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Rasmussen Closed Form Expression for Shock Wave Angle Formula

GoSimilarity Constant Equation using Wave Angle Formula

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

K β = K \cdot \sqrt{\frac{γ + 1}{2} + \frac{1}{K^{2}}}

K_β - Wave Angle Similarity Parameter?K - Hypersonic Similarity Parameter?γ - Specific Heat Ratio?

Rasmussen Closed Form Expression for Shock Wave Angle Example

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Here is how the Rasmussen Closed Form Expression for Shock Wave Angle equation looks like with Values.

Here is how the Rasmussen Closed Form Expression for Shock Wave Angle equation looks like with Units.

Here is how the Rasmussen Closed Form Expression for Shock Wave Angle equation looks like.

1.7454 = 1.396 \cdot \sqrt{\frac{1.1 + 1}{2} + \frac{1}{{1.396}^{2}}}

1.7454 = 1.396rad \cdot \sqrt{\frac{1.1 + 1}{2} + \frac{1}{{1.396rad}^{2}}}

1.7454 = 1.396 \cdot \sqrt{\frac{1.1 + 1}{2} + \frac{1}{{1.396}^{2}}}

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Rasmussen Closed Form Expression for Shock Wave Angle Solution

Follow our step by step solution on how to calculate Rasmussen Closed Form Expression for Shock Wave Angle?

FIRST Step Consider the formula

K β = K \cdot \sqrt{\frac{γ + 1}{2} + \frac{1}{K^{2}}}

Next Step Substitute values of Variables

∴

K β = 1.396rad \cdot \sqrt{\frac{1.1 + 1}{2} + \frac{1}{{1.396rad}^{2}}}

Next Step Prepare to Evaluate

∴

K β = 1.396 \cdot \sqrt{\frac{1.1 + 1}{2} + \frac{1}{{1.396}^{2}}}

Next Step Evaluate

∴

K β = 1.74535291560188

LAST Step Rounding Answer

∴

K β = 1.7454

Rasmussen Closed Form Expression for Shock Wave Angle Formula Elements

Variables

Functions

Wave Angle Similarity Parameter

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

Symbol: K_β

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Angle Similarity Parameter

Hypersonic Similarity Parameter

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.

Symbol: K

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Hypersonic Similarity Parameter

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.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Heat Ratio

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.

Syntax: sqrt(Number)

Other Formulas to find Wave Angle Similarity Parameter

Go Similarity Constant Equation using Wave Angle

K β = M \cdot β \cdot \frac{180}{π}

Other formulas in Hypersonic Flow and Disturbances category

Go Change in Velocity for Hypersonic Flow in X Direction

u' = v fluid - U ∞

Go Similarity Constant Equation with Slenderness Ratio

K = M \cdot λ

Go Density Ratio with Similarity Constant having Slenderness Ratio

ρ ratio = (\frac{γ + 1}{γ - 1}) \cdot (\frac{1}{1 + \frac{2}{(γ - 1) \cdot K^{2}}})

Go Coefficient of Pressure with Slenderness Ratio

C p = \frac{2}{γ} \cdot M^{2} \cdot (p - \cdot γ \cdot M^{2} \cdot λ^{2} - 1)

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

Rasmussen Closed Form Expression for Shock Wave Angle evaluator uses Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2) to evaluate 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 evaluate Rasmussen Closed Form Expression for Shock Wave Angle using this online evaluator? To use this online evaluator for Rasmussen Closed Form Expression for Shock Wave Angle, enter Hypersonic Similarity Parameter (K) & Specific Heat Ratio (γ) and hit the calculate button.

FAQs on Rasmussen Closed Form Expression for Shock Wave Angle

What is the formula to find Rasmussen Closed Form Expression for Shock Wave Angle?

The formula of Rasmussen Closed Form Expression for Shock Wave Angle is expressed as Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2). Here is an example- 1.745574 = 1.396*sqrt((1.1+1)/2+1/1.396^2).

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

With Hypersonic Similarity Parameter (K) & Specific Heat Ratio (γ) we can find Rasmussen Closed Form Expression for Shock Wave Angle using the formula - Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Wave Angle Similarity Parameter?

Here are the different ways to Calculate Wave Angle Similarity Parameter-

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

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