Mach Number behind Shock Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
M2 = ((2+γ*M1^2-M1^2)/(2*γ*M1^2-γ+1))^(1/2)
This formula uses 3 Variables
Variables Used
Mach Number Behind Normal Shock - Mach Number Behind Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound 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
M2 = ((2+γ*M1^2-M1^2)/(2*γ*M1^2-γ+1))^(1/2) --> ((2+1.4*1.49^2-1.49^2)/(2*1.4*1.49^2-1.4+1))^(1/2)
Evaluating ... ...
M2 = 0.704658912439046
STEP 3: Convert Result to Output's Unit
0.704658912439046 --> No Conversion Required
FINAL ANSWER
0.704658912439046 0.704659 <-- Mach Number Behind Normal Shock
(Calculation completed in 00.004 seconds)

Credits

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 Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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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

Mach Number behind Shock Formula

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)
M2 = ((2+γ*M1^2-M1^2)/(2*γ*M1^2-γ+1))^(1/2)

What is the regime of Mach number behind a normal shock?

The Mach number behind a normal shock is always subsonic since there is a loss in speed of body after the shockwave.

How to Calculate Mach Number behind Shock?

Mach Number behind Shock calculator uses 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) to calculate the Mach Number Behind Normal Shock, The Mach Number behind Shock calculates the Mach number of a fluid behind a normal shock wave. It utilizes parameters such as the Mach number ahead of the shock and the ratio of specific heats for the fluid. This formula provides insight into the change in Mach number as the fluid passes through the shock wave, aiding in the analysis of compressible flow behavior. Mach Number Behind Normal Shock is denoted by M2 symbol.

How to calculate Mach Number behind Shock using this online calculator? To use this online calculator for Mach Number behind Shock, enter Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M1) and hit the calculate button. Here is how the Mach Number behind Shock calculation can be explained with given input values -> 0.704659 = ((2+1.4*1.49^2-1.49^2)/(2*1.4*1.49^2-1.4+1))^(1/2).

FAQ

What is Mach Number behind Shock?
The Mach Number behind Shock calculates the Mach number of a fluid behind a normal shock wave. It utilizes parameters such as the Mach number ahead of the shock and the ratio of specific heats for the fluid. This formula provides insight into the change in Mach number as the fluid passes through the shock wave, aiding in the analysis of compressible flow behavior and is represented as M2 = ((2+γ*M1^2-M1^2)/(2*γ*M1^2-γ+1))^(1/2) or 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). 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 Mach Number behind Shock?
The Mach Number behind Shock calculates the Mach number of a fluid behind a normal shock wave. It utilizes parameters such as the Mach number ahead of the shock and the ratio of specific heats for the fluid. This formula provides insight into the change in Mach number as the fluid passes through the shock wave, aiding in the analysis of compressible flow behavior is calculated using 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). To calculate Mach Number behind 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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