Question

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?

Answer #1

Diameter of big pipe = d_{0} = 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 = Q_{1} = 24
L/min

Flow rate of water through second small pipe = Q_{2} =
15 L/min

Flow rate of water through third small pipe = Q_{3} = 11
L/min

Flow rate of water through big pipe = Q_{0}

Q_{0} = Q_{1} + Q_{2} +
Q_{3}

Q_{0} = 24 + 15 + 11

Q_{0} = 50 L/min

Speed of water through the big pipe = V_{0}

Speed of water through the first small pipe = V_{1}

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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