Nozzle Choked Flow Equations

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):

Nozzle Area (A):

ft²

Upstream Pressure (P₁):

psi

Specific Heat Ratio (γ):

Gas Constant (R):

ft·lb/lb·°R

Upstream Temperature (T₁):

°R

Choked Mass Flow Rate (W):

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1. What is Nozzle Choked Flow?

Definition: Choked flow occurs when fluid velocity at the nozzle throat reaches sonic velocity (Mach 1), limiting the maximum possible mass flow rate.

Purpose: This calculator determines the maximum (choked) mass flow rate through a nozzle for compressible fluids like gases.

2. How Does the Calculator Work?

The calculator uses the isentropic flow equation for choked conditions:

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

Where:

\( W \) — Mass flow rate (lb/s)
\( C_d \) — Discharge coefficient (dimensionless, typically 0.85)
\( A \) — Nozzle throat area (ft²)
\( P_1 \) — Upstream pressure (psi)
\( \gamma \) — Specific heat ratio (~1.4 for air)
\( R \) — Gas constant (ft·lb/lb·°R)
\( T_1 \) — Upstream temperature (°R)

Explanation: The equation accounts for fluid properties and nozzle geometry to determine the maximum possible flow rate under choked conditions.

3. Importance of Choked Flow Calculation

Details: Critical for designing and analyzing rocket nozzles, gas turbines, relief valves, and any system where compressible fluids flow through restrictions.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided where applicable. All values must be positive with γ > 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the discharge coefficient (C_d)?
A: It accounts for flow losses and typically ranges from 0.85 to 0.95 for well-designed nozzles.

Q2: How do I convert temperature to °R?
A: °R = °F + 459.67. For °C: convert to °F first, then add 459.67.

Q3: What's a typical γ value?
A: For air/diatomic gases: ~1.4. For monatomic gases: ~1.67. For complex molecules: ~1.1-1.3.

Q4: When does choked flow occur?
A: When downstream pressure is ≤ ~53% of upstream pressure (for γ=1.4).

Q5: How does area affect the flow rate?
A: Flow rate is directly proportional to nozzle throat area.