Mach Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Mach Number = Speed of Object/Speed of Sound
M = Vb/a
This formula uses 3 Variables
Variables Used
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
Speed of Object - (Measured in Meter per Second) - Speed of Object is equal to the distance travelled by the body in one second.
Speed of Sound - (Measured in Meter per Second) - The speed of sound is defined as speed of the dynamic propagation of sound waves.
STEP 1: Convert Input(s) to Base Unit
Speed of Object: 700 Meter per Second --> 700 Meter per Second No Conversion Required
Speed of Sound: 343 Meter per Second --> 343 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
M = Vb/a --> 700/343
Evaluating ... ...
M = 2.04081632653061
STEP 3: Convert Result to Output's Unit
2.04081632653061 --> No Conversion Required
FINAL ANSWER
2.04081632653061 2.040816 <-- Mach Number
(Calculation completed in 00.004 seconds)

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 Maiarutselvan V
PSG College of Technology (PSGCT), Coimbatore
Maiarutselvan V has verified this Calculator and 300+ more calculators!

19 Thermodynamics and Governing Equations Calculators

Max work output in Brayton cycle
Go Maximum Work done in Brayton Cycle = (1005*1/Compressor Efficiency)*Temperature at Inlet of Compressor in Brayton*(sqrt(Temperature at Inlet to Turbine in Brayton Cycle/Temperature at Inlet of Compressor in Brayton*Compressor Efficiency*Turbine Efficiency)-1)^2
Choked Mass Flow Rate given specific heat ratio
Go Choked Mass Flow Rate = (Heat Capacity Ratio/(sqrt(Heat Capacity Ratio-1)))*((Heat Capacity Ratio+1)/2)^(-((Heat Capacity Ratio+1)/(2*Heat Capacity Ratio-2)))
Choked Mass Flow Rate
Go Choked Mass Flow Rate = (Mass Flow Rate*sqrt(Specific Heat Capacity at Constant Pressure*Temperature))/(Nozzle Throat Area*Throat Pressure)
Stagnation Velocity of Sound given Specific Heat at Constant Pressure
Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Specific Heat Capacity at Constant Pressure*Stagnation Temperature)
Specific Heat of mixed out gas
Go Specific Heat of Mixed Gas = (Specific Heat of Core Gas+Bypass Ratio*Specific Heat of Bypass Air)/(1+Bypass Ratio)
Stagnation Temperature
Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)
Stagnation Velocity of Sound
Go Stagnation Velocity of Sound = sqrt(Heat Capacity Ratio*[R]*Stagnation Temperature)
Speed of Sound
Go Speed of Sound = sqrt(Heat Capacity Ratio*[R-Dry-Air]*Static Temperature)
Stagnation Velocity of Sound given Stagnation Enthalpy
Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Stagnation Enthalpy)
Heat Capacity Ratio
Go Heat Capacity Ratio = Specific Heat Capacity at Constant Pressure/Specific Heat Capacity at Constant Volume
Efficiency of cycle
Go Efficiency of Cycle = (Turbine Work-Compressor Work)/Heat
Internal Energy of Perfect Gas at given Temperature
Go Internal Energy = Specific Heat Capacity at Constant Volume*Temperature
Enthalpy of Ideal Gas at given Temperature
Go Enthalpy = Specific Heat Capacity at Constant Pressure*Temperature
Stagnation enthalpy
Go Stagnation Enthalpy = Enthalpy+(Velocity of Fluid Flow^2)/2
Efficiency of Joule cycle
Go Efficiency of Joule Cycle = Net Work Output/Heat
Pressure Ratio
Go Pressure Ratio = Final Pressure/Initial Pressure
Work ratio in practical cycle
Go Work Ratio = 1-(Compressor Work/Turbine Work)
Mach Number
Go Mach Number = Speed of Object/Speed of Sound
Mach Angle
Go Mach Angle = asin(1/Mach Number)

