When I pressurize a box whats the total force.?

Question

If I have an Aluminum box that is 24" X 20" X 4" deep and I add 80 PSI into the box is the total Pounds of force

20 X 24 X 80?

or

38400?

Answer 1

BS alert*

The total force on the box is zero. Note that force is a vector, and that any set of forces that totaled to a nonzero value would cause the box to accelerate in some direction. In this case, the force on any one side of the box due to internal pressure is equal in magnitude, but opposite in direction, to the force on the opposite side. The forces therefore cancel out (add to zero), so the box just sits there.

In order to create a nonzero force on the box using internal air pressure P, one could drill a hole in one side of area A. This would reduce the force on that side by P*A, throwing the net force off balance and causing the box to accelerate in the opposite direction. Of course, this would cause the air to leak out quickly, so the force would only be applied for a short time. Such a device is called a rocket.

Now, if the asker actually wanted to know what the force is on *one* side or something like that, he asked the wrong question. If that's the case, don't blame me for giving the correct answer to the wrong question; learn something from it, dummy-thumby-downers.

* A BS alert is issued when the majority of other respondents are giving answers which are wrong or, worse yet, not even wrong.

Answer 2

Yes!

The total force on one of its 24" X 20"  sides is

indeed 38400 lb at 80 PSI

Answer 3

Use dimensional analysis

Calculate the area of a side, eg, 24 x 20 = 480 square inches

480 square inches x 80 pounds per sq in = 38400 lbs.

Other walls have corresponding forces on them, some of them canceling.

Total force on all of the walls is the surface area x 80 psi

SA = 2*20*24 + 2*20*4 + 2*24*4 = 76800 + 160 + 192 = 77152 in²

total force is 77152 in² x 80 psi = 4630000 lbs

This is the force that tends to make the box explode. And if the material is weak enough it will.

.

Answer 4

There are actually three different forces that can be calculated in this problem, each force being dependent on what surface area is being considered.

By definition,

Force = Pressure * Area

and since the box has three surfaces with different areas, namely,

Area 1 = 24 x 20 = 480 in^2

Area 2 = 24 x 4 = 96 in ^2

Area 3 = 20 * 4 = 80 in^2

then, the forces on the box are the following:

Force 1 = 80*480 = 38,400 pounds

Force 2 = 80 * 96 = 7680 pounds

Force 3 = 80 * 80 = 6400 pounds