Simple Pressure\Speed question

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In summary, the conversation discusses the calculation of pressure inside a water cannon based on the velocity of the water coming out. The solution involves using Bernoulli's equation and the formula for pressure in a liquid. However, the answer given in the book takes into account atmospheric pressure, which was not considered in the initial solution.
  • #1
ChickysPusss
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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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  • #2
Absolute pressure? Did You take into consideration atmospheric pressure?
 
  • #3
Oh jeeze, I guess that would give me the ~100000 Pascals I need for the answer, thanks!
 

What is pressure?

Pressure is the force exerted on an object per unit area. It is typically measured in units of Pascals (Pa) or pounds per square inch (psi).

What is the relationship between pressure and speed?

The relationship between pressure and speed is known as Bernoulli's principle. According to this principle, as the speed of a fluid (such as air or water) increases, the pressure exerted by that fluid decreases.

How does pressure affect the speed of an object?

In general, an increase in pressure will result in an increase in speed. This is because the higher pressure will push the object with a greater force, causing it to move faster.

How can pressure and speed be measured?

Pressure can be measured using a variety of instruments, such as a barometer or manometer. Speed can be measured using tools like a speedometer or radar gun. Both pressure and speed can also be calculated using mathematical equations.

What are some real-life examples of how pressure and speed are related?

One common example is the lift force generated by an airplane's wings. As the air moves faster over the curved shape of the wing, the pressure above the wing decreases, creating a pressure difference that results in lift. Another example is the use of high-pressure water jets to cut through materials, which is only effective at high speeds.

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