Max Nozzle Size to Reach 35m: Solving the Fire-Hose Puzzle

[EzaMoo]

Homework Statement

A fire-hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m³.s¯¹ and shoots out of a round nozzle.

(a) What is the maximum diameter that this nozzle can have?

(b) If the only nozzle available is twice as great, what is the highest point that the water can reach?

Homework Equations

flow rate = pir^2 x h/1

The Attempt at a Solution

(a) 0.5 = pi r^2 x 35 / 1
r = 0.067m

(b) 0.5 = pi x 0.134^2 x h/1
h = 8.86m

Can someone please check I am doing this correctly. Thanks!

 

[rock.freak667]

Homework Statement

A fire-hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m³.s¯¹ and shoots out of a round nozzle.

(a) What is the maximum diameter that this nozzle can have?

(b) If the only nozzle available is twice as great, what is the highest point that the water can reach?

https://www.physicsforums.com/showthread.php?p=2731200#post2731200"

Homework Equations

flow rate = pir^2 x h/1

If your volume is V=πr²h and you divide throughout by time t to get flow rate Q

you will get Q=πr²(h/t)

h/t is distance per unit time which is velocity.

so you have Q=πr²v

you need to get v from the fact that the height the water must reach is 35m.

 

[EzaMoo]

Thanks Rock freak... did this too quick without thinking much! All good now.