Thermodynamics: filling a gas tank with air

[kwak]

Homework Statement

From a previous post in this forum, unfortunately the thread is closed for answers otherwise I would have posted it there: https://www.physicsforums.com/threads/thermodynamic-filling-of-tank-matlab.479112/

A 70 ft3 rigid insulated tank contains air at 14.7 psia and 80 º F. The tank is connected to a supply line through a valve. Air is flowing in the supply line at 75 psia and 80 º F. The valve is opened, and air is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. The diameter of the connecting pipe is 1 inch.

Write a computer program to model the pressurization process in the tank. The computer program will calculate the pressure, temperature, mass flowrate into the tank and resident mass during the process. Determine the final temperature, mass of air in the tank and time required to pressurize the tank.

Homework Equations

mass flow rate mdot=A1*sqrt(((2*k)/(k-1))*P1*g*rho1*(P2/P1)^(2/k)*(1-(P2/P1))^(k-1/k))

where k = Cp/Cv

The Attempt at a Solution

I modeled a comparable situation in SI units using vanderWaals EOS and I would like to compare it to the results from the thread mentioned above. However I do not know where this equation for the mass flow rate came from. Does someone recognize it?[/B]

 

[KataKoniK]

Hello,

Thank you for reaching out to our forum for assistance with your computer program. The equation for mass flow rate that you have provided appears to be a variation of the isentropic flow equation, which is commonly used in thermodynamics to calculate the flow of gas through a pipe. It is derived from the equations of continuity, Bernoulli's equation, and the ideal gas law. This equation is often used in engineering and physics applications to model gas flow in pipes and tanks.

I am not sure where the specific equation you have provided came from, as it may be a simplified version or a variation of the original equation. However, it should still provide a reasonable approximation for your calculations. I suggest checking your units and constants to ensure they are consistent and accurate for your specific problem.

I hope this helps and good luck with your computer program! Let us know if you have any further questions or need any additional assistance.