Characteristic 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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Normal Shock Wave

Governing Equations and Sound Wave

Oblique Shock and Expansion Waves

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Normal Shock Relations

Downstream Shock Waves

Property Change Across Shock Waves

Upstream Shock Waves

✖Fluid Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area.ⓘ Fluid Velocity [u_f]			+10% -10%
✖The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow.ⓘ Critical Speed of Sound [a_cr]			+10% -10%

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

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Formula

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Characteristic Mach Number

Formula

`"M"_{"cr"} = "u"_{"f"}/"a"_{"cr"}`

Example

`"0.150487"="12m/s"/"79.741m/s"`

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Characteristic Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound
M_cr = u_f/a_cr
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.
Fluid Velocity - (Measured in Meter per Second) - Fluid Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area.
Critical Speed of Sound - (Measured in Meter per Second) - The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow.

STEP 1: Convert Input(s) to Base Unit

Fluid Velocity: 12 Meter per Second --> 12 Meter per Second No Conversion Required
Critical Speed of Sound: 79.741 Meter per Second --> 79.741 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_cr = u_f/a_cr --> 12/79.741

Evaluating ... ...

M_cr = 0.150487202317503

STEP 3: Convert Result to Output's Unit

0.150487202317503 --> No Conversion Required

FINAL ANSWER

0.150487202317503 ≈ 0.150487 <-- Characteristic Mach Number

(Calculation completed in 00.004 seconds)

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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

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< 7 Normal Shock Relations Calculators

Enthalpy Difference using Hugoniot Equation

Go Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock))

Relation between Mach Number and Characteristic Mach Number

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

Critical Speed of Sound from Prandtl Relation

Go Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock)

Downstream Velocity using Prandtl Relation

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

Upstream Velocity using Prandtl Relation

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

Mach Number given Impact and Static Pressure

Go Mach Number = (5*((Impact Pressure/Static Pressure+1)^(2/7)-1))^(0.5)

Characteristic Mach Number

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

Characteristic Mach Number Formula

Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound
M_cr = u_f/a_cr

What is the difference between Mach number and Characteristic Mach number?

Characteristic Mach number varies qualitative same as the actual Mach number except that the characteristic Mach number reaches to finite value when actual Mach number reaches infinity.

How to Calculate Characteristic Mach Number?

Characteristic Mach Number calculator uses Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound to calculate the Characteristic Mach Number, The Characteristic Mach number is defined as the ratio of the velocity of the fluid at a given point in flow and the critical speed of sound. Characteristic Mach Number is denoted by M_cr symbol.

How to calculate Characteristic Mach Number using this online calculator? To use this online calculator for Characteristic Mach Number, enter Fluid Velocity (u_f) & Critical Speed of Sound (a_cr) and hit the calculate button. Here is how the Characteristic Mach Number calculation can be explained with given input values -> 0.150487 = 12/79.741.

FAQ

What is Characteristic Mach Number?

The Characteristic Mach number is defined as the ratio of the velocity of the fluid at a given point in flow and the critical speed of sound and is represented as M_cr = u_f/a_cr or Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound. Fluid Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area & The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow.

How to calculate Characteristic Mach Number?

The Characteristic Mach number is defined as the ratio of the velocity of the fluid at a given point in flow and the critical speed of sound is calculated using Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound. To calculate Characteristic Mach Number, you need Fluid Velocity (u_f) & Critical Speed of Sound (a_cr). With our tool, you need to enter the respective value for Fluid Velocity & Critical Speed of Sound 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 Fluid Velocity & Critical Speed of Sound. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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