Similarity Constant Equation using Wave Angle Calculator

✖Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%
✖Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.ⓘ Wave Angle [β]			+10% -10%

✖Wave Angle Similarity Parameter is used by Rasmussen to obtained the closed-form expression for the shock-wave angle.ⓘ Similarity Constant Equation using Wave Angle [K_β]

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Formula

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Similarity Constant Equation using Wave Angle

Formula

`"K"_{"β"} = "M"*"β"*180/pi`

Example

`"88.4876"="5.4"*"0.286rad"*180/pi`

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Similarity Constant Equation using Wave Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi
K_β = M*β*180/pi
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Wave Angle Similarity Parameter - Wave Angle Similarity Parameter is used by Rasmussen to obtained the closed-form expression for the shock-wave angle.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
Wave Angle - (Measured in Radian) - Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.

STEP 1: Convert Input(s) to Base Unit

Mach Number: 5.4 --> No Conversion Required
Wave Angle: 0.286 Radian --> 0.286 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_β = M*β*180/pi --> 5.4*0.286*180/pi

Evaluating ... ...

K_β = 88.4876018800043

STEP 3: Convert Result to Output's Unit

88.4876018800043 --> No Conversion Required

FINAL ANSWER

88.4876018800043 ≈ 88.4876 <-- Wave Angle Similarity Parameter

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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National Institute Of Technology (NIT), Hamirpur

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< 17 Hypersonic Flow and Disturbances Calculators

Inverse of Density for Hypersonic Flow using Mach Number

Go Inverse of Density = (2+(Specific Heat Ratio-1)*Mach Number^2*sin(Deflection Angle)^2)/(2+(Specific Heat Ratio+1)*Mach Number^2*sin(Deflection Angle)^2)

Coefficient of Pressure with Slenderness Ratio and Similarity Constant

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

Coefficient of Pressure with Slenderness Ratio

Go Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1)

Non Dimensional Pressure Equation with Slenderness Ratio

Go Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure)

Density Ratio with Similarity Constant having Slenderness Ratio

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

Rasmussen Closed Form Expression for Shock Wave Angle

Go Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2)

Non Dimensional Change in Hypersonic Disturbance Velocity in y Direction

Go Non Dimensional Disturbance Y Velocity = Change in Velocity for Hypersonic Flow y direction/(Freestream Velocity Normal*Slenderness Ratio)

Non Dimensional Change in Hypersonic Disturbance Velocity in x Direction

Go Non Dimensional Disturbance X Velocity = Change in Velocity for Hypersonic Flow/(Freestream Velocity for Blast Wave*Slenderness Ratio^2)

Doty and Rasmussen- Normal Force Coefficient

Go Coefficient of Force = 2*Normal Force/(Density of Fluid*Freestream Velocity Normal^2*Area)

Constant G used for Finding Location of Perturbed Shock

Go Perturbed Shock Location Constant = Perturbed Shock Location Constant at Normal Force/Perturbed Shock Location Constant at Drag Force

Non Dimensional Velocity Disturbance in y Direction in Hypersonic Flow

Go Non Dimensional Disturbance Y Velocity = (2/(Specific Heat Ratio+1))*(1-1/Hypersonic Similarity Parameter^2)

Non Dimensionalised Time

Go Non Dimensionalized Time = Time/(Length/Freestream Velocity Normal)

Similarity Constant Equation using Wave Angle

Go Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi

Change in Velocity for Hypersonic Flow in X Direction

Go Change in Velocity for Hypersonic Flow = Fluid Velocity-Freestream Velocity Normal

Distance from Tip of Leading Edge to Base

Go Distance from X-Axis = Freestream Velocity for Blast Wave*Total Time Taken

Similarity Constant Equation with Slenderness Ratio

Go Hypersonic Similarity Parameter = Mach Number*Slenderness Ratio

Inverse of Density for Hypersonic Flow

Go Inverse of Density = 1/(Density*Wave Angle)

Similarity Constant Equation using Wave Angle Formula

Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi
K_β = M*β*180/pi

What is kinematic similarity?

Kinematic similarity – fluid flow of both the model and real application must undergo similar time rates of change motions.

How to Calculate Similarity Constant Equation using Wave Angle?

Similarity Constant Equation using Wave Angle calculator uses Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi to calculate the Wave Angle Similarity Parameter, Similarity constant equation using wave angle formula is defined as the product of mach number at infinite and wave angle of the shock. Wave Angle Similarity Parameter is denoted by K_β symbol.

How to calculate Similarity Constant Equation using Wave Angle using this online calculator? To use this online calculator for Similarity Constant Equation using Wave Angle, enter Mach Number (M) & Wave Angle (β) and hit the calculate button. Here is how the Similarity Constant Equation using Wave Angle calculation can be explained with given input values -> 88.56 = 5.4*0.286*180/pi.

FAQ

What is Similarity Constant Equation using Wave Angle?

Similarity constant equation using wave angle formula is defined as the product of mach number at infinite and wave angle of the shock and is represented as K_β = M*β*180/pi or Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi. Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound & Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.

How to calculate Similarity Constant Equation using Wave Angle?

Similarity constant equation using wave angle formula is defined as the product of mach number at infinite and wave angle of the shock is calculated using Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi. To calculate Similarity Constant Equation using Wave Angle, you need Mach Number (M) & Wave Angle (β). With our tool, you need to enter the respective value for 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 Wave Angle Similarity Parameter?

In this formula, Wave Angle Similarity Parameter uses Mach Number & Wave Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2)

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