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Density before Shock Formation for Expansion Wave Formula

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Density behind shock is the density of the fluid in the upstream direction of shock. Check FAQs

ρ 2 = \frac{p 01}{{(1 - (\frac{γ - 1}{2}) \cdot (\frac{Vn}{c old}))}^{2 \cdot \frac{γ}{γ - t sec}}}

ρ₂ - Density Behind Shock?p₀₁ - Stagnation pressure ahead of shock?γ - Specific Heat Ratio?Vn - Normal velocity?c_old - Old Speed of Sound?t_sec - Time in Seconds?

Density before Shock Formation for Expansion Wave Example

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Here is how the Density before Shock Formation for Expansion Wave equation looks like with Values.

Here is how the Density before Shock Formation for Expansion Wave equation looks like with Units.

Here is how the Density before Shock Formation for Expansion Wave equation looks like.

83.1633 = \frac{100}{{(1 - (\frac{1.6 - 1}{2}) \cdot (\frac{1000}{342}))}^{2 \cdot \frac{1.6}{1.6 - 38}}}

83.1633kg/m³ = \frac{100Pa}{{(1 - (\frac{1.6 - 1}{2}) \cdot (\frac{1000m/s}{342m/s}))}^{2 \cdot \frac{1.6}{1.6 - 38s}}}

83.1633 = \frac{100}{{(1 - (\frac{1.6 - 1}{2}) \cdot (\frac{1000}{342}))}^{2 \cdot \frac{1.6}{1.6 - 38}}}

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Density before Shock Formation for Expansion Wave Solution

Follow our step by step solution on how to calculate Density before Shock Formation for Expansion Wave?

FIRST Step Consider the formula

ρ 2 = \frac{p 01}{{(1 - (\frac{γ - 1}{2}) \cdot (\frac{Vn}{c old}))}^{2 \cdot \frac{γ}{γ - t sec}}}

Next Step Substitute values of Variables

∴

ρ 2 = \frac{100Pa}{{(1 - (\frac{1.6 - 1}{2}) \cdot (\frac{1000m/s}{342m/s}))}^{2 \cdot \frac{1.6}{1.6 - 38s}}}

Next Step Prepare to Evaluate

∴

ρ 2 = \frac{100}{{(1 - (\frac{1.6 - 1}{2}) \cdot (\frac{1000}{342}))}^{2 \cdot \frac{1.6}{1.6 - 38}}}

Next Step Evaluate

∴

ρ 2 = 83.1632989062157kg/m³

LAST Step Rounding Answer

∴

ρ 2 = 83.1633kg/m³

Density before Shock Formation for Expansion Wave Formula Elements

Variables

Density Behind Shock

Density behind shock is the density of the fluid in the upstream direction of shock.

Symbol: ρ₂

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Behind Shock

Stagnation pressure ahead of shock

Stagnation pressure ahead of shock is the stagnation or total or pitot pressure before a shockwave has occurred.

Symbol: p₀₁

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Stagnation pressure ahead of shock

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.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Heat Ratio

Normal velocity

Normal velocity is the velocity normal to the shock formation.

Symbol: Vn

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Normal velocity

Old Speed of Sound

Old speed of sound is the speed of sound before the shock.

Symbol: c_old

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Old Speed of Sound

Time in Seconds

Time in seconds is what a clock reads, it is a scalar quantity.

Symbol: t_sec

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time in Seconds

Other formulas in Expansion Waves category

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

P = ρ 1 \cdot {(1 - (\frac{γ - 1}{2}) \cdot (\frac{Vn}{c old}))}^{2 \cdot \frac{γ}{γ - t sec}}

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

r p = {(1 - (\frac{γ - 1}{2}) \cdot (\frac{u'}{c speed}))}^{2 \cdot \frac{γ}{γ - 1}}

Go Ratio of New and Old Temperature for Expansion Waves

Tshock ratio = {(1 - (\frac{γ - 1}{2}) \cdot (\frac{Vn}{c old}))}^{2}

Go Temperature Ratio for Unsteady Expansion Wave

T ratio = {(1 - (\frac{γ - 1}{2}) \cdot (\frac{u'}{c speed}))}^{2}

How to Evaluate Density before Shock Formation for Expansion Wave?

Density before Shock Formation for Expansion Wave evaluator 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 evaluate the Density Behind Shock, Density before Shock Formation for Expansion Wave formula is defined as a measure of the density of a fluid before the formation of a shock wave in hypersonic inviscid flow, which is crucial in understanding the behavior of high-speed fluids and gases in aerospace engineering and other related fields. Density Behind Shock is denoted by ρ₂ symbol.

How to evaluate Density before Shock Formation for Expansion Wave using this online evaluator? To use this online evaluator 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.

FAQs on Density before Shock Formation for Expansion Wave

What is the formula to find Density before Shock Formation for Expansion Wave?

The formula of Density before Shock Formation for Expansion Wave is expressed as 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)). Here is an example- 83.1633 = 100/(1-((1.6-1)/2)*(1000/342))^(2*1.6/(1.6-38)).

How to calculate Density before Shock Formation for Expansion Wave?

With Stagnation pressure ahead of shock (p₀₁), Specific Heat Ratio (γ), Normal velocity (Vn), Old Speed of Sound (c_old) & Time in Seconds (t_sec) we can find Density before Shock Formation for Expansion Wave using the formula - 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)).

Can the Density before Shock Formation for Expansion Wave be negative?

No, the Density before Shock Formation for Expansion Wave, measured in Density cannot be negative.

Which unit is used to measure Density before Shock Formation for Expansion Wave?

Density before Shock Formation for Expansion Wave is usually measured using the Kilogram per Cubic Meter[kg/m³] for Density. Kilogram per Cubic Centimeter[kg/m³], Gram per Cubic Meter[kg/m³], Gram per Cubic Centimeter[kg/m³] are the few other units in which Density before Shock Formation for Expansion Wave can be measured.

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Density before Shock Formation for Expansion Wave Formula

Density before Shock Formation for Expansion Wave Example

Density before Shock Formation for Expansion Wave Solution

Density before Shock Formation for Expansion Wave Formula Elements

Other formulas in Expansion Waves category

How to Evaluate Density before Shock Formation for Expansion Wave?

FAQs on Density before Shock Formation for Expansion Wave

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