Fire Hydrants, pressure and velocity

[vaxop]

Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.020 m. Water enters the hydrant through an underground pipe of radius 0.080 m. In this pipe the water has a speed of 3.0 m/s. (a) How many kilograms of water are poured onto a fire in one hour? (b) Find the water speed in each hose.

Anyone know how to do this ?

I get a strange answer and I am pretty sure its wrong.. probably because I don't know how to factor in the >3< hoses :(

 

[Andrew Mason]

Three fire hoses are connected to a fire hydrant. Each hose has a radius of 0.020 m. Water enters the hydrant through an underground pipe of radius 0.080 m. In this pipe the water has a speed of 3.0 m/s. (a) How many kilograms of water are poured onto a fire in one hour? (b) Find the water speed in each hose.

Anyone know how to do this ?

Hint: you know that the volume of water coming into the hydrant has to be the volume of water leaving the hydrant.

Try Bernouilli's equation:

$$P_{hydrant} + \frac{1}{2}\rho v_{hydrant}^2 = P_{hose} + \frac{1}{2}\rho v_{hose}^2$$

and see what you get.

AM

 

[vincentchan]

?bernouilli's equation?

the rate of water flow = $\rho v A$
use this equation for your part a and b...

Try Bernouilli's equation:
and see what you get.

PS. if you try bernouilli's equation, you will get a mess.

 

[HallsofIvy]

As vincentchan implied, pressure is irrelevant. The volume of water exiting the hose, in one second, must be equal to the volume of water entering the hydrant, in one second. The weight of that water is just the volume times the density of water. The volume entering or exiting in one second is just the speed (in m/s) times the cross section area of the hose (in m²).

 

[Andrew Mason]

?bernouilli's equation?

the rate of water flow = $\rho v A$
use this equation for your part a and b...



PS. if you try bernouilli's equation, you will get a mess.

You get the hydrant pressure after you work out the velocity (which you get after taking my hint) - assuming it exits horizontally.

AM