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Bernoulli's Equation and fire hose

  1. Oct 6, 2009 #1
    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.
     
  2. jcsd
  3. Oct 6, 2009 #2
    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?
     
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