Enter the initial pressure, initial temperature, Mach number, and expansion angle into the calculator to determine the final pressure after an expansion fan. This calculator assumes isentropic flow conditions and an ideal gas.
Expansion Fan Formula
The following formula is used to calculate the final pressure after an expansion fan:
P<sub>2</sub> = P<sub>1</sub> * (1 + 0.2 * M<sup>2</sup> * (1 - cos<sup>2</sup>(θ)))<sup>-3.5</sup>
Variables:
- P1 is the initial pressure [Pa]
- T1 is the initial temperature [K]
- M is the Mach number
- θ is the expansion angle [degrees]
- P2 is the final pressure [Pa]
To calculate the final pressure after an expansion fan, use the initial conditions of the gas and the expansion angle to apply the formula above.
What is an Expansion Fan?
An expansion fan is a pattern of waves that occur when a supersonic flow encounters a sharp corner that causes the flow to expand. It results in a decrease in pressure and temperature and an increase in volume and velocity of the gas. Expansion fans are a fundamental concept in supersonic aerodynamics and are used in the design of supersonic nozzles, wings, and other aerodynamic components.
How to Calculate Final Pressure after an Expansion Fan?
The following steps outline how to calculate the final pressure after an expansion fan:
- First, determine the initial pressure (P1) in pascals.
- Next, determine the initial temperature (T1) in kelvin.
- Next, determine the Mach number (M).
- Next, determine the expansion angle (θ) in degrees.
- Next, gather the formula from above.
- Finally, calculate the final pressure (P2) in pascals.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Initial pressure (P1) = 101325 Pa
Initial temperature (T1) = 300 K
Mach number (M) = 2
Expansion angle (θ) = 10 degrees