Simple Fluid Flow

  • #1
3,003
3
Doing some review here:

Homework Statement



A fire hose has an inner diameter of 5 inches and water is flowing at 600 gal/min. The flow exits through a nozzle contraction with
diameter dn. For steady flow, what should dn be in inches in order for the exit velocity to be 25 m/s.

My only question here is really do I even need the given inlet diameter = 5 in ?

As far as I can see. Since density is constant, the volume flow rates at inlet and exit should be equal. That is,

[tex]Q_1=Q_2[/tex]

[tex]\Rightarrow Q_1 = \frac{500\,\text{gal}}{\text{min}} = A_2V_2[/tex]

[tex](\frac{\pi}{4}d_n^2)V_2=\frac{500\,\text{gal}}{\text{min}}[/tex]

Now assuming I convert my units properly, this should be correct? It's just that given inlet diameter that's bugging me.

Thanks.
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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Can you convert gal/min to A*V?
 
  • #3
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Can you convert gal/min to A*V?

I would have to say yes.

[tex]\frac{gal}{min}\equiv\frac{Volume}{time}[/tex]

[tex]Area*V\equiv\frac{dx}{dt}*A\equiv\frac{Volume}{time}[/tex]
 
  • #4
rl.bhat
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Inner diameter is given. Find the velocity of inflow. Velocity of the outflow is given. Find dn
 
  • #5
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I am sorry rl, I still do not see what I am supposed to use the inner diameter for. I thought that we just said.

Q1=Q2=A2V2

I am given Q1, why should I bother finding V1?
 
  • #6
rl.bhat
Homework Helper
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Yes. You are right.
 
  • #7
3,003
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Okay. Thank you. :smile:
 

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