Relation between Mach Number and Characteristic Mach Number Calculator

✖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%

✖Characteristic Mach number is defined as the speed of an object to the speed of sound at the sonic condition.ⓘ Relation between Mach Number and Characteristic Mach Number [M_cr]

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Relation between Mach Number and Characteristic Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5
M_cr = ((γ+1)/(γ-1+2/(M^2)))^0.5
This formula uses 3 Variables

Variables Used

Characteristic Mach Number - Characteristic Mach number is defined as the speed of an object to the speed of sound at the sonic condition.
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

Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number: 1.03 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_cr = ((γ+1)/(γ-1+2/(M^2)))^0.5 --> ((1.4+1)/(1.4-1+2/(1.03^2)))^0.5

Evaluating ... ...

M_cr = 1.02481220882507

STEP 3: Convert Result to Output's Unit

1.02481220882507 --> No Conversion Required

FINAL ANSWER

1.02481220882507 ≈ 1.024812 <-- Characteristic Mach Number

(Calculation completed in 00.004 seconds)

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Created by Vinay Mishra

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

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Relation between Mach Number and Characteristic Mach Number

LaTeX Go Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5

Downstream Velocity using Prandtl Relation

LaTeX Go Velocity Downstream of Shock = (Critical Speed of Sound^2)/Velocity Upstream of Shock

Upstream Velocity using Prandtl Relation

LaTeX Go Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock

Characteristic Mach Number

LaTeX Go Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound

Relation between Mach Number and Characteristic Mach Number Formula

LaTeX Go

Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5
M_cr = ((γ+1)/(γ-1+2/(M^2)))^0.5

How is the Characteristic Mach number different from the actual Mach number?

Qualitatively, the Characteristic Mach number behaves in the same manner as the actual Mach number, except when the actual Mach number goes to infinity. Characteristic Mach number is a useful parameter while dealing with shocks and expansion waves because it approaches a finite value as the actual Mach number approaches infinity.

How to Calculate Relation between Mach Number and Characteristic Mach Number?

Relation between Mach Number and Characteristic Mach Number calculator uses Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5 to calculate the Characteristic Mach Number, The Relation between Mach Number and Characteristic Mach Number calculates the characteristic Mach number of a fluid at a normal shock wave based on the Mach number of the flow. This formula incorporates the ratio of specific heats for the fluid and provides insight into the relationship between the Mach number and the characteristic Mach number under compressible flow conditions. Characteristic Mach Number is denoted by M_cr symbol.

How to calculate Relation between Mach Number and Characteristic Mach Number using this online calculator? To use this online calculator for Relation between Mach Number and Characteristic Mach Number, enter Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button. Here is how the Relation between Mach Number and Characteristic Mach Number calculation can be explained with given input values -> 1.024812 = ((1.4+1)/(1.4-1+2/(1.03^2)))^0.5.

FAQ

What is Relation between Mach Number and Characteristic Mach Number?

The Relation between Mach Number and Characteristic Mach Number calculates the characteristic Mach number of a fluid at a normal shock wave based on the Mach number of the flow. This formula incorporates the ratio of specific heats for the fluid and provides insight into the relationship between the Mach number and the characteristic Mach number under compressible flow conditions and is represented as M_cr = ((γ+1)/(γ-1+2/(M^2)))^0.5 or Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5. 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 Relation between Mach Number and Characteristic Mach Number?

The Relation between Mach Number and Characteristic Mach Number calculates the characteristic Mach number of a fluid at a normal shock wave based on the Mach number of the flow. This formula incorporates the ratio of specific heats for the fluid and provides insight into the relationship between the Mach number and the characteristic Mach number under compressible flow conditions is calculated using Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5. To calculate Relation between Mach Number and Characteristic Mach Number, you need Specific Heat Ratio (γ) & Mach Number (M). With our tool, you need to enter the respective value for 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 Characteristic Mach Number?

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

Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound

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