Exact Pressure Ratio Calculator

✖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 [Y]			+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%
✖Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.ⓘ Wave Angle [β]			+10% -10%

✖Pressure Ratio is ratio of final to initial pressure.ⓘ Exact Pressure Ratio [r_p]

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Formula

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Exact Pressure Ratio

Formula

`"r"_{"p"} = 1+2*"Y"/("Y"+1)*(("M"*sin("β"))^2-1)`

Example

`"6.038473"=1+2*"1.6"/("1.6"+1)*(("8"*sin("0.286rad"))^2-1)`

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Exact Pressure Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1)
r_p = 1+2*Y/(Y+1)*((M*sin(β))^2-1)
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Pressure Ratio - Pressure Ratio is ratio of final to initial pressure.
Specific Heat Ratio - 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.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
Wave Angle - (Measured in Radian) - Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Mach Number: 8 --> No Conversion Required
Wave Angle: 0.286 Radian --> 0.286 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_p = 1+2*Y/(Y+1)*((M*sin(β))^2-1) --> 1+2*1.6/(1.6+1)*((8*sin(0.286))^2-1)

Evaluating ... ...

r_p = 6.03847274405726

STEP 3: Convert Result to Output's Unit

6.03847274405726 --> No Conversion Required

FINAL ANSWER

6.03847274405726 ≈ 6.038473 <-- Pressure Ratio

(Calculation completed in 00.004 seconds)

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Credits

Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has created this Calculator and 300+ more calculators!

Verified by Rushi Shah

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

Rushi Shah has verified this Calculator and 200+ more calculators!

< 15 Oblique Shock Relation Calculators

Exact Density Ratio

Go Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2)

Temperature Ratio when Mach Becomes Infinite

Go Temperature Ratio = (2*Specific Heat Ratio*(Specific Heat Ratio-1))/(Specific Heat Ratio+1)^2*(Mach Number*sin(Wave Angle))^2

Exact Pressure Ratio

Go Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1)

Pressure Ratio when Mach becomes Infinite

Go Pressure Ratio = (2*Specific Heat Ratio)/(Specific Heat Ratio+1)*(Mach Number*sin(Wave Angle))^2

Parallel Upstream Flow Components after Shock as Mach Tends to Infinite

Go Parallel upstream flow components = Velocity of the fluid at 1*(1-(2*(sin(Wave Angle))^2)/(Specific Heat Ratio-1))

Perpendicular Upstream Flow Components behind Shock Wave

Go Perpendicular upstream flow components = (Velocity of the fluid at 1*(sin(2*Wave Angle)))/(Specific Heat Ratio-1)

Pressure Coefficient behind Oblique Shock Wave

Go Pressure Coefficient = 4/(Specific Heat Ratio+1)*((sin(Wave Angle))^2-1/Mach Number^2)

Wave Angle for Small Deflection Angle

Go Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180

Velocity of Sound using Dynamic Pressure and Density

Go Speed of Sound = sqrt((Specific Heat Ratio*Pressure)/Density)

Dynamic Pressure for given Specific Heat Ratio and Mach Number

Go Dynamic Pressure = Specific Heat Ratio Dynamic*Static Pressure*(Mach Number^2)/2

Pressure Coefficient behind Oblique Shock Wave for Infinite Mach Number

Go Pressure Coefficient = 4/(Specific Heat Ratio+1)*(sin(Wave Angle))^2

Non-Dimensional Pressure Coefficient

Go Pressure Coefficient = Change in static pressure/Dynamic Pressure

Density Ratio when Mach Becomes Infinite

Go Density Ratio = (Specific Heat Ratio+1)/(Specific Heat Ratio-1)

Temperature Ratios

Go Temperature Ratio = Pressure Ratio/Density Ratio

Coefficient of Pressure Derived from Oblique Shock Theory

Go Pressure Coefficient = 2*(sin(Wave Angle))^2

Exact Pressure Ratio Formula

Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1)
r_p = 1+2*Y/(Y+1)*((M*sin(β))^2-1)

What is exact pressure ratio of oblique shock relation?

Pressure ratio or overall pressure ratio, is the ratio of the stagnation pressure as measured at the front and rear of the body moving in hypersonic flow.

How to Calculate Exact Pressure Ratio?

Exact Pressure Ratio calculator uses Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1) to calculate the Pressure Ratio, The Exact pressure ratio formula is defined as product of specific heat ratio and the mach number of the flow before impact at an angle. Pressure Ratio is denoted by r_p symbol.

How to calculate Exact Pressure Ratio using this online calculator? To use this online calculator for Exact Pressure Ratio, enter Specific Heat Ratio (Y), Mach Number (M) & Wave Angle (β) and hit the calculate button. Here is how the Exact Pressure Ratio calculation can be explained with given input values -> 6.048454 = 1+2*1.6/(1.6+1)*((8*sin(0.286))^2-1).

FAQ

What is Exact Pressure Ratio?

The Exact pressure ratio formula is defined as product of specific heat ratio and the mach number of the flow before impact at an angle and is represented as r_p = 1+2*Y/(Y+1)*((M*sin(β))^2-1) or Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1). 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, Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound & Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.

How to calculate Exact Pressure Ratio?

The Exact pressure ratio formula is defined as product of specific heat ratio and the mach number of the flow before impact at an angle is calculated using Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1). To calculate Exact Pressure Ratio, you need Specific Heat Ratio (Y), Mach Number (M) & Wave Angle (β). With our tool, you need to enter the respective value for Specific Heat Ratio, Mach Number & Wave Angle 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 Ratio?

In this formula, Pressure Ratio uses Specific Heat Ratio, Mach Number & Wave Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Pressure Ratio = (2*Specific Heat Ratio)/(Specific Heat Ratio+1)*(Mach Number*sin(Wave Angle))^2

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