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)*Mr^(2)+2))/(2*Y*Mr^(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 of any component is nothing but ratio of its velocity to velocity of sound.
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)*Mr^(2)+2))/(2*Y*Mr^(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)

Credits

Created by Abhinav Gupta
Defence institute of advanced technology (DRDO) (DIAT), pune
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Verified by Peri Krishna Karthik
National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala
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17 Preliminary Aerodynamics Calculators

Power required at sea-level conditions
Go Power required at sea-level = sqrt((2*Weight of body^3*Drag Coefficient^2)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient^3))
Mach Number-2
Go Mach number 2 = sqrt(((((Heat Capacity Ratio-1)*Mach Number^(2)+2))/(2*Heat Capacity Ratio*Mach Number^(2)-(Heat Capacity Ratio-1))))
Power required at Altitude
Go Power required at an altitude = sqrt((2*Weight of body^3*Drag Coefficient^2)/(Density*Reference Area*Lift Coefficient^3))
Velocity at Sea-level given Lift Coefficient
Go Velocity at sea-level = sqrt((2*Weight of body)/([Std-Air-Density-Sea]*Reference Area*Lift Coefficient))
Dynamic pressure given gas constant
Go Dynamic Pressure = 1/2*Ambient air density*Mach Number^2*Specific Heat of Air*Gas Constant*Temperature
Velocity at Altitude
Go Velocity at an altitude = sqrt(2*Weight of body/(Density*Reference Area*Lift Coefficient))
Power required at Altitude given Power at sea-level
Go Power required at an altitude = Power required at sea-level*sqrt([Std-Air-Density-Sea]/Density)
Velocity at Altitude given Velocity at Sea-Level
Go Velocity at an altitude = Velocity at sea-level*sqrt([Std-Air-Density-Sea]/Density)
Dynamic pressure given induced drag
Go Dynamic Pressure = Lift Force^2/(pi*Induced Drag*Lateral plane span^2)
Dynamic pressure given mach number
Go Dynamic Pressure = 1/2*Ambient air density*(Mach Number*Sonic speed)^2
Dynamic pressure given normal pressure
Go Dynamic Pressure = 1/2*Specific Heat of Air*Pressure*Mach Number^2
Flight speed given dynamic pressure
Go Flight speed = sqrt((2*Dynamic Pressure)/Ambient air density)
Dynamic pressure aircraft
Go Dynamic Pressure = 1/2*Ambient air density*Flight speed^2
Dynamic pressure given lift coefficient
Go Dynamic Pressure = Lift Force/Lift Coefficient
Dynamic pressure given drag coefficient
Go Dynamic Pressure = Drag Force/Drag Coefficient
Aerodynamic force
Go Aerodynamic Force = Drag Force+Lift Force
Mach number of moving object
Go Mach Number = Velocity/Speed of Sound

Mach Number-2 Formula

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)*Mr^(2)+2))/(2*Y*Mr^(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, The Mach Number-2 is calculated with the help of an established relationship between mach number 1 and mach number 2. 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 (Mr) 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?
The Mach Number-2 is calculated with the help of an established relationship between mach number 1 and mach number 2 and is represented as M = sqrt(((((Y-1)*Mr^(2)+2))/(2*Y*Mr^(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?
The Mach Number-2 is calculated with the help of an established relationship between mach number 1 and mach number 2 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 (Mr). 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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