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

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:

where

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

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

is the velocity of the water in section 1

is the velocity of the water in section 2

For the pipe in the problem we have:

is the diameter of the hose, so the area is

is the diameter of the nozzle, so the area is

is the velocity of water in the hose

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

learn it on the intertant so you can solve

see earlier answer