Solution of DE in Pneumatics (orifice in series)

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The discussion focuses on finding the pressure decay in two connected volumes, V1 and V2, each with orifices at their outlets. The user successfully solved the differential equations using the RK4 method but encountered issues when both volumes are at the same pressure and one outlet is suddenly opened. This scenario leads to a negative k1 and a positive k2, resulting in an imaginary k3, creating confusion about the behavior of the system. Participants emphasize that when P1 equals P2, mass flow should be zero, suggesting a need for clarity on the system's configuration. A diagram of the system is requested to better understand the differential equations' application.
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I want to find the pressure decay of two volumes V1 and V2 having orifices d1 and d2 at their outlets respectively. The differential equations for the pressure and temperature for the two volumes are given below.

upload_2014-10-15_0-43-37-png.74421.png
i solved these equations using RK4 method. The solutions I got are quite realistic. But the solutions fails when : both the volumes are at same pressure (P2=P1) outlet of V2 is closed at t=0. It is suddenly opened at t=0. when we solve the above DE for P2, k1 in this case is negative (since first term becomes 0) whereas k2 becomes positive. This causes k3 to be imaginary! Can anyone help me with this? Thanks in advance!
 
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It's not clear what's going on here. Do you have a diagram of the system for which these DEs were developed?

If V1 and V2 are connected, then when P1 = P2, the mass flow between the two volumes should be zero.
 
SteamKing said:
It's not clear what's going on here. Do you have a diagram of the system for which these DEs were developed?

If V1 and V2 are connected, then when P1 = P2, the mass flow between the two volumes should be zero.
 

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