What is the maximum water speed from a compressed watergun?

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The discussion centers on calculating the maximum speed of water from a compressed water cannon when the air pressure is increased to four times atmospheric pressure. The user initially calculates the pressure as 405.2 kPa but is unsure how to proceed with the calculation. They apply Bernoulli's equation to relate pressure and velocity, ultimately isolating for the speed of the water. The conversation highlights the importance of correctly applying fluid dynamics principles to solve the problem. The user seeks confirmation on their method for determining the water's exit speed.
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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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