The formula to calculate the choked flow rate (Q) is:
\[ Q = C_v \sqrt{\Delta P (2 P_1 - \Delta P)} \]
Where:
Choked flow is a phenomenon that occurs when the flow rate of a compressible fluid through a valve or orifice is limited by the sonic velocity of the fluid. It happens when the pressure drop across the valve or orifice is equal to or greater than half of the upstream pressure. At this point, the flow rate does not increase with a further decrease in downstream pressure, and the velocity of the fluid at the smallest cross-section of the valve or orifice reaches the speed of sound.
Consider an example where:
Using the formula to calculate the choked flow rate:
\[ Q = 10 \sqrt{5 (2 \times 15 - 5)} = 10 \sqrt{5 \times 25} = 10 \sqrt{125} \approx 111.8 \]
This means that the choked flow rate for this example is approximately 111.8 gallons per minute.
