Question

6. Water flows through a 9,6-cm-diameter fire hose with a speed of 1.3 m/s. At the end of
the hose, the water flows out through a nozzle whose diameter is 2.5 cm. What is the
speed of water coming out of the nozzle?
A) 4.99cm/s
B) 0.339m/s
C) 0.088m/s
D) 19.2m/s
Can someone please answer this question

Answer 1

Answer:

D) 19.2 m/s

Explanation:

We can solve this problem by using the continuity equation: in fact, the flow rate a fluid through a pipe must remain constant.

Therefore, we can write:

$A_1 v_1 = A_2 v_2$

where

$A_1$ is the cross-sectional area of the 1st section of the pipe

$A_2$ is the cross-sectional area of the 2nd section of the pipe

$v_1$ is the velocity of the water in section 1

$v_2$ is the velocity of the water in section 2

For the pipe in the problem we have:

$d_1=9.6 cm = 0.096 m$ is the diameter of the hose, so the area is

$A_1=\pi (\frac{d_1}{2})^2$

$d_2=2.5 cm = 0.025 m$ is the diameter of the nozzle, so the area is

$A_2=\pi (\frac{d_2}{2})^2$

$v_1=1.3 m/s$ is the velocity of water in the hose

Solving the equation for v2, we find the speed of water in the nozzle:

$v_2=v_1\frac{A_1}{A_2}=v_1 \frac{d_1^2}{d_2^2}=(1.3)\frac{(0.096)^2}{(0.025)^2}=19.2 m/s$