Compressible Flow Through Nozzle Calculator

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

Nozzle Area (A):

ft²

Upstream Pressure (P₁):

psi

Specific Heat Ratio (γ):

(1.4 for air)

Gas Constant (R):

ft·lb/lb·°R

Upstream Temperature (T₁):

°R

Choked Mass Flow Rate (W):

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1. What is the Compressible Flow Through Nozzle Calculator?

Definition: This calculator determines the choked mass flow rate for compressible flow through a nozzle using isentropic flow equations.

Purpose: It helps engineers and technicians calculate the maximum possible flow rate through a nozzle when the flow becomes choked (reaches Mach 1 at the throat).

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( W \) — Choked mass flow rate (lb/s)
\( C_d \) — Discharge coefficient (dimensionless, typically 0.95-0.98)
\( A \) — Nozzle throat area (ft²)
\( P_1 \) — Upstream pressure (psi)
\( \gamma \) — Specific heat ratio (~1.4 for air)
\( R \) — Gas constant (53.35 ft·lb/lb·°R for air)
\( T_1 \) — Upstream temperature (°R)

Explanation: The formula calculates the maximum possible mass flow rate through a nozzle when the flow is choked (sonic at the throat).

3. Importance of Choked Flow Calculation

Details: Understanding choked flow is critical for designing propulsion systems, pneumatic systems, and any application involving compressible flow through restrictions.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for γ (1.4) and R (53.35) for air. Temperature must be in Rankine (°R = °F + 459.67).

5. Frequently Asked Questions (FAQ)

Q1: What is choked flow?
A: Choked flow occurs when the flow velocity at the nozzle throat reaches the speed of sound (Mach 1), limiting the maximum possible mass flow rate.

Q2: What's a typical discharge coefficient (C_d)?
A: For well-designed nozzles, C_d typically ranges from 0.95 to 0.98, accounting for friction and flow losses.

Q3: How do I convert temperature to Rankine?
A: °R = °F + 459.67 or K × 1.8. For example, 70°F = 529.67°R.

Q4: What happens if downstream pressure decreases further?
A: Once flow is choked, decreasing downstream pressure further won't increase mass flow rate, though the flow will expand supersonically.

Q5: Can this be used for gases other than air?
A: Yes, but you must use the correct γ and R values for the specific gas.