Bernoulli's Equation and fire hose

[ChemIsHard]

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 and shoots out of a round nozzle.

i) What is the maximum diameter this nozzle can have?

ii) If the only nozzle available has a diameter twice as great, what is the highest point the water can reach?

I know that Flow rate=0.500 m3/s=A*V. I know the pressure needed to obtain this height from P=35*9.8*1000=3.43X10^5 Pa.

I know I should be applying Bernoulli's equation but I'm stuck. Any pointers are appreciated.

 

[ChemIsHard]

I just had an idea.

P+1/2PV^2+Pgh=pgh+1/2pv^2+P

We can cross out both p's since they're both exposed to atmosphere. The first equation has no potential while the second has no kinetic.

1/2pv^2=pgh

v=root(2g(35m))
v=26.2 m/s

0.5=26.2*Pi(r^2)

Calculate for r then times by two for maximum diameter. Then just recalculate using the previous equation with 2r.

Looks good?