Pressure Coefficient behind Oblique Shock Wave Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pressure Coefficient = 4/(Specific Heat Ratio+1)*((sin(Wave Angle))^2-1/Mach Number^2)
Cp = 4/(Y+1)*((sin(β))^2-1/M^2)
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 Coefficient - Pressure coefficient defines the value of local pressure at a point in terms of free stream pressure and dynamic 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.
Wave Angle - (Measured in Radian) - Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
STEP 1: Convert Input(s) to Base Unit
Specific Heat Ratio: 1.6 --> No Conversion Required
Wave Angle: 0.286 Radian --> 0.286 Radian No Conversion Required
Mach Number: 8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cp = 4/(Y+1)*((sin(β))^2-1/M^2) --> 4/(1.6+1)*((sin(0.286))^2-1/8^2)
Evaluating ... ...
Cp = 0.0984076707823684
STEP 3: Convert Result to Output's Unit
0.0984076707823684 --> No Conversion Required
FINAL ANSWER
0.0984076707823684 0.098408 <-- Pressure Coefficient
(Calculation completed in 00.004 seconds)

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

Pressure Coefficient behind Oblique Shock Wave Formula

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

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 Pressure Coefficient behind Oblique Shock Wave?

Pressure Coefficient behind 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 Pressure Coefficient behind Oblique Shock Wave formula is defined as the interrelation between specific heat ratio and Mach Number. Pressure Coefficient is denoted by Cp symbol.

How to calculate Pressure Coefficient behind Oblique Shock Wave using this online calculator? To use this online calculator for Pressure Coefficient behind Oblique Shock Wave, enter Specific Heat Ratio (Y), Wave Angle (β) & Mach Number (M) and hit the calculate button. Here is how the Pressure Coefficient behind Oblique Shock Wave calculation can be explained with given input values -> 0.098603 = 4/(1.6+1)*((sin(0.286))^2-1/8^2).

FAQ

What is Pressure Coefficient behind Oblique Shock Wave?
The Pressure Coefficient behind Oblique Shock Wave formula is defined as the interrelation between specific heat ratio and Mach Number and is represented as Cp = 4/(Y+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 & Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
How to calculate Pressure Coefficient behind Oblique Shock Wave?
The Pressure Coefficient behind Oblique Shock Wave formula is defined as 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 Pressure Coefficient behind Oblique Shock Wave, you need Specific Heat Ratio (Y), Wave Angle (β) & Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio, Wave Angle & 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 & Mach Number. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Pressure Coefficient = 2*(sin(Wave Angle))^2
  • Pressure Coefficient = Change in static pressure/Dynamic Pressure
  • Pressure Coefficient = 4/(Specific Heat Ratio+1)*(sin(Wave Angle))^2
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!