Solution of DE in Pneumatics (orifice in series)

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SUMMARY

The discussion focuses on solving differential equations (DE) for pressure decay in two connected volumes, V1 and V2, with orifices d1 and d2. The RK4 method was utilized for solving these equations, yielding realistic results except when both volumes are at the same pressure (P2 = P1) and the outlet of V2 is closed at t=0, leading to an imaginary k3 value. The participants seek clarification on the behavior of the system under these conditions and request a diagram for better understanding.

PREREQUISITES
  • Understanding of differential equations in fluid dynamics
  • Familiarity with the RK4 numerical method for solving DEs
  • Knowledge of pneumatic systems and pressure dynamics
  • Ability to interpret system diagrams related to fluid flow
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  • Research the implications of pressure equalization in connected volumes
  • Study the RK4 method in detail for solving complex DEs
  • Explore the behavior of orifices in pneumatic systems under varying pressure conditions
  • Investigate methods for visualizing fluid dynamics through system diagrams
USEFUL FOR

Engineers, physicists, and students working with pneumatic systems, fluid dynamics, or numerical methods for solving differential equations will benefit from this discussion.

shekhar
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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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