Pressure change from one box to another

[heepofajeep]

Homework Statement

A .25L box at 1PSI is inserted into a 1L box at 5psi.
The .25L box has a leak.
The pressure of the 1L box at t=2sec. is 4.8psi

A) How long will it take for the Pressure in Box 1 to equal the pressure in Box 2.
B) What is the size of the leak in Box 2?

Homework Equations

PV=nRT
1/2*density*velocity^2 + P1 = P2 [Bernoulli]
P = Po e^-Ct [generic Pressure Decay] ?

The Attempt at a Solution

Stuck in a rut... >=(.

Note: this is not actually a true homework problem. In fact, it is a real-world problem for leak testing a product.

 

[jbsteele]

I am trying to find a general equation and/or solution to this problem, but I'm not sure how to approach it.

 

[kerimek]

To answer this question, we need to consider the principles of gas laws and fluid dynamics. According to the ideal gas law, PV=nRT, the pressure of a gas is directly proportional to its volume. In this case, the volume of the 1L box is 4 times larger than the .25L box, so we can assume that the pressure in the 1L box will also be 4 times higher.

However, we also need to consider the fact that the .25L box has a leak. This means that the pressure inside the box will decrease over time, following a generic pressure decay equation P = Po e^-Ct. We can use this equation to calculate the pressure in the .25L box at any given time.

For Part A, to find the time it will take for the pressure in Box 1 to equal the pressure in Box 2, we can set up an equation using the ideal gas law for both boxes:

P1V1 = nRT1
P2V2 = nRT2

Where P1 is the pressure in the .25L box, V1 is the volume of the .25L box, P2 is the pressure in the 1L box, V2 is the volume of the 1L box, n is the number of moles of gas, R is the gas constant, and T1 and T2 are the temperatures in the .25L and 1L boxes respectively.

Since we know that P1 decreases over time due to the leak, we can substitute P1 with the generic pressure decay equation: P = Po e^-Ct. This gives us:

Po e^-Ct * V1 = nRT1
P2V2 = nRT2

By setting these two equations equal to each other, we can solve for t, the time it takes for the pressure in Box 1 to equal the pressure in Box 2.

For Part B, we can use Bernoulli's equation, 1/2*density*velocity^2 + P1 = P2, to calculate the velocity of the gas escaping from the leak in Box 2. From there, we can use the equation for volumetric flow rate, Q = A * v, where A is the area of the leak and v is the velocity of the gas, to calculate the size of the leak in Box 2.

In conclusion, solving this problem requires a