Exact relation for pressure coefficient behind an oblique shock wave Calculator

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Mechanical	Fluid Mechanics ↺
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Hypersonic-Flow	oblique shock relation ↺

✖The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volumeⓘ Specific Heat Ratio [γ]			+10% -10%
✖Wave angle is the shock angle created by the oblique shock, this is not similar to the mach angleⓘ Wave angle [β]			+10% -10%
✖Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of soundⓘ Mach Number [M]			+10% -10%

✖Pressure coefficient defines the value of local pressure at a point in terms of free stream pressure and dynamic pressure.ⓘ Exact relation for pressure coefficient behind an oblique shock wave [C_p]

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Exact relation for pressure coefficient behind an oblique shock wave

Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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

Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

Rushi Shah has verified this Calculator and 100+ more calculators!

< 11 Other formulas that you can solve using the same Inputs

Exact Density Ratio

Density ratio=((Specific Heat Ratio+1)*((Mach Number*(sin(Wave angle)))^2))/((Specific Heat Ratio-1)*((Mach Number*(sin(Wave angle)))^2)+2) GO

Ratio of stagnation and static pressure

Stagnation to Static Pressure=(1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(Specific Heat Ratio/(Specific Heat Ratio-1)) GO

Ratio of Stagnation and Static Density

Stagnation to Static Density=(1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(1/(Specific Heat Ratio-1)) GO

Deflection angle

deflection angle=(2/(Specific Heat Ratio-1))*((1/Mach Number ahead of shock)-(1/Mach Number behind shock)) GO

Relation between Characteristic Mach number and Mach number

Characteristic Mach number=((Specific heat ratio+1)/((Specific heat ratio-1)+(2/(Mach Number^2))))^0.5 GO

Exact pressure ratio

pressure ratio=1+(2*Specific Heat Ratio/(Specific Heat Ratio+1))*(((Mach Number*sin(Wave angle))^2)-1) GO

Pressure ratio when Mach becomes infinite

pressure ratio=(2*Specific Heat Ratio/(Specific Heat Ratio+1))*((Mach Number*sin(Wave angle))^2) GO

Mach number

Mach Number=Fluid Velocity/(sqrt(Specific Heat Ratio*Universal Gas Constant*final temp.)) GO

Ratio of Stagnation and Static Temperature

Stagnation to Static Temperature=1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)) GO

Speed of Sound

Speed of Sound=sqrt(Specific Heat Ratio*[R-Dry-Air]*Temperature of Gas) GO

Mach Angle

Mach Angle=asin(1/Mach Number) GO

< 11 Other formulas that calculate the same Output

Coefficient of pressure with similarity parameters

Pressure coefficient=(2*(Flow Deflection angle)^2)*(((Specific Heat Ratio+1)/4)+sqrt((((Specific Heat Ratio+1)/4)^2)+(1/(Hypersonic similarity parameter)^2))) GO

Coefficient of pressure with slenderness ratio

Pressure coefficient=(2/Specific Heat Ratio*Mach Number^2)*(Non-dimensionalized Pressure*Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)-1) GO

Coefficient of pressure with slenderness ratio

Pressure coefficient=2*(Slenderness Ratio^2)*(Non-dimensionalized Pressure-(1/(Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)))) GO

Pressure coefficient for slender bodies of revolution

Pressure coefficient=2*(Angle of Deflection^2)+(Curvature of the surface *Distance of Point from Centroidal Axis) GO

Pressure coefficient for slender 2-D bodies

Pressure coefficient=2*((deflection angle^2)+(Curvature of the surface *Distance of Point from Centroidal Axis)) GO

Modified Newtonian Law

Pressure coefficient=The maximum pressure coefficient*(sin(deflection angle))^2 GO

Exact relation for pressure coefficient behind an oblique shock wave when Mach no. tends to infinite

Pressure coefficient=(4/(Specific Heat Ratio+1))*(sin(Wave angle))^2 GO

Supersonic expression for pressure coefficient on a surface with local deflection angle θ

Pressure coefficient=(2*deflection angle)/(sqrt(Mach Number^2-1)) GO

Non-dimensional pressure coefficient

Pressure coefficient=Change in static pressure/Dynamic Pressure GO

Newtonian sine-squared law for pressure coefficient

Pressure coefficient=2*(sin(deflection angle))^2 GO

Coefficient of pressure derived from oblique shock theory

Pressure coefficient=2*(sin(Wave angle))^2 GO

Exact relation for pressure coefficient behind an oblique shock wave Formula

Pressure coefficient=(4/(Specific Heat Ratio+1))*(((sin(Wave angle))^2)-(1/Mach Number^2))
C<sub>p</sub>=(4/(γ+1))*(((sin(β))^2)-(1/M^2))

