Enter the mass flow rate, throat area, stagnation pressure, stagnation temperature, specific gas constant, and gamma into the calculator to determine the missing variable.’
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Choked Mass Flow Rate Formula
The following formula is used to calculate the choked mass flow rate for a given set of conditions (ideal gas, isentropic flow, choked at the throat).
\dot{m} = A_t\,P_0\sqrt{\frac{\gamma}{R\,T_0}}\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}}Variables:
- (ṁ) is the mass flow rate
- (At) is the throat area
- (P0) is the stagnation pressure
- (T0) is the stagnation temperature
- (R) is the specific gas constant
- (γ) is the ratio of specific heats (gamma)
To calculate the choked mass flow rate, multiply the throat area by the stagnation pressure. Multiply that by \(\sqrt{\gamma}\) and by \(\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}}\). Then divide by \(\sqrt{R\,T_0}\).
What is Choked Mass Flow Rate?
Choked mass flow rate occurs when the flow of a compressible fluid reaches its maximum possible rate through a given cross-sectional area. This phenomenon happens when the fluid velocity at the throat of a nozzle or other constriction reaches the speed of sound (Mach 1), causing the flow to become “choked.” Once choking occurs (i.e., when the downstream/back pressure is at or below the critical pressure ratio), the mass flow rate becomes independent of further reductions in downstream pressure and is determined primarily by upstream conditions such as stagnation pressure and temperature, throat area, specific gas constant, and the ratio of specific heats (gamma). Choked flow is a critical concept in various engineering applications, including jet engines, rocket nozzles, and other high-speed fluid dynamics systems.
How to Calculate Choked Mass Flow Rate?
The following steps outline how to calculate the Choked Mass Flow Rate.
- First, determine the throat area ((A_t)).
- Next, determine the stagnation pressure ((P_0)).
- Next, determine the stagnation temperature ((T_0)).
- Next, determine the specific gas constant ((R)).
- Next, determine the ratio of specific heats ((gamma)).
- Finally, calculate the Choked Mass Flow Rate using the formula provided above.
- 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.
Throat Area ((A_t)) = 0.01 m²
Stagnation Pressure ((P_0)) = 101325 Pa
Stagnation Temperature ((T_0)) = 300 K
Specific Gas Constant ((R)) = 287 J/(kg·K)
Gamma ((gamma)) = 1.4