Enter the pressure ratio, Mach number, and specific heat ratio into the calculator to determine the missing variable.
Mach Number Pressure Ratio Formula
The following formula is used to calculate the pressure ratio for a given Mach number and specific heat ratio.
PR = \left(1 + \frac{\gamma - 1}{2} M^2\right)^{\frac{\gamma}{\gamma - 1}}Variables:
- PR is the pressure ratio
- γ (gamma) is the specific heat ratio
- M is the Mach number
To calculate the pressure ratio, use the formula above, which involves the specific heat ratio and the Mach number.
What is Mach Number Pressure Ratio?
The Mach number pressure ratio is a dimensionless quantity used in fluid dynamics and aerodynamics to describe the relationship between the pressure at a given point in a flow and the pressure in the undisturbed flow. It is particularly useful in the study of compressible flows, such as those encountered in high-speed aircraft and rocket engines. The Mach number itself is a measure of the speed of an object moving through a fluid, expressed as a ratio of the object’s speed to the speed of sound in that fluid. The specific heat ratio, also known as the adiabatic index, is a property of the fluid that affects how pressure and temperature change during compression and expansion processes.
How to Calculate Mach Number Pressure Ratio?
The following steps outline how to calculate the Mach number pressure ratio.
- First, determine the Mach number (M).
- Next, determine the specific heat ratio (γ).
- Next, calculate the pressure ratio using the formula PR = (1 + ((γ – 1) / 2) * M²)^(γ / (γ – 1)).
- Finally, calculate the Mach number pressure ratio.
- After inserting the values 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.
Mach number (M) = 2
Specific heat ratio (γ) = 1.4