Maintaining constant air pressure in leaky container

[airpressure]

How can I calculate the air-supply flow (q=cfm) needed to maintain, say, p=50 psi of pressure in a (quasi-rigid) cylinder with a Volume of V=30,000 cft, when this cylinder has an open gap (leak) 50 ft long (L=50 ft) and 1/8 inch wide (w=1/8 inch)?

Is there a simple formula I can use to compute the necessary capacity of an air compressor (needed for supplying the air flow) as a function of the parameters given above
[q=f(p,V,L,w)] ?

 

[russ_watters]

Use Bernoulli's equation to figure out the airflow through the gap with 50 psi of backpressure. Then divide by 2 to figure in a 50% nozzle efficiency. You'll find it to be an enormous amount of air.

 

[astrokreng]

To calculate the air-supply flow needed to maintain a constant air pressure of 50 psi in a leaky container, you can use the following formula: q = (pA)/t, where q is the air-supply flow in cubic feet per minute (cfm), p is the pressure in pounds per square inch (psi), A is the area of the gap (L x w) in square inches, and t is the time in minutes.

In this case, A = 50 ft x (1/8 inch) = 6.25 square inches. We can assume that the air pressure will be maintained for a relatively long time, so we can use a value of t = 60 minutes.

Substituting these values into the formula, we get: q = (50 psi x 6.25 in^2)/60 min = 5.21 cfm.

This means that the air compressor needs to have a capacity of at least 5.21 cfm in order to maintain a constant air pressure of 50 psi in the given container.

To calculate the necessary capacity of the air compressor as a function of the given parameters, we can rearrange the formula to solve for p: p = (qt)/A.

Substituting the values given in the problem, we get: p = (5.21 cfm x 60 min)/6.25 in^2 = 50 psi.

Therefore, the formula for calculating the necessary capacity of the air compressor is: q = (50 pA)/t. This formula can be used to determine the required air-supply flow for any given pressure, volume, gap length, and width.