More formulas

Exact pressure ratio GO

Pressure ratio when Mach becomes infinite GO

Exact Density Ratio GO

Density ratio when Mach become infinite GO

Temperature ratios GO

Temperature ratio when Mach becomes infinite GO

Non-dimensional pressure coefficient GO

Velocity of sound using dynamic pressure and density GO

Dynamic pressure for given specific heat ratio and Mach number GO

Exact relation for pressure coefficient behind an oblique shock wave when Mach no. tends to infinite GO

Wave angle for small deflection angle GO

Coefficient of pressure derived from oblique shock theory GO

Parallel upstream flow components after shock as Mach tends to infinite GO

Perpendicular upstream flow components behind the shock wave GO

What is a pressure coefficient?

The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid flow field has its own unique pressure coefficient.

How to Calculate Exact relation for pressure coefficient behind an oblique shock wave?

Exact relation for pressure coefficient behind an oblique shock wave calculator uses Pressure coefficient=(4/(Specific Heat Ratio+1))*(((sin(Wave angle))^2)-(1/Mach Number^2)) to calculate the Pressure coefficient, The Exact relation for pressure coefficient behind an oblique shock wave formula is defined as is the interrelation between specific heat ratio and Mach Number. Pressure coefficient and is denoted by C_p symbol.

How to calculate Exact relation for pressure coefficient behind an oblique shock wave using this online calculator? To use this online calculator for Exact relation for pressure coefficient behind an oblique shock wave, enter Specific Heat Ratio (γ), Wave angle (β) and Mach Number (M) and hit the calculate button. Here is how the Exact relation for pressure coefficient behind an oblique shock wave calculation can be explained with given input values -> -1.492071 = (4/(1.6+1))*(((sin(10))^2)-(1/1^2)).

FAQ

What is Exact relation for pressure coefficient behind an oblique shock wave?

The Exact relation for pressure coefficient behind an oblique shock wave formula is defined as is the interrelation between specific heat ratio and Mach Number and is represented as C_p=(4/(γ+1))*(((sin(β))^2)-(1/M^2)) or Pressure coefficient=(4/(Specific Heat Ratio+1))*(((sin(Wave angle))^2)-(1/Mach Number^2)). The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume, Wave angle is the shock angle created by the oblique shock, this is not similar to the mach angle and Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Exact relation for pressure coefficient behind an oblique shock wave?

The Exact relation for pressure coefficient behind an oblique shock wave formula is defined as is the interrelation between specific heat ratio and Mach Number is calculated using Pressure coefficient=(4/(Specific Heat Ratio+1))*(((sin(Wave angle))^2)-(1/Mach Number^2)). To calculate Exact relation for pressure coefficient behind an oblique shock wave, you need Specific Heat Ratio (γ), Wave angle (β) and Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio, Wave angle and 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 Pressure coefficient?

In this formula, Pressure coefficient uses Specific Heat Ratio, Wave angle and Mach Number. We can use 11 other way(s) to calculate the same, which is/are as follows -

Pressure coefficient=Change in static pressure/Dynamic Pressure
Pressure coefficient=(4/(Specific Heat Ratio+1))*(sin(Wave angle))^2
Pressure coefficient=(2*(Flow Deflection angle)^2)*(((Specific Heat Ratio+1)/4)+sqrt((((Specific Heat Ratio+1)/4)^2)+(1/(Hypersonic similarity parameter)^2)))
Pressure coefficient=2*(sin(deflection angle))^2
Pressure coefficient=(2*deflection angle)/(sqrt(Mach Number^2-1))
Pressure coefficient=The maximum pressure coefficient*(sin(deflection angle))^2
Pressure coefficient=2*((deflection angle^2)+(Curvature of the surface *Distance of Point from Centroidal Axis))
Pressure coefficient=2*(Angle of Deflection^2)+(Curvature of the surface *Distance of Point from Centroidal Axis)
Pressure coefficient=2*(sin(Wave angle))^2
Pressure coefficient=2*(Slenderness Ratio^2)*(Non-dimensionalized Pressure-(1/(Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2))))
Pressure coefficient=(2/Specific Heat Ratio*Mach Number^2)*(Non-dimensionalized Pressure*Specific Heat Ratio*(Mach Number^2)*(Slenderness Ratio^2)-1)

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