Velocity Behind Normal Shock By Normal Shock Momentum Equation Calculator

Normal Shock Momentum Equation:

\[ V_2 = \sqrt{\frac{P_1 - P_2 + \rho_1 \cdot V_1^2}{\rho_2}} \]

Static Pressure Ahead of Normal Shock (P₁):

Static Pressure Behind Normal Shock (P₂):

Density Ahead of Normal Shock (ρ₁):

kg/m³

Velocity Upstream of Shock (V₁):

m/s

Density Behind Normal Shock (ρ₂):

kg/m³

Velocity Downstream of Shock (V₂):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Normal Shock Momentum Equation?

The Normal Shock Momentum Equation is derived from the conservation of momentum principle across a normal shock wave. It relates the velocity downstream of the shock to the pressures, densities, and velocity upstream of the shock.

2. How Does the Calculator Work?

The calculator uses the Normal Shock Momentum Equation:

\[ V_2 = \sqrt{\frac{P_1 - P_2 + \rho_1 \cdot V_1^2}{\rho_2}} \]

Where:

\( V_2 \) — Velocity Downstream of Shock (m/s)
\( P_1 \) — Static Pressure Ahead of Normal Shock (Pa)
\( P_2 \) — Static Pressure Behind Normal Shock (Pa)
\( \rho_1 \) — Density Ahead of Normal Shock (kg/m³)
\( V_1 \) — Velocity Upstream of Shock (m/s)
\( \rho_2 \) — Density Behind Normal Shock (kg/m³)

Explanation: The equation calculates the velocity behind a normal shock wave by considering the momentum conservation across the shock.

3. Importance of Velocity Calculation Behind Shock

Details: Calculating the velocity downstream of a shock wave is crucial for understanding flow properties in compressible flow applications, such as in supersonic wind tunnels, jet engines, and rocket nozzles.

4. Using the Calculator

Tips: Enter all values in appropriate units. Pressures should be in Pascals (Pa), densities in kg/m³, and velocities in m/s. All values must be positive, with densities strictly greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a normal shock wave?
A: A normal shock wave is a shock wave that is perpendicular to the flow direction, causing an abrupt change in flow properties.

Q2: When does this equation apply?
A: This equation applies to steady, one-dimensional flow of an ideal gas across a normal shock wave.

Q3: What are typical values for the input parameters?
A: Typical values vary widely depending on the application, but upstream velocities are often supersonic, while downstream velocities are subsonic.

Q4: Are there limitations to this equation?
A: This equation assumes ideal gas behavior and steady, one-dimensional flow. It may not be accurate for real gases or complex flow geometries.

Q5: How is this related to other shock equations?
A: This momentum equation is one of the three fundamental conservation equations (along with mass and energy) used to analyze normal shock waves.