Modeling a Differential Equation for Air Strut Pressure and Volume

[hail_thy_gt]

Hello all,

Would love for someone to help me get a solution for this.

So, in essence I am trying to model a differential equation for the following scenario: (I am currently achieving this through Excel, but I'm certain a mathematical representation can make things more concise and efficient.)

To give a run down: I have an initial Strut Volume and Pressure. I have calculated the Air Flow, Flow Rate. Now, the Volume added to the strut is just Flow Rate×delta time. But, the problem is that Air Flow and Flow rate change when the Strut Volume changes, and as a result the Pressure changes as well. So, apart from an iteration in Excel with small time-steps, I can't wrap my head to come up with another method. I know there's a differential equation that can be modeled around this. I just can't get the ball rolling.

I would greatly appreciate if someone can help.

 

[Achy47]

Hello there,

It sounds like you are trying to model a system with changing variables over time, which can be effectively done using differential equations. In this case, it seems like you are interested in modeling the change in pressure as the volume and air flow change. To do this, you can use the ideal gas law, which relates pressure, volume, and temperature.

The ideal gas law is given by PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. In your case, the temperature can be assumed to be constant, so the equation simplifies to P = kV, where k is a constant.

Now, to incorporate the change in air flow, you can use the continuity equation, which states that the mass flow rate (m_dot) is equal to the density (rho) times the cross-sectional area (A) times the velocity (v). This can be written as m_dot = rho * A * v.

Combining these two equations, we can write a differential equation for pressure as:

dP/dt = (k * dV/dt) + (rho * A * dv/dt)

Where dV/dt is the change in volume over time, and dv/dt is the change in velocity over time.

This equation can then be solved using numerical methods, such as Euler's method, to track the change in pressure over time. I hope this helps to get you started on finding a mathematical solution for your problem. Good luck!