Exact Pressure Ratio Calculator

✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows.ⓘ Specific Heat Ratio [Y]			+10% -10%
✖The Mach Number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.ⓘ Mach Number [M]			+10% -10%
✖The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.ⓘ Wave Angle [β]			+10% -10%

✖The Pressure Ratio is the comparison of pressures before and after an oblique shock wave, indicating changes in fluid dynamics during hypersonic flow.ⓘ Exact Pressure Ratio [r_p]

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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 - The Pressure Ratio is the comparison of pressures before and after an oblique shock wave, indicating changes in fluid dynamics during hypersonic flow.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows.
Mach Number - The Mach Number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.
Wave Angle - (Measured in Radian) - The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Mach Number: 8 --> No Conversion Required
Wave Angle: 0.5 Radian --> 0.5 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(0.5))^2-1)

Evaluating ... ...

r_p = 17.8742476458087

STEP 3: Convert Result to Output's Unit

17.8742476458087 --> No Conversion Required

FINAL ANSWER

17.8742476458087 ≈ 17.87425 <-- Pressure Ratio

(Calculation completed in 00.004 seconds)

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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

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< Oblique Shock Relation Calculators

Parallel Upstream Flow Components after Shock as Mach Tends to Infinite

LaTeX 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

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

Wave Angle for Small Deflection Angle

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

Coefficient of Pressure Derived from Oblique Shock Theory

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

Exact Pressure Ratio Formula

LaTeX Go

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, Exact Pressure Ratio formula is defined as a dimensionless quantity that characterizes the compression of a flow across an oblique shock wave, providing a crucial parameter in the analysis of high-speed fluid flows and their applications in aerospace engineering. 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 -> 17.87425 = 1+2*1.6/(1.6+1)*((8*sin(0.5))^2-1).

FAQ

What is Exact Pressure Ratio?

Exact Pressure Ratio formula is defined as a dimensionless quantity that characterizes the compression of a flow across an oblique shock wave, providing a crucial parameter in the analysis of high-speed fluid flows and their applications in aerospace engineering 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 is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows, The Mach Number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium & The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.

How to calculate Exact Pressure Ratio?

Exact Pressure Ratio formula is defined as a dimensionless quantity that characterizes the compression of a flow across an oblique shock wave, providing a crucial parameter in the analysis of high-speed fluid flows and their applications in aerospace engineering 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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