass of the water and a is the acceleration.

First, we need to calculate the change in momentum of the water. This can be done by using the formula Δp = mvf - mvi, where m is the mass of the water, vf is the final velocity, and vi is the initial velocity.

Δp = (75.0 kg/s)(-18.0 m/s) - (75.0 kg/s)(18.0 m/s)
Δp = -2700 kg*m/s

Next, we need to calculate the change in time. This can be done by dividing the distance traveled by the water (the length of the turbine blade) by the velocity of the water.

Δt = (length of blade) / (velocity of water)
Δt = (length of blade) / (18.0 m/s)

Now, we can plug these values into the formula F = Δp/Δt to calculate the average force exerted on the water by the blade.

F = (-2700 kg*m/s) / ((length of blade) / (18.0 m/s))
F = (-2700 kg*m/s) * (18.0 m/s) / (length of blade)
F = -48,600 N / (length of blade)

Therefore, the magnitude of the average force exerted on the water by the blade is -48,600 N divided by the length of the blade. This value will vary depending on the length of the blade.