Enter all but one of the Mach number, total pressure, static pressure, and specific heat ratio into the Isentropic Flow Calculator to determine the remaining variable. This calculator can also evaluate any of the variables given the others are known.

Isentropic Flow Formula

The following formula is used to calculate the Isentropic Flow Calculator:

M = SQRT[(2/(g-1)) * ((P_t/P)^{((g-1)/g) - 1)}]


  • M is the Mach number
  • P_t is the total pressure
  • P is the static pressure
  • gamma is the specific heat ratio

What is an Isentropic Flow?

Isentropic flow is a concept in fluid dynamics that describes a fluid flow in which the entropy, a measure of disorder or randomness, remains constant. This condition is typically associated with idealized, reversible processes and is often used in thermodynamic analysis. In an isentropic flow, there is no heat transfer or friction, meaning that no energy is added or removed from the fluid, and no energy is lost due to friction. This results in the total energy of the fluid remaining constant. Isentropic flows are often used to model ideal gas behavior, and they are particularly useful in the study of supersonic and hypersonic flows, as well as in the design of nozzles and diffusers. However, it’s important to note that real-world flows are rarely truly isentropic due to the presence of factors such as heat transfer and friction.

How to Calculate Isentropic Flow?

The following steps outline how to calculate the Isentropic Flow.

  1. First, determine the initial temperature (T1) and the initial pressure (P1) of the flow.
  2. Next, determine the final temperature (T2) or the final pressure (P2) of the flow, depending on the given information.
  3. Next, gather the formula from above = T2 / T1 = (P2 / P1) ^ ((gamma – 1) / gamma).
  4. Finally, calculate the Isentropic Flow.
  5. 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 temperature (T1) = 300 K

Initial pressure (P1) = 1 atm

Final temperature (T2) = 400 K

Final pressure (P2) = 2 atm