Flow Velocity Downstream of Shock Wave using Continuity Equation Calculator

Continuity Equation Formula:

\[ V_2 = \frac{\rho_1 \times V_1}{\rho_2} \]

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):

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1. What is the Continuity Equation?

The continuity equation is a fundamental principle in fluid dynamics that expresses the conservation of mass in a fluid flow. For shock waves, it states that the mass flow rate remains constant across the shock, leading to the relationship between densities and velocities upstream and downstream of the shock.

2. How Does the Calculator Work?

The calculator uses the continuity equation for shock waves:

\[ V_2 = \frac{\rho_1 \times V_1}{\rho_2} \]

Where:

\( V_2 \) — Velocity downstream of shock (m/s)
\( \rho_1 \) — 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 ensures mass conservation across the shock wave, relating the velocity change to the density change.

3. Importance of Velocity Downstream Calculation

Details: Calculating the velocity downstream of a shock wave is crucial for understanding fluid behavior in compressible flow applications, including aerodynamics, propulsion systems, and high-speed flow analysis.

4. Using the Calculator

Tips: Enter density values in kg/m³ and velocity in m/s. All values must be positive (density > 0, velocity ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a normal shock wave?
A: A normal shock wave is a discontinuity in a supersonic flow where the flow becomes subsonic, with sudden changes in pressure, density, temperature, and velocity.

Q2: Why does density change across a shock wave?
A: Density increases across a normal shock wave due to the compression effect as the flow transitions from supersonic to subsonic velocities.

Q3: What are typical applications of this calculation?
A: This calculation is used in aircraft design, rocket propulsion, wind tunnel testing, and analysis of high-speed compressible flows.

Q4: Are there limitations to the continuity equation?
A: The continuity equation assumes steady flow and conservation of mass, but doesn't account for energy losses or viscous effects across the shock.

Q5: How does this relate to other shock wave equations?
A: The continuity equation is one of the three fundamental equations (with momentum and energy) used to analyze normal shock waves in compressible flow.