Pressure Ratio having High Mach Number with Similarity Constant 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%
✖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 Ratio is ratio of final to initial pressure.ⓘ Pressure Ratio having High Mach Number with Similarity Constant [r_p]

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Formula

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Pressure Ratio having High Mach Number with Similarity Constant

Formula

`"r"_{"p"} = (1-(("Y"-1)/2)*"K")^(2*"Y"/("Y"-1))`

Example

`"0.007545"=(1-(("1.6"-1)/2)*"2rad")^(2*"1.6"/("1.6"-1))`

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Pressure Ratio having High Mach Number with Similarity Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))
r_p = (1-((Y-1)/2)*K)^(2*Y/(Y-1))
This formula uses 3 Variables

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.
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

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

r_p = (1-((Y-1)/2)*K)^(2*Y/(Y-1)) --> (1-((1.6-1)/2)*2)^(2*1.6/(1.6-1))

Evaluating ... ...

r_p = 0.0075448965092155

STEP 3: Convert Result to Output's Unit

0.0075448965092155 --> No Conversion Required

FINAL ANSWER

0.0075448965092155 ≈ 0.007545 <-- Pressure Ratio

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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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

Pressure Ratio having High Mach Number with Similarity Constant Formula

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

What is pressure ratio?

The above mentioned pressure ratio is for expansion wave which are due to the high Mach number present.

How to Calculate Pressure Ratio having High Mach Number with Similarity Constant?

Pressure Ratio having High Mach Number with Similarity Constant calculator uses Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-1)) to calculate the Pressure Ratio, Pressure ratio having high Mach number with similarity constant formula is defined as inter-relation between specific heat ratio and similarity constants. Pressure Ratio is denoted by r_p symbol.

How to calculate Pressure Ratio having High Mach Number with Similarity Constant using this online calculator? To use this online calculator for Pressure Ratio having High Mach Number with Similarity Constant, enter Specific Heat Ratio (Y) & Hypersonic Similarity Parameter (K) and hit the calculate button. Here is how the Pressure Ratio having High Mach Number with Similarity Constant calculation can be explained with given input values -> 0.007545 = (1-((1.6-1)/2)*2)^(2*1.6/(1.6-1)).

FAQ

What is Pressure Ratio having High Mach Number with Similarity Constant?

Pressure ratio having high Mach number with similarity constant formula is defined as inter-relation between specific heat ratio and similarity constants and is represented as r_p = (1-((Y-1)/2)*K)^(2*Y/(Y-1)) or Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-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 & 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 Pressure Ratio having High Mach Number with Similarity Constant?

Pressure ratio having high Mach number with similarity constant formula is defined as inter-relation between specific heat ratio and similarity constants is calculated using Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-1)). To calculate Pressure Ratio having High Mach Number with Similarity Constant, you need Specific Heat Ratio (Y) & Hypersonic Similarity Parameter (K). With our tool, you need to enter the respective value for 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 Ratio?

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

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

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