Force due to pressure on barrel lid

[rubenhero]

Homework Statement

In the seventeenth century, Blaise Pacal performed the following experiment to demonstrate the properties of pressure. A very long, thin, vertical tube was inserted into the center of the top lid of a wine barrel filled with water. Water was then added slowly to the tube until the wine barrel burst. (See figure 13-50 on page 363 of your textbook, but ignore the numbers)

Suppose the radius of the wine barrel lid has radius rl = 21.8 cm, the radius of the tube was rt = 2.67 mm, and the height of the water in the tube was h = 14.5 m. Find:

a) F, the magnitude of the force exerted on the inside of the barrel lid due to water pressure

Homework Equations

P = F/A , AP = F = ρgh∏r²

The Attempt at a Solution

F = 1000kg/m³ * 9.81m/s² * 14.5m * ∏ * (.218m)²
F = 21237.32775 N

The answer turned out wrong but i can't figure out what is wrong.

 

[dynamicsolo]

Isn't the applied pressure coming from the tube? This would then be the pressure distributed to the inside of the barrel lid.

 

[rubenhero]

i took the pressure from the tube then multiplied it by the area of the lid, isn't that right?

 

[dynamicsolo]

Disregard my first remark: I was thinking of the force value. I don't see anything obviously wrong. Are your numbers radii, and not diameters? What do you mean by saying, "The answer turned out wrong." Is there a given answer?

 

[rubenhero]

my professor uses webassign.com to give us assignments online. The answer i plugged into the website turned out to be wrong and i only have one chance left to enter the correct answer. I did ask my professor, he would only say that i did the pressure formula wrong. I used the radius numbers given but converted them to meters before plugging them into the formula.

 

[dynamicsolo]

The only thing I can think of that the problem might be looking for is that the pressure from the tube should be the sum of the hydrostatic pressure from the water, \rho gh, plus the atmospheric pressure of 101,300 N/m² (which is the "hydrostatic pressure" of the air), and that this times the area of the barrel lid gives the force acting on the inside of the lid.

Is one of the other parts, by any chance, asking for the force on the outside of the lid due to atmospheric pressure? The net force on the lid would then be the value you found, which would be an upward force on the lid of \rho gh \cdot \pi \cdot r_{l}^{2}.

Have I mentioned how much I detest WebAssign?

 

[rubenhero]

The other part of the question (part b) asked for the mass of the water inside the tube. I just emailed my professor and he said that the problem is open to air, I'm guessing the air is through the tube since the barrel is full of water. The other physics section in my college uses masteringphysics.com, but the professor i am taking only uses webassign.

 

[dynamicsolo]

I don't think the air is going through the tube if the tube has 14.5 meters of water in it. I think he is saying that atmospheric pressure is being applied to the top of the water in the tube. So the total pressure applied at the mouth of the tube at the point where it meets the water in the barrel is \rho gh + 101,300 N/m² , the sum of the water's hydrostatic pressure and the atmospheric pressure.

 

[rubenhero]

Thank you, it worked. I added air pressure to the formula and i got 36361.52404 N. I am glad this worked out since it was my last try for this question on webassign. I want to also thank you for your patience in helping me understand this problem.

 

[dynamicsolo]

You're welcome! And I quite understand your frustration with WebAssign. I work with students here who also have to wrestle with physics on that system...