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 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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< Hypersonic Flow and Disturbances Calculators

Coefficient of Pressure with Slenderness Ratio

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

Density Ratio with Similarity Constant having Slenderness Ratio

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

Change in Velocity for Hypersonic Flow in X Direction

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

Similarity Constant Equation with Slenderness Ratio

LaTeX Go Hypersonic Similarity Parameter = Mach Number*Slenderness Ratio

Rasmussen Closed Form Expression for Shock Wave Angle Formula

LaTeX Go

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, Rasmussen Closed Form Expression for Shock Wave Angle formula is defined as a mathematical representation that determines the shock wave angle in hypersonic flow, which is crucial in understanding the behavior of high-speed fluids and their interaction with solid boundaries, thereby aiding in the design of hypersonic vehicles and reentry systems. 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?

Rasmussen Closed Form Expression for Shock Wave Angle formula is defined as a mathematical representation that determines the shock wave angle in hypersonic flow, which is crucial in understanding the behavior of high-speed fluids and their interaction with solid boundaries, thereby aiding in the design of hypersonic vehicles and reentry systems 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?

Rasmussen Closed Form Expression for Shock Wave Angle formula is defined as a mathematical representation that determines the shock wave angle in hypersonic flow, which is crucial in understanding the behavior of high-speed fluids and their interaction with solid boundaries, thereby aiding in the design of hypersonic vehicles and reentry systems 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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