Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number 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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Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

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Oblique Shock

Expansion Waves

✖The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Oblique Shock [γ_o]			+10% -10%
✖Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.ⓘ Upstream Mach Normal to Oblique Shock [M_n1]			+10% -10%

✖Downstream Mach Normal to Oblique Shock denotes the Mach number component aligned with the shock wave's normal direction after passing through an oblique shock.ⓘ Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number [M_n2]

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Formula

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Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number

Formula

`"M"_{"n2"} = sqrt((1+0.5*("γ"_{"o"}-1)*"M"_{"n1"}^2)/("γ"_{"o"}*"M"_{"n1"}^2-0.5*("γ"_{"o"}-1)))`

Example

`"0.66664"=sqrt((1+0.5*("1.4"-1)*("1.606")^2)/("1.4"*("1.606")^2-0.5*("1.4"-1)))`

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Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1)))
M_n2 = sqrt((1+0.5*(γ_o-1)*M_n1^2)/(γ_o*M_n1^2-0.5*(γ_o-1)))
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Downstream Mach Normal to Oblique Shock - Downstream Mach Normal to Oblique Shock denotes the Mach number component aligned with the shock wave's normal direction after passing through an oblique shock.
Specific Heat Ratio Oblique Shock - The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Upstream Mach Normal to Oblique Shock - Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio Oblique Shock: 1.4 --> No Conversion Required
Upstream Mach Normal to Oblique Shock: 1.606 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_n2 = sqrt((1+0.5*(γ_o-1)*M_n1^2)/(γ_o*M_n1^2-0.5*(γ_o-1))) --> sqrt((1+0.5*(1.4-1)*1.606^2)/(1.4*1.606^2-0.5*(1.4-1)))

Evaluating ... ...

M_n2 = 0.666639869920256

STEP 3: Convert Result to Output's Unit

0.666639869920256 --> No Conversion Required

FINAL ANSWER

0.666639869920256 ≈ 0.66664 <-- Downstream Mach Normal to Oblique Shock

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT), Bombay

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< 10+ Oblique Shock Calculators

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

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

Flow Deflection Angle due to Oblique Shock

Go Flow Deflection Angle Oblique Shock = atan((2*cot(Oblique Shock Angle)*((Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle))^2-1))/(Mach Number Ahead of Oblique Shock^2*(Specific Heat Ratio Oblique Shock+cos(2*Oblique Shock Angle))+2))

Temperature Ratio across Oblique Shock

Go Temperature Ratio Across Oblique Shock = (1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))

Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number

Go Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1)))

Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number

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

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

Go Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))

Density Ratio across Oblique Shock

Go Density Ratio Across Oblique Shock = (Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)

Component of Downstream Mach Normal to Oblique Shock

Go Downstream Mach Normal to Oblique Shock = Mach Number Behind Oblique Shock*sin(Oblique Shock Angle-Flow Deflection Angle Oblique Shock)

Pressure Ratio across Oblique Shock

Go Pressure Ratio Across Oblique Shock = 1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)

Component of Upstream Mach Normal to Oblique Shock

Go Upstream Mach Normal to Oblique Shock = Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle)

Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number Formula

What happens when flow deflection angle is 0° in supersonic flow?

When flow deflection is 0° then the wave angle will be either 90° or μ. The case of β= 90° corresponds to a normal shock wave and β=μ corresponds to Mach wave. In both cases, the flow streamlines experience no deflection across the wave.

How to Calculate Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number?

Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number calculator uses Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1))) to calculate the Downstream Mach Normal to Oblique Shock, The Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number formula calculates the downstream Mach number component perpendicular to an oblique shock wave, given the upstream Mach number. It reveals how this downstream Mach number is influenced by the initial Mach number and the shock geometry. Downstream Mach Normal to Oblique Shock is denoted by M_n2 symbol.

How to calculate Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number using this online calculator? To use this online calculator for Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number, enter Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) and hit the calculate button. Here is how the Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number calculation can be explained with given input values -> 0.66664 = sqrt((1+0.5*(1.4-1)*1.606^2)/(1.4*1.606^2-0.5*(1.4-1))).

FAQ

What is Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number?

The Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number formula calculates the downstream Mach number component perpendicular to an oblique shock wave, given the upstream Mach number. It reveals how this downstream Mach number is influenced by the initial Mach number and the shock geometry and is represented as M_n2 = sqrt((1+0.5*(γ_o-1)*M_n1^2)/(γ_o*M_n1^2-0.5*(γ_o-1))) or Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1))). The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

How to calculate Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number?

The Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number formula calculates the downstream Mach number component perpendicular to an oblique shock wave, given the upstream Mach number. It reveals how this downstream Mach number is influenced by the initial Mach number and the shock geometry is calculated using Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1))). To calculate Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number, you need Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1). With our tool, you need to enter the respective value for Specific Heat Ratio Oblique Shock & Upstream Mach Normal to Oblique Shock 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 Downstream Mach Normal to Oblique Shock?

In this formula, Downstream Mach Normal to Oblique Shock uses Specific Heat Ratio Oblique Shock & Upstream Mach Normal to Oblique Shock. We can use 1 other way(s) to calculate the same, which is/are as follows -

Downstream Mach Normal to Oblique Shock = Mach Number Behind Oblique Shock*sin(Oblique Shock Angle-Flow Deflection Angle Oblique Shock)

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