Water drives a waterwheel (or turbine) of radius 3.3 m as shown in the figure. T

Question

Water drives a waterwheel (or turbine) of radius 3.3 m as shown in the figure. The water enters at a speed v1 = 7.2 m/s and exits from the waterwheel at a speed v2 = 4.0 m/s .

a)

If 84 kg of water passes through per second, what is the rate at which the water delivers angular momentum to the waterwheel?

Express your answer using two significant figures.

b)

What is the torque the water applies to the waterwheel?

Express your answer using two significant figures.

c)

If the water causes the waterwheel to make one revolution every 6.0 s , how much power is delivered to the wheel?

Express your answer using two significant figures.

Explanation / Answer

given that

R = 3.3 m

v1 = 7.2 m/s

v2 = 4 m/s

mass/s = 84 kg/s

(a)

we know that

rate of angular momentum L/s = (mass/s)*V*R

L/s = (m/s)*(v1-v2)*R

L/s = 84*(7.2-4)*3.3

L/s = 887.04 kg*m^2/s^2

(b)

torque T = 887.04 N*m   ( we noticed that units are same of L/s and torque)

(c)

we know that

power = T*w

where w = angular speed = 2*pi / t

w = 2*pi / 6s

power P = 887.04 * 2 * 3.14 / 6

P = 928.43 watts

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