The spout heights in the container in the figure (Figure 1) are 16 cm , 32 cm ,

Question

The spout heights in the container in the figure (Figure 1) are 16 cm , 32 cm , 48 cm , and 64 cm . The water level is maintained at a 72-cm height by an outside supply.   

Part A

What is the speed of the water out of the 16-cm high hole?

Part B

What is the speed of the water out of the 32-cm high hole?

Express your answer using two significant figures.   

Part C

What is the speed of the water out of the 48-cm high hole?

Express your answer using two significant figures.

Part D

What is the speed of the water out of the 64-cm high hole?

Express your answer using two significant figures.

Explanation / Answer

Are the heights from the bottom or from the top?. I'm assuming they are from the bottom.

From Bernoulli's eqn we know that gh + 1/2v^2 = constant Note we can divide from both sides leaving gh + v^2/2 = constant

So gh + v^2/2)top = gh + v^2/2)at the various heights...but vtop= 0 and h at the various height = 0

So gh = v^2/2...So v = sqrt(2gh) [note h is the distance from the top to the listed height]

Part A

16cm hole v = sqrt(2*g*h) = sqrt(2*9.8*(0.72-0.16)) = 3.313 m/s ............Ans.

Part B

32cm hole v = sqrt(2*g*h) = sqrt(2*9.8*(0.72-0.32)) = 2.8 m/s .................Ans.
Part C
48 cm v = sqrt(2*g*h) = sqrt(2*9.8*(0.72-0.48)) = 2.168 m/s ........................Ans.
Part D
64cm v = sqrt(2*g*h) = sqrt(2*9.8*(0.72-0.64)) = 1.252 m/s..................Ans.

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