Sonic Nozzle Flow Meter by Tons of Concrete

Sonic Flow 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

Mass Flow Rate (W):

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1. What is a Sonic Nozzle Flow Meter?

Definition: This calculator determines the mass flow rate of gas through a nozzle when the flow is choked (sonic conditions at the throat).

Purpose: Used in engineering applications to measure or predict gas flow rates in pipelines, ventilation systems, and process equipment.

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 0.95-0.99)
\( A \) — 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 gas properties and choked flow conditions where velocity at the throat equals sonic velocity.

3. Importance of Sonic Flow Calculation

Details: Accurate flow measurement is critical for system design, safety, and efficiency in gas handling systems.

4. Using the Calculator

Tips: Enter the discharge coefficient (default 0.98), nozzle area, upstream pressure, specific heat ratio (default 1.4 for air), gas constant (default 53.3 for air), and absolute temperature in Rankine.

5. Frequently Asked Questions (FAQ)

Q1: When does flow become choked in a nozzle?
A: Flow becomes choked (sonic at throat) when downstream pressure is ≤ ~53% of upstream pressure for air (γ=1.4).

Q2: What's a typical discharge coefficient?
A: Well-designed nozzles typically have Cd between 0.95 and 0.99.

Q3: How do I convert temperature to Rankine?
A: °R = °F + 459.67. The calculator requires absolute temperature.

Q4: What's the gas constant for common gases?
A: Air = 53.3, Nitrogen = 55.2, Oxygen = 48.3, Hydrogen = 766.5 ft·lb/lb·°R.

Q5: Can I use this for subsonic flow?
A: No, this equation is only valid for choked (sonic) flow conditions.