Density Ratio across Normal Shock Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Normal Shock Wave

Governing Equations and Sound Wave

Oblique Shock and Expansion Waves

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Property Change Across Shock Waves

Downstream Shock Waves

Normal Shock Relations

Upstream Shock Waves

✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.ⓘ Mach Number Ahead of Normal Shock [M₁]			+10% -10%

✖Density Ratio Across Normal Shock indicates the ratio of densities before and after passing through a normal shock wave.ⓘ Density Ratio across Normal Shock [ρ_r]

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Formula

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Density Ratio across Normal Shock

Formula

`"ρ"_{"r"} = ("γ"+1)*("M"_{"1"}^2)/(2+("γ"-1)*"M"_{"1"}^2)`

Example

`"1.844933"=("1.4"+1)*(("1.49")^2)/(2+("1.4"-1)*("1.49")^2)`

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Density Ratio across Normal Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)
ρ_r = (γ+1)*(M₁^2)/(2+(γ-1)*M₁^2)
This formula uses 3 Variables

Variables Used

Density Ratio Across Normal Shock - Density Ratio Across Normal Shock indicates the ratio of densities before and after passing through a normal shock wave.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number Ahead of Normal Shock - Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number Ahead of Normal Shock: 1.49 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ_r = (γ+1)*(M₁^2)/(2+(γ-1)*M₁^2) --> (1.4+1)*(1.49^2)/(2+(1.4-1)*1.49^2)

Evaluating ... ...

ρ_r = 1.84493289566627

STEP 3: Convert Result to Output's Unit

1.84493289566627 --> No Conversion Required

FINAL ANSWER

1.84493289566627 ≈ 1.844933 <-- Density Ratio Across Normal Shock

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< 6 Property Change Across Shock Waves Calculators

Static Enthalpy Ratio across Normal Shock

Go Static Enthalpy Ratio Across Normal Shock = (1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))

Temperature Ratio across Normal Shock

Go Temperature Ratio Across Normal Shock = (1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+((Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)))

Density Ratio across Normal Shock

Go Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)

Entropy Change across Normal Shock

Go Entropy Change = Specific Gas Constant*ln(Stagnation Pressure Ahead of Normal Shock/Stagnation Pressure Behind Normal Shock)

Pressure Ratio across Normal Shock

Go Pressure Ratio Across Normal Shock = 1+(2*Specific Heat Ratio)/(Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2-1)

Shock Strength

Go Shock Strength = ((2*Specific Heat Ratio)/(1+Specific Heat Ratio))*(Mach Number Ahead of Normal Shock^2-1)

Density Ratio across Normal Shock Formula

How to obtain density ratio across normal shock?

Density ratio across the normal shock is obtained by rearranging the continuity equation and using Prandtl relation.

How to Calculate Density Ratio across Normal Shock?

Density Ratio across Normal Shock calculator uses Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2) to calculate the Density Ratio Across Normal Shock, The Density Ratio across Normal Shock calculates the ratio of densities across a normal shock wave. This formula incorporates the ratio of specific heats for the fluid and the Mach number ahead of the shock to determine the density ratio. It provides insight into the change in density across the shock wave, aiding in the analysis of compressible flow behavior. Density Ratio Across Normal Shock is denoted by ρ_r symbol.

How to calculate Density Ratio across Normal Shock using this online calculator? To use this online calculator for Density Ratio across Normal Shock, enter Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button. Here is how the Density Ratio across Normal Shock calculation can be explained with given input values -> 1.844933 = (1.4+1)*(1.49^2)/(2+(1.4-1)*1.49^2).

FAQ

What is Density Ratio across Normal Shock?

The Density Ratio across Normal Shock calculates the ratio of densities across a normal shock wave. This formula incorporates the ratio of specific heats for the fluid and the Mach number ahead of the shock to determine the density ratio. It provides insight into the change in density across the shock wave, aiding in the analysis of compressible flow behavior and is represented as ρ_r = (γ+1)*(M₁^2)/(2+(γ-1)*M₁^2) or Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2). The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

How to calculate Density Ratio across Normal Shock?

The Density Ratio across Normal Shock calculates the ratio of densities across a normal shock wave. This formula incorporates the ratio of specific heats for the fluid and the Mach number ahead of the shock to determine the density ratio. It provides insight into the change in density across the shock wave, aiding in the analysis of compressible flow behavior is calculated using Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2). To calculate Density Ratio across Normal Shock, you need Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁). With our tool, you need to enter the respective value for Specific Heat Ratio & Mach Number Ahead of Normal Shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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