What is the maximum water speed from a compressed watergun?

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SUMMARY

The maximum speed of water from a compressed water cannon can be calculated using Bernoulli's equation. When the air above the water is compressed to four times atmospheric pressure (4Po), the equation simplifies to 4Po = Po + ρ(v2/2). By isolating for velocity (v), the correct formula for maximum water speed can be derived. The calculated pressure of 405.2 kPa is relevant, but proper application of Bernoulli's equation is essential for accurate results.

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  • Knowledge of fluid dynamics principles
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  • Basic algebra for isolating variables in equations
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Homework Statement


A child's water cannon consists of a water chamber that can be compressed by an air pump. If the air above the water in the chamber is compressed to 4 times atmospheric pressure, what is the maximum speed of water from the cannon when the trigger is released?
Ignore any height difference between top of water in the chamber and the opening of the barrel.


Homework Equations





The Attempt at a Solution


All i can figure is 405.2 kPa...but I'm not sure how to apply this without any other variables. Any help would be appreciated.
 
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Oh, I might have figured it out...

I used Bernouilli's equation... constant= P_o + rho (v^2+2gy/2)

so...
4P_o = P_o + rho (v^2+2gy/2)

then i isolated for v to get the speed... is this correct?
 

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