Density before Shock Formation for Expansion Wave Calculator

✖Stagnation pressure ahead of shock is the stagnation or total or pitot pressure before a shockwave has occurred.ⓘ Stagnation pressure ahead of shock [p₀₁]			+10% -10%
✖The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Normal velocity is the velocity normal to the shock formation.ⓘ Normal velocity [Vn]			+10% -10%
✖Old speed of sound is the speed of sound before the shock.ⓘ Old Speed of Sound [c_old]			+10% -10%
✖Time in seconds is what a clock reads, it is a scalar quantity.ⓘ Time in seconds [t_sec]			+10% -10%

✖Density behind shock is the density of the fluid in the upstream direction of shock.ⓘ Density before Shock Formation for Expansion Wave [ρ₂]

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Density before Shock Formation for Expansion Wave

Formula

`"ρ"_{"2"} = "p"_{"01"}/(1-(("γ"-1)/2)*("Vn"/"c"_{"old"}))^(2*"γ"/("γ"-"t"_{"sec"}))`

Example

`"83.1633kg/m³"="100Pa"/(1-(("1.6"-1)/2)*("1000m/s"/"342m/s"))^(2*"1.6"/("1.6"-"38s"))`

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Density before Shock Formation for Expansion Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density behind Shock = Stagnation pressure ahead of shock/(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds))
ρ₂ = p₀₁/(1-((γ-1)/2)*(Vn/c_old))^(2*γ/(γ-t_sec))
This formula uses 6 Variables

Variables Used

Density behind Shock - (Measured in Kilogram per Cubic Meter) - Density behind shock is the density of the fluid in the upstream direction of shock.
Stagnation pressure ahead of shock - (Measured in Pascal) - Stagnation pressure ahead of shock is the stagnation or total or pitot pressure before a shockwave has occurred.
Specific Heat Ratio - The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Normal velocity - (Measured in Meter per Second) - Normal velocity is the velocity normal to the shock formation.
Old Speed of Sound - (Measured in Meter per Second) - Old speed of sound is the speed of sound before the shock.
Time in seconds - (Measured in Second) - Time in seconds is what a clock reads, it is a scalar quantity.

STEP 1: Convert Input(s) to Base Unit

Stagnation pressure ahead of shock: 100 Pascal --> 100 Pascal No Conversion Required
Specific Heat Ratio: 1.6 --> No Conversion Required
Normal velocity: 1000 Meter per Second --> 1000 Meter per Second No Conversion Required
Old Speed of Sound: 342 Meter per Second --> 342 Meter per Second No Conversion Required
Time in seconds: 38 Second --> 38 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ₂ = p₀₁/(1-((γ-1)/2)*(Vn/c_old))^(2*γ/(γ-t_sec)) --> 100/(1-((1.6-1)/2)*(1000/342))^(2*1.6/(1.6-38))

Evaluating ... ...

ρ₂ = 83.1632989062157

STEP 3: Convert Result to Output's Unit

83.1632989062157 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

83.1632989062157 ≈ 83.1633 Kilogram per Cubic Meter <-- Density behind Shock

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< 5 Expansion Waves Calculators

Density before Shock Formation for Expansion Wave

Go Density behind Shock = Stagnation pressure ahead of shock/(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds))

New Pressure after Shock Formation, Subtracted to Velocity for Expansion Wave

Go Pressure = Density ahead of shock*(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds))

Pressure Ratio for Unsteady Waves with Subtracted Induced Mass Motion for Expansion Waves

Go Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Ratio of New and Old Temperature for Expansion Waves

Go Temperature Ratio across Shock = (1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2)

Temperature Ratio for Unsteady Expansion Wave

Go Temperature Ratio = (1-((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^2

Density before Shock Formation for Expansion Wave Formula

What is specific heat ratio?

In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV).

How to Calculate Density before Shock Formation for Expansion Wave?

Density before Shock Formation for Expansion Wave calculator uses Density behind Shock = Stagnation pressure ahead of shock/(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds)) to calculate the Density behind Shock, The Density before shock formation for expansion wave formula is defined as the interrelation between specific heat ratio , speed of sound during the unsteady waves and normal velocity and old speed of sound and pressure after shock formation. Density behind Shock is denoted by ρ₂ symbol.

How to calculate Density before Shock Formation for Expansion Wave using this online calculator? To use this online calculator for Density before Shock Formation for Expansion Wave, enter Stagnation pressure ahead of shock (p₀₁), Specific Heat Ratio (γ), Normal velocity (Vn), Old Speed of Sound (c_old) & Time in seconds (t_sec) and hit the calculate button. Here is how the Density before Shock Formation for Expansion Wave calculation can be explained with given input values -> 83.1633 = 100/(1-((1.6-1)/2)*(1000/342))^(2*1.6/(1.6-38)).

FAQ

What is Density before Shock Formation for Expansion Wave?

The Density before shock formation for expansion wave formula is defined as the interrelation between specific heat ratio , speed of sound during the unsteady waves and normal velocity and old speed of sound and pressure after shock formation and is represented as ρ₂ = p₀₁/(1-((γ-1)/2)*(Vn/c_old))^(2*γ/(γ-t_sec)) or Density behind Shock = Stagnation pressure ahead of shock/(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds)). Stagnation pressure ahead of shock is the stagnation or total or pitot pressure before a shockwave has occurred, The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume, Normal velocity is the velocity normal to the shock formation, Old speed of sound is the speed of sound before the shock & Time in seconds is what a clock reads, it is a scalar quantity.

How to calculate Density before Shock Formation for Expansion Wave?

The Density before shock formation for expansion wave formula is defined as the interrelation between specific heat ratio , speed of sound during the unsteady waves and normal velocity and old speed of sound and pressure after shock formation is calculated using Density behind Shock = Stagnation pressure ahead of shock/(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds)). To calculate Density before Shock Formation for Expansion Wave, you need Stagnation pressure ahead of shock (p₀₁), Specific Heat Ratio (γ), Normal velocity (Vn), Old Speed of Sound (c_old) & Time in seconds (t_sec). With our tool, you need to enter the respective value for Stagnation pressure ahead of shock, Specific Heat Ratio, Normal velocity, Old Speed of Sound & Time in seconds 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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