Non-Dimensional Pressure Coefficient Calculator

✖Change in static pressure is the static pressure change occurring in hypersonic flow after shock occurs.ⓘ Change in static pressure [Δp]			+10% -10%
✖Dynamic Pressure is simply a convenient name for the quantity which represents the decrease in the pressure due to the velocity of the fluid.ⓘ Dynamic Pressure [P_dynamic]			+10% -10%

✖Pressure coefficient defines the value of local pressure at a point in terms of free stream pressure and dynamic pressure.ⓘ Non-Dimensional Pressure Coefficient [C_p]

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Formula

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Non-Dimensional Pressure Coefficient

Formula

`"C"_{"p"} = "Δp"/"P"_{"dynamic"}`

Example

`"0.581395"="5Pa"/"8.6Pa"`

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Non-Dimensional Pressure Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Coefficient = Change in static pressure/Dynamic Pressure
C_p = Δp/P_dynamic
This formula uses 3 Variables

Variables Used

Pressure Coefficient - Pressure coefficient defines the value of local pressure at a point in terms of free stream pressure and dynamic pressure.
Change in static pressure - (Measured in Pascal) - Change in static pressure is the static pressure change occurring in hypersonic flow after shock occurs.
Dynamic Pressure - (Measured in Pascal) - Dynamic Pressure is simply a convenient name for the quantity which represents the decrease in the pressure due to the velocity of the fluid.

STEP 1: Convert Input(s) to Base Unit

Change in static pressure: 5 Pascal --> 5 Pascal No Conversion Required
Dynamic Pressure: 8.6 Pascal --> 8.6 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_p = Δp/P_dynamic --> 5/8.6

Evaluating ... ...

C_p = 0.581395348837209

STEP 3: Convert Result to Output's Unit

0.581395348837209 --> No Conversion Required

FINAL ANSWER

0.581395348837209 ≈ 0.581395 <-- Pressure Coefficient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Oblique Shock Relation » Non-Dimensional Pressure Coefficient

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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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< 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

Non-Dimensional Pressure Coefficient Formula

Pressure Coefficient = Change in static pressure/Dynamic Pressure
C_p = Δp/P_dynamic

What is the pressure coefficient of oblique shock?

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.

How to Calculate Non-Dimensional Pressure Coefficient?

Non-Dimensional Pressure Coefficient calculator uses Pressure Coefficient = Change in static pressure/Dynamic Pressure to calculate the Pressure Coefficient, The Non-dimensional pressure coefficient formula is defined as ratio of change in static pressure of upstream and downstream Mach after shock to the dynamic pressure of the freestream. Pressure Coefficient is denoted by C_p symbol.

How to calculate Non-Dimensional Pressure Coefficient using this online calculator? To use this online calculator for Non-Dimensional Pressure Coefficient, enter Change in static pressure (Δp) & Dynamic Pressure (P_dynamic) and hit the calculate button. Here is how the Non-Dimensional Pressure Coefficient calculation can be explained with given input values -> 0.581395 = 5/8.6.

FAQ

What is Non-Dimensional Pressure Coefficient?

The Non-dimensional pressure coefficient formula is defined as ratio of change in static pressure of upstream and downstream Mach after shock to the dynamic pressure of the freestream and is represented as C_p = Δp/P_dynamic or Pressure Coefficient = Change in static pressure/Dynamic Pressure. Change in static pressure is the static pressure change occurring in hypersonic flow after shock occurs & Dynamic Pressure is simply a convenient name for the quantity which represents the decrease in the pressure due to the velocity of the fluid.

How to calculate Non-Dimensional Pressure Coefficient?

The Non-dimensional pressure coefficient formula is defined as ratio of change in static pressure of upstream and downstream Mach after shock to the dynamic pressure of the freestream is calculated using Pressure Coefficient = Change in static pressure/Dynamic Pressure. To calculate Non-Dimensional Pressure Coefficient, you need Change in static pressure (Δp) & Dynamic Pressure (P_dynamic). With our tool, you need to enter the respective value for Change in static pressure & Dynamic Pressure 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 Change in static pressure & Dynamic Pressure. 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 = 4/(Specific Heat Ratio+1)*((sin(Wave Angle))^2-1/Mach Number^2)
Pressure Coefficient = 4/(Specific Heat Ratio+1)*(sin(Wave Angle))^2

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