4) [8 pts] Water in a channel drives a waterwheel, as shown in the figure. The w

Question

4) [8 pts] Water in a channel drives a waterwheel, as shown in the figure. The water enters at a speed of V1=8.5 m/s and exits at a speed of v,-3.4 m/s·The waterwheel has a radius of 4.3 m and the channel delivers 85 kg of water per second. a. b. c. At what rate does the water deliver angular momentum to the waterwheel? What torque does the water apply to the waterwheel? If the waterwheel makes one revolution each 5.3 s, what is the power delivered to the waterwheel? (Hint: think of power-F v and find and solve the rotational analogue of this equation). waterwheel water

Explanation / Answer

a) rate of delivery of angular momentum = loss in angular momentum of water per sec

rate of delivery of angular momentum = 85 * 4.3 * (8.5 - 3.4)

rate of delivery of angular momentum = 1864.1 Kg.m^2/s^2

b)

torque = rate of change of angular momentum

torque = 1864.1 N.m

c)

angular speed , w = 2pi/T

w = 2pi/5.3 rad/s

power delivered = Torque * w

power delivered = 2pi/5.3 * 1864.1

power delivered = 2210 W

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