Answer to Question #89514 in Mechanics | Relativity for Rein

Question

Water enters a round fire hose of diameter 3.5cm and exits from a round, 0.60cm diameter nozzle. If the water enters the house at 2.0 m/s, what is the velocity of the existing water?

Answer 1

By the definition of the Law of Continuity, we have:

$$A_1v_1 = A_2v_2,$$

here, $A_1 = \pi r_1^2$ is the cross-sectional area of the entry side of the hose, $A_2 = \pi r_2^2$ is the cross-sectional area of the exit side of the hose (or the nozzle), $r_1 = 0.0175 m$ is the radius of the entry side of the hose, $r_2 = 0.003 m$ is the radius of the exit side of the hose, $v_1$ is the velocity of the entering water, $v_2$ is the velocity of the existing water.

Then, from this formula we can find the velocity of the existing water:

$$v_2 = \dfrac{A_1 v_1}{A_2} = \dfrac{\pi r_1^2 v_1}{\pi r_2^2} = \dfrac{\pi( 0.0175 m)^2 \cdot 2.0 \dfrac{m}{s}}{\pi(0.003 m)^2} = 68 \dfrac{m}{s}.$$

Answer:

$v_2 = 68 \dfrac{m}{s}.$