Nozzles

Overview

Engineering reference data for Nozzles in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Sonic Choke Operation

A critical flow nozzle (also called a sonic choke) establishes a fixed flow rate unaffected by downstream pressure fluctuations. By creating a shock wave, the sonic choke provides a simple method to regulate gas flow. This occurs when the flow accelerates to the local velocity of sound in the fluid.

Critical Pressure Ratios

The critical pressure ratio values for common gas applications:

Mass Flow at Sonic Conditions

When the minimum pressure equals the critical pressure, the mass flow rate through the nozzle is given by:

$\dot{m}_c = A_c \sqrt{n \cdot p_1 \cdot \rho_1} \left(\frac{2}{n + 1}\right)^{\frac{n + 1}{2(n - 1)}}$

Where:

• $\dot{m}_c$ = mass flow at sonic conditions (kg/s)
• $A_c$ = nozzle throat area (m²)
• $n$ = polytropic index (-)
• $p_1$ = inlet pressure (Pa)
• $\rho_1$ = inlet density (kg/m³)

Polytropic Index Notes

For a perfect gas undergoing an adiabatic process, the polytropic index $n$ equals the ratio of specific heats $k = c_p / c_v$. There is no unique value for $n$—it depends on the gas and process conditions.

Interactive Charts

References

• Original Source