Water is flowing through a rectangular channel that is 12 m wide with a speed of 0.75 m/s. The water then flows into four identical rectangular channels that have a width of 3.0 m. The depth of the water does not change as it flows into the four channels. What is the speed of the water in one of the smaller channels?
A)0.56 m/s
B)2.3 m/s
C)0.25 m/s
D)0.75 m/s
E)3.0 m/s

Question

Water is flowing through a rectangular channel that is 12 m wide with a speed of 0.75 m/s. The water then flows into four identical rectangular channels that have a width of 3.0 m. The depth of the water does not change as it flows into the four channels. What is the speed of the water in one of the smaller channels? 
A)0.56 m/s 
B)2.3 m/s 
C)0.25 m/s 
D)0.75 m/s 
E)3.0 m/s

Quizplus · Accepted Answer

The volume of water flowing through the larger channel per unit time must equal the sum of the volumes of water flowing through each of the four smaller channels. Since the depth of water remains the same in all channels, we can use the formula Q = Av, where Q is the volume of water flowing per unit time, A is the cross-sectional area of the channel, and v is the speed of the water.

For the larger channel: 
Q = Av 
Q = (12 m)(1 m)(0.75 m/s) 
Q = 9 m^3/s

For each of the smaller channels: 
Q = Av 
9 m^3/s = (3 m)(1 m)v 
v = 3 m/s

Therefore, the speed of the water in one of the smaller channels is 0.75 m/s. The correct answer is D.

Water Is Flowing Through a Rectangular Channel That Is 12