Rasmussen Closed Form Expression for Shock Wave Angle Calculator

✖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%
✖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 [γ]			+10% -10%

✖Wave Angle Similarity Parameter is used by Rasmussen to obtained the closed-form expression for the shock-wave angle.ⓘ Rasmussen Closed Form Expression for Shock Wave Angle [K_β]

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Rasmussen Closed Form Expression for Shock Wave Angle

Formula

`"K"_{"β"} = "K"*sqrt(("γ"+1)/2+1/"K"^2)`

Example

`"1.745353"="1.396rad"*sqrt(("1.1"+1)/2+1/("1.396rad")^2)`

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Rasmussen Closed Form Expression for Shock Wave Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2)
K_β = K*sqrt((γ+1)/2+1/K^2)
This formula uses 1 Functions, 3 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

Wave Angle Similarity Parameter - Wave Angle Similarity Parameter is used by Rasmussen to obtained the closed-form expression for the shock-wave angle.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Hypersonic Similarity Parameter: 1.396 Radian --> 1.396 Radian No Conversion Required
Specific Heat Ratio: 1.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_β = K*sqrt((γ+1)/2+1/K^2) --> 1.396*sqrt((1.1+1)/2+1/1.396^2)

Evaluating ... ...

K_β = 1.74535291560188

STEP 3: Convert Result to Output's Unit

1.74535291560188 --> No Conversion Required

FINAL ANSWER

1.74535291560188 ≈ 1.745353 <-- Wave Angle Similarity Parameter

(Calculation completed in 00.004 seconds)

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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)

Rasmussen Closed Form Expression for Shock Wave Angle Formula

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

What is a dynamic similarity?

Dynamic similarity – ratios of all forces acting on corresponding fluid particles and boundary surfaces in the two systems are constant.

How to Calculate Rasmussen Closed Form Expression for Shock Wave Angle?

Rasmussen Closed Form Expression for Shock Wave Angle calculator uses Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2) to calculate the Wave Angle Similarity Parameter, The Rasmussen closed form expression for shock wave angle formula is defined as the interrelation between hypersonic similarity constant and specific heat ratio. Wave Angle Similarity Parameter is denoted by K_β symbol.

How to calculate Rasmussen Closed Form Expression for Shock Wave Angle using this online calculator? To use this online calculator for Rasmussen Closed Form Expression for Shock Wave Angle, enter Hypersonic Similarity Parameter (K) & Specific Heat Ratio (γ) and hit the calculate button. Here is how the Rasmussen Closed Form Expression for Shock Wave Angle calculation can be explained with given input values -> 1.745574 = 1.396*sqrt((1.1+1)/2+1/1.396^2).

FAQ

What is Rasmussen Closed Form Expression for Shock Wave Angle?

The Rasmussen closed form expression for shock wave angle formula is defined as the interrelation between hypersonic similarity constant and specific heat ratio and is represented as K_β = K*sqrt((γ+1)/2+1/K^2) or Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2). 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 & 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.

How to calculate Rasmussen Closed Form Expression for Shock Wave Angle?

The Rasmussen closed form expression for shock wave angle formula is defined as the interrelation between hypersonic similarity constant and specific heat ratio is calculated using Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2). To calculate Rasmussen Closed Form Expression for Shock Wave Angle, you need Hypersonic Similarity Parameter (K) & Specific Heat Ratio (γ). With our tool, you need to enter the respective value for Hypersonic Similarity Parameter & Specific Heat Ratio 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 Hypersonic Similarity Parameter & Specific Heat Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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