How To Calculate Velocity From Pressure And Temperature

Isentropic Velocity Equation:

\[ V = \sqrt{ \frac{2}{\gamma - 1} \cdot \frac{R T}{M} \cdot \left( \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right) } \]

Specific Heat Ratio (γ):

dimensionless

Gas Constant (R):

J/mol·K

Temperature (T):

Molar Mass (M):

kg/mol

Downstream Pressure (P₂):

Upstream Pressure (P₁):

Isentropic Velocity (V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Isentropic Velocity Equation?

The isentropic velocity equation calculates the velocity of a gas flow under isentropic (adiabatic and reversible) conditions from pressure ratio and temperature. It's derived from the fundamental principles of thermodynamics and fluid dynamics.

2. How Does The Calculator Work?

The calculator uses the isentropic velocity equation:

\[ V = \sqrt{ \frac{2}{\gamma - 1} \cdot \frac{R T}{M} \cdot \left( \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right) } \]

Where:

\( V \) — Isentropic velocity (m/s)
\( \gamma \) — Specific heat ratio (dimensionless)
\( R \) — Universal gas constant (J/mol·K)
\( T \) — Temperature (K)
\( M \) — Molar mass (kg/mol)
\( P_2 \) — Downstream pressure (Pa)
\( P_1 \) — Upstream pressure (Pa)

Explanation: The equation calculates the velocity achieved when a gas expands isentropically from pressure P₁ to pressure P₂ at temperature T.

3. Importance Of Velocity Calculation

Details: Accurate velocity calculation is crucial for designing nozzles, jet engines, turbines, and other fluid flow systems where isentropic expansion occurs.

4. Using The Calculator

Tips: Enter all parameters in consistent SI units. Ensure γ > 1, all values positive, and P₂ < P₁ for expansion flow. Temperature must be in Kelvin.

5. Frequently Asked Questions (FAQ)

Q1: What is specific heat ratio (γ)?
A: The ratio of specific heat at constant pressure to specific heat at constant volume (Cp/Cv). For air, γ ≈ 1.4.

Q2: When is this equation valid?
A: For ideal gases undergoing isentropic (adiabatic and reversible) expansion or compression processes.

Q3: What is the universal gas constant value?
A: R = 8.314 J/mol·K for all ideal gases.

Q4: How does temperature affect velocity?
A: Higher temperatures generally result in higher velocities due to increased thermal energy available for conversion to kinetic energy.

Q5: What are typical velocity ranges?
A: Depending on application, velocities can range from subsonic (<340 m/s) to supersonic (>340 m/s) in various engineering systems.