Choked Mass Flow Rate Equation

Choked Mass Flow Rate Formula:

\[ W = C_d \times A \times P_1 \times \sqrt{\frac{\gamma}{R \times T_1}} \times \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{2(\gamma - 1)}} \]

Discharge Coefficient (C_d):

dimensionless

Area (A):

ft²

Upstream Pressure (P₁):

psi

Specific Heat Ratio (γ):

dimensionless

Gas Constant (R):

ft·lb/lb·°R

Temperature (T₁):

°R

Choked Mass Flow Rate (W):

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1. What is the Choked Mass Flow Rate Equation?

Definition: This equation calculates the maximum possible mass flow rate through a nozzle when the flow is choked (reaches Mach 1 at the throat).

Purpose: It's essential for designing and analyzing compressible flow systems like rocket nozzles, gas turbines, and pneumatic systems.

2. How Does the Equation Work?

The equation is:

\[ W = C_d \times A \times P_1 \times \sqrt{\frac{\gamma}{R \times T_1}} \times \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{2(\gamma - 1)}} \]

Where:

\( W \) — Mass flow rate (lb/s)
\( C_d \) — Discharge coefficient (dimensionless, typically 0.6-0.9)
\( A \) — Cross-sectional area (ft²)
\( P_1 \) — Upstream pressure (psi)
\( \gamma \) — Specific heat ratio (dimensionless, ~1.4 for air)
\( R \) — Gas constant (ft·lb/lb·°R)
\( T_1 \) — Upstream temperature (°R)

Explanation: The equation combines thermodynamic properties with nozzle geometry to determine the maximum flow rate under choked conditions.

3. Importance of Choked Flow Calculation

Details: Accurate choked flow calculations ensure proper system design, prevent underperformance, and maintain safety in high-pressure systems.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for common gases (air). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does "choked flow" mean?
A: Choked flow occurs when the flow velocity reaches the speed of sound at the nozzle throat, limiting the maximum possible mass flow rate.

Q2: What's a typical discharge coefficient (C_d)?
A: For well-designed nozzles, C_d is typically 0.8-0.95. For sharp-edged orifices, it's often 0.6-0.65.

Q3: What units should temperature be in?
A: Temperature must be in absolute units (Rankine, °R) for this equation. °R = °F + 459.67.

Q4: Can this be used for any gas?
A: Yes, but you must use the correct γ and R values for the specific gas.

Q5: What if my flow isn't choked?
A: This equation only applies to choked flow. For subsonic flow, a different equation is needed.