Velocity behind 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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Downstream Shock Waves

Normal Shock Relations

Property Change Across Shock Waves

Upstream Shock Waves

✖Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.ⓘ Velocity Upstream of Shock [V₁]			+10% -10%
✖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 is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%

✖Velocity Downstream of Shock is the velocity of flow behind the shock wave.ⓘ Velocity behind Normal Shock [V₂]

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Formula

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Velocity behind Normal Shock

Formula

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

Example

`"76.30065m/s"="80.134m/s"/(("1.4"+1)/(("1.4"-1)+2/(("1.03")^2)))`

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Velocity behind Normal Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))
V₂ = V₁/((γ+1)/((γ-1)+2/(M^2)))
This formula uses 4 Variables

Variables Used

Velocity Downstream of Shock - (Measured in Meter per Second) - Velocity Downstream of Shock is the velocity of flow behind the shock wave.
Velocity Upstream of Shock - (Measured in Meter per Second) - Velocity Upstream of Shock is the velocity of flow ahead of the 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 - Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Velocity Upstream of Shock: 80.134 Meter per Second --> 80.134 Meter per Second No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number: 1.03 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V₂ = V₁/((γ+1)/((γ-1)+2/(M^2))) --> 80.134/((1.4+1)/((1.4-1)+2/(1.03^2)))

Evaluating ... ...

V₂ = 76.3006504854369

STEP 3: Convert Result to Output's Unit

76.3006504854369 Meter per Second --> No Conversion Required

FINAL ANSWER

76.3006504854369 ≈ 76.30065 Meter per Second <-- Velocity Downstream of Shock

(Calculation completed in 00.020 seconds)

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Created by Vinay Mishra

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

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Sai Venkata Phanindra Chary Arendra

Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

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< 15 Downstream Shock Waves Calculators

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula

Go Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1))

Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number

Go Temperature Behind Normal Shock = Temperature Ahead of 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)))

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number

Go Enthalpy Behind Normal Shock = Enthalpy Ahead of 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))

Mach Number behind Shock

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

Velocity behind Normal Shock by Normal Shock Momentum Equation

Go Velocity Downstream of Shock = sqrt((Static Pressure Ahead of Normal Shock-Static pressure Behind Normal shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2)/Density Behind Normal Shock)

Density behind Normal Shock using Normal Shock Momentum Equation

Go Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2)

Static Pressure behind Normal Shock using Normal Shock Momentum Equation

Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Density Behind Normal Shock*Velocity Downstream of Shock^2

Density behind Normal Shock given Upstream Density and Mach Number

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

Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number

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

Velocity behind Normal Shock from Normal Shock Energy Equation

Go Velocity Downstream of Shock = sqrt(2*(Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2)/2-Enthalpy Behind Normal Shock))

Velocity behind Normal Shock

Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))

Enthalpy behind Normal Shock from Normal Shock Energy Equation

Go Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2-Velocity Downstream of Shock^2)/2

Flow Velocity Downstream of Shock Wave using Continuity Equation

Go Velocity Downstream of Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Density Behind Normal Shock

Density Downstream of Shock Wave using Continuity Equation

Go Density Behind Normal Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Velocity Downstream of Shock

Characteristic Mach Number behind Shock

Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Velocity behind Normal Shock Formula

Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))
V₂ = V₁/((γ+1)/((γ-1)+2/(M^2)))

What is a Normal shockwave?

If the shock wave is perpendicular to the flow direction, it is called a normal shockwave. A normal shock occurs in front of a supersonic object if the flow is turned by a large amount and the shock cannot remain attached to the body.

How to Calculate Velocity behind Normal Shock?

Velocity behind Normal Shock calculator uses Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2))) to calculate the Velocity Downstream of Shock, The Velocity behind Normal Shock calculates the velocity of a fluid downstream of a normal shock wave. This formula incorporates parameters such as the velocity upstream of the shock, the ratio of specific heats for the fluid, and the Mach number of the flow. It provides valuable insights into the change in velocity resulting from the passage of the shock wave. Velocity Downstream of Shock is denoted by V₂ symbol.

How to calculate Velocity behind Normal Shock using this online calculator? To use this online calculator for Velocity behind Normal Shock, enter Velocity Upstream of Shock (V₁), Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button. Here is how the Velocity behind Normal Shock calculation can be explained with given input values -> 138.0637 = 80.134/((1.4+1)/((1.4-1)+2/(1.03^2))).

FAQ

What is Velocity behind Normal Shock?

The Velocity behind Normal Shock calculates the velocity of a fluid downstream of a normal shock wave. This formula incorporates parameters such as the velocity upstream of the shock, the ratio of specific heats for the fluid, and the Mach number of the flow. It provides valuable insights into the change in velocity resulting from the passage of the shock wave and is represented as V₂ = V₁/((γ+1)/((γ-1)+2/(M^2))) or Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2))). Velocity Upstream of Shock is the velocity of flow ahead of the shock wave, The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Velocity behind Normal Shock?

The Velocity behind Normal Shock calculates the velocity of a fluid downstream of a normal shock wave. This formula incorporates parameters such as the velocity upstream of the shock, the ratio of specific heats for the fluid, and the Mach number of the flow. It provides valuable insights into the change in velocity resulting from the passage of the shock wave is calculated using Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2))). To calculate Velocity behind Normal Shock, you need Velocity Upstream of Shock (V₁), Specific Heat Ratio (γ) & Mach Number (M). With our tool, you need to enter the respective value for Velocity Upstream of Shock, Specific Heat Ratio & Mach Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Velocity Downstream of Shock?

In this formula, Velocity Downstream of Shock uses Velocity Upstream of Shock, Specific Heat Ratio & Mach Number. We can use 3 other way(s) to calculate the same, which is/are as follows -

Velocity Downstream of Shock = sqrt(2*(Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2)/2-Enthalpy Behind Normal Shock))
Velocity Downstream of Shock = sqrt((Static Pressure Ahead of Normal Shock-Static pressure Behind Normal shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2)/Density Behind Normal Shock)
Velocity Downstream of Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Density Behind Normal Shock

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