11 Dimensionless Numbers Calculators

Archimedes Number
Go Archimedes Number = ([g]*Characteristic Length^(3)*Density of Fluid*(Density of Body-Density of Fluid))/(Dynamic Viscosity)^(2)
Sommerfeld Number
Go Sommerfeld Number = ((Radius of Shaft/Radial Clearance)^(2))*(Absolute Viscosity*Speed of Rotating Shaft)/(Load per Unit of Area)
Reynolds Number
Go Reynolds Number = (Density of Liquid*Fluid Velocity*Pipe Diameter)/Dynamic Viscosity
Euler Number using Fluid Velocity
Go Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid))
Weber Number
Go Weber Number = ((Density*(Velocity of Fluid^2)*Length)/Surface Tension)
Eckert Number
Go Eckert Number = (Flow Velocity)^2/(Specific Heat Capacity*Temperature Difference)
Grashof Number
Go Grashof Number = (Buoyant Force)/(Viscous Force)
Rayleigh Number
Go Rayleigh Number = Grashof Number*Prandtl Number
Mach Number
Go Mach Number = Speed of Object/Speed of Sound
Froude Number
Go Froude Number = Inertia Force/Gravity Force
Euler Number
Go Euler Number = Pressure Force/Inertia Force

18 Governing Equations and Sound Wave Calculators

Speed of Sound Downstream of Sound Wave
Go Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))
Speed of Sound Upstream of Sound Wave
Go Sound Speed Upstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Downstream of Sound^2-Flow Velocity Upstream of Sound^2)/2+Sound Speed Downstream^2/(Specific Heat Ratio-1)))
Flow Velocity Downstream of Sound Wave
Go Flow Velocity Downstream of Sound = sqrt(2*((Sound Speed Upstream^2-Sound Speed Downstream^2)/(Specific Heat Ratio-1)+Flow Velocity Upstream of Sound^2/2))
Flow Velocity Upstream of Sound Wave
Go Flow Velocity Upstream of Sound = sqrt(2*((Sound Speed Downstream^2-Sound Speed Upstream^2)/(Specific Heat Ratio-1)+Flow Velocity Downstream of Sound^2/2))
Ratio of Stagnation and Static Pressure
Go Stagnation to Static Pressure = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(Specific Heat Ratio/(Specific Heat Ratio-1))
Critical Pressure
Go Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure
Stagnation Temperature
Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)
Speed of Sound
Go Speed of Sound = sqrt(Heat Capacity Ratio*[R-Dry-Air]*Static Temperature)
Ratio of Stagnation and Static Density
Go Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))
Critical Density
Go Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))
Mayer's Formula
Go Specific Gas Constant = Specific Heat Capacity at Constant Pressure-Specific Heat Capacity at Constant Volume
Ratio of Stagnation and Static Temperature
Go Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2
Critical Temperature
Go Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)
Isentropic Compressibility for given Density and Speed of Sound
Go Isentropic Compressibility = 1/(Density*Speed of Sound^2)
Mach Number
Go Mach Number = Speed of Object/Speed of Sound
Speed of Sound given Isentropic Change
Go Speed of Sound = sqrt(Isentropic Change)
Mach Angle
Go Mach Angle = asin(1/Mach Number)
Isentropic Change across Sound Wave
Go Isentropic Change = Speed of Sound^2

Mach Number Formula

Mach Number = Speed of Object/Speed of Sound
M = Vb/a

Where do we have the value of Mach number as 1?

If the Mach number is ~ 1, the flow speed is approximately like the speed of sound - and the speed is transonic. If the Mach number is > 1, the flow speed is higher than the speed of sound - and the speed is supersonic.

What is Mach number in aircraft?

The ratio between the true airspeed (TAS) and the local speed of sound (LSS). This ratio, which equals one when the TAS is equal to the LSS, is known as the Mach Number (M) and is very important in aircraft operating at high speed.

How to Calculate Mach Number?

Mach Number calculator uses Mach Number = Speed of Object/Speed of Sound to calculate the Mach Number, The Mach Number is defined as the ratio of the speed of a body to the speed of sound in the surrounding medium. Mach Number is denoted by M symbol.

How to calculate Mach Number using this online calculator? To use this online calculator for Mach Number, enter Speed of Object (Vb) & Speed of Sound (a) and hit the calculate button. Here is how the Mach Number calculation can be explained with given input values -> 2.040816 = 700/343.

FAQ

What is Mach Number?
The Mach Number is defined as the ratio of the speed of a body to the speed of sound in the surrounding medium and is represented as M = Vb/a or Mach Number = Speed of Object/Speed of Sound. Speed of Object is equal to the distance travelled by the body in one second & The speed of sound is defined as speed of the dynamic propagation of sound waves.
How to calculate Mach Number?
The Mach Number is defined as the ratio of the speed of a body to the speed of sound in the surrounding medium is calculated using Mach Number = Speed of Object/Speed of Sound. To calculate Mach Number, you need Speed of Object (Vb) & Speed of Sound (a). With our tool, you need to enter the respective value for Speed of Object & Speed of Sound 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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