What Is the Pressure Inside a Water Cannon Shooting at 25m/s?

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The discussion centers on calculating the pressure inside a water cannon that shoots water at 25 m/s. Using Bernoulli's principle, the user calculated the height required for this velocity to be approximately 31 meters, leading to a pressure of 303,800 Pa. However, the textbook answer is 4.125 x 10^5 Pa absolute, prompting questions about the inclusion of atmospheric pressure in the calculations. It was clarified that the discrepancy arises from not accounting for atmospheric pressure, which adds approximately 100,000 Pa to the calculated gauge pressure. The conversation emphasizes the importance of considering absolute pressure in fluid dynamics problems.
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Homework Statement



Water is coming out of a water cannon at 25m/s, what is the pressure inside the cannon?


Homework Equations


Bernoulli's (modifiedd): v = √(2gh) -> h = v^2/2g
Prssure(liquid) : P = ρgh


The Attempt at a Solution



Well, I wasn't too sure how a water cannon works, so I "made one" that is just a giant vat with a lot of water, and a hole at the bottom.

I figured that for the water to come out at 25m/s, the height would have to be ~31m.
h = (25^2)/2g

So then I said, Pressure must be equal to ρgh, which is 1000 * 9.8 * 31m = 303,800Pa

But the answer the book gives says its "4.125 x 10^5 Pa absolute."

Any idea why my solution is incorrect?
 
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Absolute pressure? Did You take into consideration atmospheric pressure?
 
Oh jeeze, I guess that would give me the ~100000 Pascals I need for the answer, thanks!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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