Question

The water flowing through a 2.1 cm (inside diameter) pipe flows out through three 1.2 cm pipes. (a) If the flow rates in the three smaller pipes are 26, 19, and 10 L/min, what is the flow rate in the 2.1 cm pipe? (b) What is the ratio of the speed of water in the 2.1 cm pipe to that in the pipe carrying 26 L/min?

Answer 1

a) using equation of continuity

water flow in 2.1 cm pipe = sum of water flow in smaller pipes

water flow in 2.1 cm pipe = 26 + 19 + 10

water flow in 2.1 cm pipe = 55 L/min

the water rate in 2.1 cm pipe is 55 L/min

b)

rate of speed of water

as flow rate = area * speed

speed = flow rate/area

Now, for the ratio speed of water in the 2.1 cm pipe to that in the pipe carrying 26 L/min

ratio = 55/26 * (pi * 1.2^2)/(pi * 2.1)^2

ratio = 0.22

the speed of water in the 2.1 cm pipe to that in the pipe carrying 26 L/min is 0.22