Coefficient of Pressure with Similarity Parameters Calculator

✖Flow Deflection angle is defined as the angle by which the flow turns towards the oblique shock.ⓘ Flow Deflection angle [θ]			+10% -10%
✖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%
✖Hypersonic Similarity Parameter, In the study of hypersonic flow over slender bodies, the product M1u is an important governing parameter, where, as before. It is to simplify the equations.ⓘ Hypersonic Similarity Parameter [K]			+10% -10%

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

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Formula

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Coefficient of Pressure with Similarity Parameters

Formula

`"C"_{"p"} = 2*"θ"^2*(("Y"+1)/4+sqrt((("Y"+1)/4)^2+1/"K"^2))`

Example

`"0.82588"=2*("0.53rad")^2*(("1.6"+1)/4+sqrt((("1.6"+1)/4)^2+1/("2rad")^2))`

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Coefficient of Pressure with Similarity Parameters Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2))
C_p = 2*θ^2*((Y+1)/4+sqrt(((Y+1)/4)^2+1/K^2))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Pressure Coefficient - Pressure coefficient defines the value of local pressure at a point in terms of free stream pressure and dynamic pressure.
Flow Deflection angle - (Measured in Radian) - Flow Deflection angle is defined as the angle by which the flow turns towards the oblique shock.
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.
Hypersonic Similarity Parameter - (Measured in Radian) - Hypersonic Similarity Parameter, In the study of hypersonic flow over slender bodies, the product M1u is an important governing parameter, where, as before. It is to simplify the equations.

STEP 1: Convert Input(s) to Base Unit

Flow Deflection angle: 0.53 Radian --> 0.53 Radian No Conversion Required
Specific Heat Ratio: 1.6 --> No Conversion Required
Hypersonic Similarity Parameter: 2 Radian --> 2 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_p = 2*θ^2*((Y+1)/4+sqrt(((Y+1)/4)^2+1/K^2)) --> 2*0.53^2*((1.6+1)/4+sqrt(((1.6+1)/4)^2+1/2^2))

Evaluating ... ...

C_p = 0.825880254824006

STEP 3: Convert Result to Output's Unit

0.825880254824006 --> No Conversion Required

FINAL ANSWER

0.825880254824006 ≈ 0.82588 <-- Pressure Coefficient

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< 20 Hypersonic Flow Parameters Calculators

Coefficient of Pressure with Similarity Parameters

Go 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 Ratio having High Mach Number with Similarity Constant

Go Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Mach Number with Fluids

Go Mach Number = Fluid Velocity/(sqrt(Specific Heat Ratio*Universal Gas Constant*Final Temperature))

Pressure Ratio for High Mach Number

Go Pressure Ratio = (Mach Number ahead of shock/Mach Number behind shock)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Moment Coefficient

Go Moment Coefficient = Moment/(Dynamic Pressure*Area for Flow*Chord Length)

Deflection Angle

Go Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock)

Normal Force Coefficient

Go Coefficient of Force = Normal Force/(Dynamic Pressure*Area for Flow)

Supersonic Expression for Pressure Coefficient on Surface with Local Deflection Angle

Go Pressure Coefficient = (2*Deflection Angle)/(sqrt(Mach Number^2-1))

Dynamic Pressure given Coefficient of Lift

Go Dynamic Pressure = Lift Force/(Lift Coefficient*Area for Flow)

Coefficient of Drag

Go Drag Coefficient = Drag Force/(Dynamic Pressure*Area for Flow)

Dynamic Pressure

Go Dynamic Pressure = Drag Force/(Drag Coefficient*Area for Flow)

Lift Coefficient

Go Lift Coefficient = Lift Force/(Dynamic Pressure*Area for Flow)

Axial Force Coefficient

Go Coefficient of Force = Force/(Dynamic Pressure*Area for Flow)

Drag Force

Go Drag Force = Drag Coefficient*Dynamic Pressure*Area for Flow

Lift Force

Go Lift Force = Lift Coefficient*Dynamic Pressure*Area for Flow

Mach Ratio at High Mach Number

Go Mach Ratio = 1-Hypersonic Similarity Parameter*((Specific Heat Ratio-1)/2)

Hypersonic Similarity Parameter

Go Hypersonic Similarity Parameter = Mach Number*Flow Deflection angle

Shear-Stress Distribution

Go Shear Stress = Viscosity Coefficient*Velocity Gradient

Fourier's Law of Heat Conduction

Go Heat Flux = Thermal Conductivity*Temperature Gradient

Newtonian Sine Squared Law for Pressure Coefficient

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

Coefficient of Pressure with Similarity Parameters Formula

Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2))
C_p = 2*θ^2*((Y+1)/4+sqrt(((Y+1)/4)^2+1/K^2))

What is a similarity parameter?

Similarity parameters mean some independent dimensionless parameter groups that represent the quantitative characteristics of physical similarity.

How to Calculate Coefficient of Pressure with Similarity Parameters?

Coefficient of Pressure with Similarity Parameters calculator uses Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2)) to calculate the Pressure Coefficient, Coefficient of pressure with similarity parameters formula is the interrelation of similarity parameters of hypersonic flaw and deflection angle. Pressure Coefficient is denoted by C_p symbol.

How to calculate Coefficient of Pressure with Similarity Parameters using this online calculator? To use this online calculator for Coefficient of Pressure with Similarity Parameters, enter Flow Deflection angle (θ), Specific Heat Ratio (Y) & Hypersonic Similarity Parameter (K) and hit the calculate button. Here is how the Coefficient of Pressure with Similarity Parameters calculation can be explained with given input values -> 0.82588 = 2*0.53^2*((1.6+1)/4+sqrt(((1.6+1)/4)^2+1/2^2)).

FAQ

What is Coefficient of Pressure with Similarity Parameters?

Coefficient of pressure with similarity parameters formula is the interrelation of similarity parameters of hypersonic flaw and deflection angle and is represented as C_p = 2*θ^2*((Y+1)/4+sqrt(((Y+1)/4)^2+1/K^2)) or Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2)). Flow Deflection angle is defined as the angle by which the flow turns towards the oblique shock, 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 & Hypersonic Similarity Parameter, In the study of hypersonic flow over slender bodies, the product M1u is an important governing parameter, where, as before. It is to simplify the equations.

How to calculate Coefficient of Pressure with Similarity Parameters?

Coefficient of pressure with similarity parameters formula is the interrelation of similarity parameters of hypersonic flaw and deflection angle is calculated using Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2)). To calculate Coefficient of Pressure with Similarity Parameters, you need Flow Deflection angle (θ), Specific Heat Ratio (Y) & Hypersonic Similarity Parameter (K). With our tool, you need to enter the respective value for Flow Deflection angle, Specific Heat Ratio & Hypersonic Similarity Parameter 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 Flow Deflection angle, Specific Heat Ratio & Hypersonic Similarity Parameter. We can use 2 other way(s) to calculate the same, which is/are as follows -

Pressure Coefficient = 2*sin(Deflection Angle)^2
Pressure Coefficient = (2*Deflection Angle)/(sqrt(Mach Number^2-1))

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