Solution of DE in Pneumatics (orifice in series)

  • Thread starter shekhar
  • Start date
  • Tags
    Series
In summary, the conversation discusses solving differential equations for the pressure and temperature of two volumes with orifices at their outlets. The solutions obtained using the RK4 method are realistic, but fail when both volumes are at the same pressure and the outlet of V2 is suddenly opened. This causes one of the constants to become imaginary. The conversation also mentions the need for a diagram to understand the system and the fact that when the two volumes are connected, the mass flow should be zero if the pressures are equal.
  • #1
shekhar
4
0
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!
 
Engineering news on Phys.org
  • #2
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.
 
  • #3
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.
 

Attachments

  • Untitled.png
    Untitled.png
    60.6 KB · Views: 461

FAQ: Solution of DE in Pneumatics (orifice in series)

1. What is the differential equation for the solution of an orifice in series in pneumatics?

The differential equation for the solution of an orifice in series in pneumatics is:
dy/dt = (P1-P2)/R - C * sqrt(y)
Where y is the pressure drop across the orifice, P1 and P2 are the inlet and outlet pressures, R is the resistance of the orifice, and C is a constant.

2. How is the differential equation solved for the pressure drop across the orifice?

The differential equation can be solved using various methods, such as separation of variables, Laplace transforms, or numerical methods. The solution will depend on the specific parameters and conditions of the system.

3. What factors affect the solution of the differential equation for an orifice in series in pneumatics?

The solution of the differential equation is influenced by factors such as the size and shape of the orifice, the properties of the fluid, the pressure and temperature of the system, and the flow rate through the orifice.

4. How can the solution of the differential equation be used in practical applications?

The solution of the differential equation can be used to predict the pressure drop across the orifice and the resulting flow rate in a pneumatic system. This information can be used for design and optimization purposes, as well as troubleshooting and maintenance of the system.

5. Are there any limitations to the solution of the differential equation for an orifice in series in pneumatics?

Yes, the solution of the differential equation is based on certain assumptions and simplifications, such as assuming laminar flow and neglecting the effects of turbulence and compressibility. It may not accurately represent the behavior of the system in all cases, and experimental data may be needed for validation.

Similar threads

Finding Pressure Decay in Pneumatic System with RK4 Method
Replies
2
Views
467
I Two-Mass Oscillator: Plotting Amplitudes Over Frequency in Hertz
Replies
10
Views
1K
I How Do You Calculate Equilibrium Conditions After Mixing Two Different Gases?
Replies
3
Views
2K
Pressure profile of a gas flow through an orifice
Replies
10
Views
4K
How Can I Determine the Maximum Flow Rate for a Heat Exchanger Cooling Oil?
Replies
1
Views
1K
Free Air Delivered and Relative humidity
Replies
1
Views
1K
Pipe Design - One Inlet, 3 Outlets
Replies
2
Views
3K
A Calculate the work done by pressure rupturing a spherical containment
Replies
7
Views
1K
To find total work done from multiple reversible processes
Replies
3
Views
1K
I How Do You Calculate Initial Pressure and Final Volume in Adiabatic Expansion?
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top