Which variable below is used in the determination of the mass flow rate of a free expansion gas release but is NOT used in the determination of the maximum flow rate of choked flow?

• A. P, the pressure of the gas at the throat of the opening
• B. T, the temperature of the gas
• C. V, the velocity of the gas
• D. rho, the density of the gas

Answer: (A)

In free expansion (effusive flow into vacuum), the mass flow rate is governed by how many molecules are available to escape through the opening, which scales directly with the pressure at the opening. Higher pressure there means more molecules try to pass through, so the pressure at the throat plays a direct role in determining the rate.

When flow is choked at the throat, the situation changes: once the flow reaches sonic speed at the throat, the maximum mass flux is set by the upstream stagnation conditions (pressure and temperature) and the gas properties, along with the throat area. The throat pressure itself is not an independent input in this regime; it is determined by the upstream conditions and gamma, and the standard choked-flow formula uses the stagnation pressure and temperature rather than the local throat pressure as a separate parameter.

So the pressure at the throat is the variable that matters for free expansion but is not used as an independent input in calculating the maximum choked-flow rate. Temperature, density, and the sonic condition at the throat all play roles in the choking formula through their relationships to P0, T0, and the gas properties.