Calculating Inlet and Outlet Times: c=451.8, u=135.5

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In summary, the conversation discusses the calculation of 6.3s for the inlet and 3.4s for the outlet, which were obtained by dividing 2000/c-u and 2000/c+u where c=451.8 and u=135.5. The wave starts at the valve located in the middle of the pipe and travels towards the inlet and outlet. It takes 3.4s to reach the outlet and then returns to the inlet at 6.3s. The sound speed, c, is the same on both sides of the valve, but the apparent velocity of the wave changes depending on whether it is going with or against the flow of methane. This results in a faster travel time for the
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FannoFlow88
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Homework Statement
Methane is transported along a 4km pipeline at a Mach number of 0.3 and temperature 30◦C. A valve positioned 2km from the inlet begins to close, creating a pressure wave up and down the pipe. Calculate the time it takes for the pressure wave to reach a) the inlet, and b) the outlet of the pipe. [for methane: Cp = 2.2537kJ/kgK, Cv = 1.7354kJ/kgK, R = 0.5182kJ/kgK
Relevant Equations
Methane is transported along a 4km pipeline at a Mach number of 0.3 and temperature 30◦C. A valve positioned 2km from the inlet begins to close, creating a pressure wave up and down the pipe. Calculate the time it takes for the pressure wave to reach a) the inlet, and b) the outlet of the pipe. [for methane: Cp = 2.2537kJ/kgK, Cv = 1.7354kJ/kgK, R = 0.5182kJ/kgK Relevant Equations: The answers given are 6.3s for inlet and 3.4s for outlet, which I was able to obtain by dividing 2000/c-u and 2000/c+u
c=451.8 i calculated and u=135.5...

Could someone explain why 2000m is used instead of length of pipe which is 4km.
Struggling to visualise this in operation. Thanks
The answers given are 6.3s for inlet and 3.4s for outlet, which I was able to obtain by dividing 2000/c-u and 2000/c+u
c=451.8 i calculated and u=135.5...
 
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  • #2
The wave starts at the valve which is in the middle of the pipe (i.e., 2000m from the inlet and outlet).
 
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  • #3
so the wave goes from valve to outlet in 3.4s and then hits a wall? and returns to inlet at 6.3s. wish i had a diagram of this
 
  • #4
Two waves emanate from closing of the valve. One travels toward the inlet and one travels towards the outlet.
 
  • #5
oh inlet and outlet 2km away from valve which is middle, so why is outlet quicker. is it because methane is flowing in that direction, giving it a push etc. thanks for reply
 
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  • #6
The sound speed, c, of the methane is identical on both sides of the valve. Imagine if you were traveling with the methane on either side of the valve at velocity u. It would look like the wave was moving towards you with the speed c on both sides. Now go to the lab frame. The apparent velocity of the wave also needs to change to reflect this. You end up with c+u as it goes with the flow and c-u when you go against it.
 
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  • #7
brilliant explanation.
 

Related to Calculating Inlet and Outlet Times: c=451.8, u=135.5

1. What do c and u represent in the equation c=451.8, u=135.5?

C and u represent the velocity of the fluid at the inlet and outlet, respectively. They are measured in units of meters per second (m/s).

2. How do you calculate the inlet and outlet times using this equation?

The inlet time can be calculated by dividing the distance of the inlet by the velocity of the fluid at the inlet, c. The outlet time can be calculated by dividing the distance of the outlet by the velocity of the fluid at the outlet, u.

3. What is the significance of calculating inlet and outlet times?

Calculating inlet and outlet times is important in fluid dynamics, as it helps determine the flow rate and pressure of a fluid in a system. It is also useful in designing and optimizing systems that involve fluid flow, such as pipelines and pumps.

4. Can this equation be used for all types of fluids?

No, this equation is specifically for incompressible, Newtonian fluids. It may not accurately represent the behavior of other types of fluids, such as gases or non-Newtonian fluids.

5. Are there any limitations or assumptions when using this equation?

Yes, this equation assumes that the fluid is flowing in a straight line and that there are no external forces acting on it. It also assumes that the fluid is incompressible and has a constant density and viscosity. These assumptions may not hold true in all situations and can affect the accuracy of the calculated inlet and outlet times.

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