Density Downstream of Shock Wave using Continuity Equation Calculator

Continuity Equation:

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

Density Ahead of Normal Shock (ρ₁):

kg/m³

Velocity Upstream of Shock (V₁):

m/s

Velocity Downstream of Shock (V₂):

m/s

Density Behind Normal Shock (ρ₂):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Continuity Equation for Shock Waves?

The continuity equation for shock waves describes the conservation of mass across a normal shock wave. It states that the mass flow rate remains constant, 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:

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

Where:

\( \rho_2 \) — Density behind normal shock (kg/m³)
\( \rho_1 \) — Density ahead of normal shock (kg/m³)
\( V_1 \) — Velocity upstream of shock (m/s)
\( V_2 \) — Velocity downstream of shock (m/s)

Explanation: The equation ensures mass conservation across the shock wave, relating the density and velocity changes that occur when a fluid passes through a normal shock.

3. Importance of Density Calculation in Shock Waves

Details: Calculating density changes across shock waves is crucial for understanding compressible flow behavior, designing supersonic aircraft, analyzing rocket nozzles, and studying high-speed aerodynamic phenomena.

4. Using the Calculator

Tips: Enter density ahead of shock in kg/m³, velocity upstream in m/s, and velocity downstream in m/s. All values must be positive and non-zero for accurate calculation.

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, characterized by sudden changes in pressure, temperature, density, and velocity.

Q2: Why does density increase across a normal shock?
A: Density increases across a normal shock because the flow decelerates from supersonic to subsonic speeds, causing compression of the fluid.

Q3: What are typical applications of this calculation?
A: This calculation is used in aerospace engineering, gas dynamics, turbomachinery design, and analysis of high-speed flow phenomena in nozzles, diffusers, and wind tunnels.

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

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 solve for all flow properties across a normal shock wave.