Mach Number-2 Calculator

✖The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Heat Capacity Ratio [Y]			+10% -10%
✖Mach Number is a dimensionless quantity defined as ratio of speed of object to speed on sound.ⓘ Mach Number [M_r]			+10% -10%

✖Mach Number 2 is ratio of its velocity to velocity of sound at downstream of point 1.ⓘ Mach Number-2 [M]

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Mach Number-2 Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mach Number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1))))
M = sqrt(((((Y-1)*M_r^(2)+2))/(2*Y*M_r^(2)-(Y-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

Mach Number 2 - Mach Number 2 is ratio of its velocity to velocity of sound at downstream of point 1.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number - Mach Number is a dimensionless quantity defined as ratio of speed of object to speed on sound.

STEP 1: Convert Input(s) to Base Unit

Heat Capacity Ratio: 1.4 --> No Conversion Required
Mach Number: 7.67 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = sqrt(((((Y-1)*M_r^(2)+2))/(2*Y*M_r^(2)-(Y-1)))) --> sqrt(((((1.4-1)*7.67^(2)+2))/(2*1.4*7.67^(2)-(1.4-1))))

Evaluating ... ...

M = 0.39417787762409

STEP 3: Convert Result to Output's Unit

0.39417787762409 --> No Conversion Required

FINAL ANSWER

0.39417787762409 ≈ 0.394178 <-- Mach Number 2

(Calculation completed in 00.004 seconds)

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Created by Abhinav Gupta

Defence institute of advanced technology (DRDO) (DIAT), pune

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< Preliminary Aerodynamics Calculators

Power required at sea-level conditions

LaTeX Go Power Required at Sea-level = sqrt((2*Weight of Body^3*Drag Coefficient^2)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient^3))

Power required at Altitude

LaTeX Go Power Required at Altitude = sqrt((2*Weight of Body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))

Velocity at Sea-Level given Lift Coefficient

LaTeX Go Velocity at Sea-Level = sqrt((2*Weight of Body)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient))

Velocity at Altitude

LaTeX Go Velocity at an Altitude = sqrt(2*Weight of Body/(Density*Reference Area*Lift Coefficient))

Mach Number-2 Formula

LaTeX Go

Mach Number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1))))
M = sqrt(((((Y-1)*M_r^(2)+2))/(2*Y*M_r^(2)-(Y-1))))

Relationship between mach number 2 and mach number 1

Mach number 1 or Mach number 2 can be calculated with the help of relationship between themThe Mach number due to the local speed of sound is dependent on the surrounding mediums in specific temperature and pressure. Flow can be determined as an incompressible flow with the help of the Mach number. The medium can either be a liquid or a gas. The medium can be flowing, whereas the boundary may be stable or the boundary may be travelling in a medium that is at rest. The medium and boundary both may be travelling with a certain speed, but their velocities with respect to each other are what matters. The medium may be channelled through several devices such as wind tunnels or may be immersed in the medium. The Mach number is termed as a dimensionless number because it is a ratio of two speeds

Classification of Mach number as per range

Subsonic:
Commercial aircraft with aerodynamic features such as the rounded nose and leading edges. The Mach is below 0.8.

Transonic:
Aircraft that are built with swept wings. The Mach value is between 0.8-2.1.

Supersonic:
The aircraft created to go supersonic have a definite design, it has the complete movement of the canards, thin aerofoil sections, and sharp edges. The Mach levels are between 1.2 and 5.0.

Hypersonic:
These planes have several distinctive features such as nickel-titanium skin that is cooled and small wings. The Mach values are between 5.0 and 10.0. The U.S. plane X-15 created the world record of flying at Mach 6.72.

High-Hypersonic:
The Mach levels are between 10.0 -25.0. When flying at such huge speeds thermal controls becomes an integral portion of the design. The hotness of the surface must be considered beforehand.

Re-entry speeds:
The Mach speed is above 25.0. This does not require wings and a blunt design.

How to Calculate Mach Number-2?

Mach Number-2 calculator uses Mach Number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1)))) to calculate the Mach Number 2, Mach Number-2 is a measure of the ratio of the velocity of an object to the speed of sound in a given medium, calculated by taking into account the adiabatic index and the Mach number, providing a critical value that determines the characteristics of compressible fluid flow. Mach Number 2 is denoted by M symbol.

How to calculate Mach Number-2 using this online calculator? To use this online calculator for Mach Number-2, enter Heat Capacity Ratio (Y) & Mach Number (M_r) and hit the calculate button. Here is how the Mach Number-2 calculation can be explained with given input values -> 0.394178 = sqrt(((((1.4-1)*7.67^(2)+2))/(2*1.4*7.67^(2)-(1.4-1)))).

FAQ

What is Mach Number-2?

Mach Number-2 is a measure of the ratio of the velocity of an object to the speed of sound in a given medium, calculated by taking into account the adiabatic index and the Mach number, providing a critical value that determines the characteristics of compressible fluid flow and is represented as M = sqrt(((((Y-1)*M_r^(2)+2))/(2*Y*M_r^(2)-(Y-1)))) or Mach Number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1)))). The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number is a dimensionless quantity defined as ratio of speed of object to speed on sound.

How to calculate Mach Number-2?

Mach Number-2 is a measure of the ratio of the velocity of an object to the speed of sound in a given medium, calculated by taking into account the adiabatic index and the Mach number, providing a critical value that determines the characteristics of compressible fluid flow is calculated using Mach Number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1)))). To calculate Mach Number-2, you need Heat Capacity Ratio (Y) & Mach Number (M_r). With our tool, you need to enter the respective value for Heat Capacity Ratio & Mach Number 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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