Can You Prove the Steady Flow Equation for Ideal Gases?

In summary, the conversation discusses an equation with variables representing temperature, pressure, and a constant value of 1.4. It also mentions a possible equation involving Mach numbers. The participants inquire about the physical significance of the variables and the type of process involved.
  • #1
drftr87
2
0
Does anybody know how to prove this equation

t1/t2 = (p1/p2)^(n-1/n)

thanks
 
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  • #2
Tell us about the equation. What are the variables, what does it represent. The more information you can provide the more we will be able to help.
 
  • #3
t= temperature
p= pressure
n can be written as gamma(γ) which is 1.4
ive found out that t1/t2 = 1+((γ-1)/2)(m^2)
where m is the mach number
 
  • #4
so, are (p1,t1) and (p2,t2) thermodynamic variable for two states? Is the state an ideal gas? Is the process which takes you to the new state adiabatic?

It'll be easier to help if you post the exact question.
 

1. What is the steady flow equation?

The steady flow equation, also known as the continuity equation, is a fundamental principle in fluid mechanics that states that the mass flow rate into a control volume must equal the mass flow rate out of the control volume, assuming no mass is created or destroyed within the control volume.

2. How is the steady flow equation derived?

The steady flow equation is derived from the principle of conservation of mass. It can be mathematically derived by equating the mass entering a control volume to the mass exiting the control volume, and then simplifying the resulting equation.

3. What are the assumptions made in the steady flow equation?

The steady flow equation assumes that the fluid is incompressible, the flow is steady (i.e. no changes in flow properties over time), and that there is no internal sources or sinks of mass within the control volume.

4. How is the steady flow equation used in real-world applications?

The steady flow equation is used to analyze and design various fluid systems, such as pipelines, pumps, and turbines. It is also used in the field of hydraulics to calculate flow rates and pressures in open channels and closed conduits.

5. What are the limitations of the steady flow equation?

The steady flow equation is only applicable to steady-state flows, meaning that it cannot be used to analyze unsteady or transient flow situations. It also assumes that the fluid is incompressible, which may not be the case for certain fluids under certain conditions. Additionally, it does not take into account frictional losses or other complexities that may affect the flow within the system.

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