Question

A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.5 cm diameter hose delivering 450 L/min through a 0.80cm diameter nozzle?

Answer 1

The velocity will be increased as the inverse ratio of areas:

New velocity/oldvelocity=(7.5/.8)^2

The old velocity can be solved by

450L/min*1dm^3/L * 1min/60sec is flow in dm^3/sec, so divide that by area and you get linear flow.

acceleration=changevelocity/time so on a per second basis,
acceleartion=newvelocity-oldvelocity
=oldvelocity((7.5/.8)^2-1)

and then, Force=mass/second*acceleration
= density*450L/60sec*acceleratin

check my thinking.