Water moving through a fire hydrant with an internal cross-sectional area of about 20 sq. in. goes into a fire hose with a cross-sectional area of about 5 sq. in. Which of the following is the best estimate of the change in speed of the water?
A)The speed of the water in the hose is 0.25 times the speed of the water in the hydrant.
B)The speed of the water in the hose is 0.5 times the speed of the water in the hydrant.
C)The speed of the water in the hose is 2 times the speed of the water in the hydrant.
D)The speed of the water in the hose is 4 times the speed of the water in the hydrant.

Question

Quizplus · Accepted Answer

According to the principle of conservation of mass, the mass flow rate must be constant throughout the system. This means that the product of cross-sectional area and velocity must be constant. Therefore, if the cross-sectional area of the hose is 1/4th that of the hydrant (5 sq. in. vs. 20 sq. in.), the speed of the water in the hose must be 4 times the speed of the water in the hydrant to maintain the same mass flow rate.

Water Moving Through a Fire Hydrant with an Internal Cross-Sectional