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The water flowing through a 2.0 cm (inside diameter) pipe flows out through three 1.4 cm...


The water flowing through a 2.0 cm (inside diameter) pipe flows out through three 1.4 cm pipes. (a) If the flow rates in the three smaller pipes are 24, 15, and 11 L/min, what is the flow rate in the 2.0 cm pipe? (b) What is the ratio of the speed of water in the 2.0 cm pipe to that in the pipe carrying 24 L/min?

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Answer #1

Diameter of big pipe = d0 = 2 cm = 0.02 m

Diameters of the 3 small pipes = d = 1.4 cm = 0.014 m

Flow rate of water through first small pipe = Q1 = 24 L/min

Flow rate of water through second small pipe = Q2 = 15 L/min

Flow rate of water through third small pipe = Q3 = 11 L/min

Flow rate of water through big pipe = Q0

Q0 = Q1 + Q2 + Q3

Q0 = 24 + 15 + 11

Q0 = 50 L/min

Speed of water through the big pipe = V0

Speed of water through the first small pipe = V1

Q = AV

a) Flow rate in the 2 cm pipe = 50 L/min

b) Ratio of speed of water in the 2 cm pipe to that in the pipe carrying 24L/min = 1.021

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