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Density Ratio with Similarity Constant having Slenderness Ratio Formula

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Density Ratio higher is also one of the definitions of hypersonic flow. Density ratio across normal shock would reach 6 for calorically perfect gas (air or diatomic gas) at very high Mach numbers. Check FAQs

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

ρ_ratio - Density Ratio?γ - Specific Heat Ratio?K - Hypersonic Similarity Parameter?

Density Ratio with Similarity Constant having Slenderness Ratio Example

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Here is how the Density Ratio with Similarity Constant having Slenderness Ratio equation looks like with Values.

Here is how the Density Ratio with Similarity Constant having Slenderness Ratio equation looks like with Units.

Here is how the Density Ratio with Similarity Constant having Slenderness Ratio equation looks like.

1.8646 = (\frac{1.1 + 1}{1.1 - 1}) \cdot (\frac{1}{1 + \frac{2}{(1.1 - 1) \cdot {1.396}^{2}}})

1.8646 = (\frac{1.1 + 1}{1.1 - 1}) \cdot (\frac{1}{1 + \frac{2}{(1.1 - 1) \cdot {1.396rad}^{2}}})

1.8646 = (\frac{1.1 + 1}{1.1 - 1}) \cdot (\frac{1}{1 + \frac{2}{(1.1 - 1) \cdot {1.396}^{2}}})

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Density Ratio with Similarity Constant having Slenderness Ratio Solution

Follow our step by step solution on how to calculate Density Ratio with Similarity Constant having Slenderness Ratio?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ρ ratio = (\frac{1.1 + 1}{1.1 - 1}) \cdot (\frac{1}{1 + \frac{2}{(1.1 - 1) \cdot {1.396rad}^{2}}})

Next Step Prepare to Evaluate

∴

ρ ratio = (\frac{1.1 + 1}{1.1 - 1}) \cdot (\frac{1}{1 + \frac{2}{(1.1 - 1) \cdot {1.396}^{2}}})

Next Step Evaluate

∴

ρ ratio = 1.86457146481159

LAST Step Rounding Answer

∴

ρ ratio = 1.8646

Density Ratio with Similarity Constant having Slenderness Ratio Formula Elements

Variables

Density Ratio

Density Ratio higher is also one of the definitions of hypersonic flow. Density ratio across normal shock would reach 6 for calorically perfect gas (air or diatomic gas) at very high Mach numbers.

Symbol: ρ_ratio

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Density Ratio

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

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

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 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)

Go Coefficient of Pressure with Slenderness Ratio and Similarity Constant

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

How to Evaluate Density Ratio with Similarity Constant having Slenderness Ratio?

Density Ratio with Similarity Constant having Slenderness Ratio evaluator uses Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2))) to evaluate the Density Ratio, Density Ratio with Similarity Constant having Slenderness Ratio formula is defined as a dimensionless quantity used to characterize the behavior of hypersonic flows, incorporating the effects of slenderness ratio and similarity constant, providing valuable insights into the dynamics of disturbances in hypersonic flow regimes. Density Ratio is denoted by ρ_ratio symbol.

How to evaluate Density Ratio with Similarity Constant having Slenderness Ratio using this online evaluator? To use this online evaluator for Density Ratio with Similarity Constant having Slenderness Ratio, enter Specific Heat Ratio (γ) & Hypersonic Similarity Parameter (K) and hit the calculate button.

FAQs on Density Ratio with Similarity Constant having Slenderness Ratio

What is the formula to find Density Ratio with Similarity Constant having Slenderness Ratio?

The formula of Density Ratio with Similarity Constant having Slenderness Ratio is expressed as Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2))). Here is an example- 1.864571 = ((1.1+1)/(1.1-1))*(1/(1+2/((1.1-1)*1.396^2))).

How to calculate Density Ratio with Similarity Constant having Slenderness Ratio?

With Specific Heat Ratio (γ) & Hypersonic Similarity Parameter (K) we can find Density Ratio with Similarity Constant having Slenderness Ratio using the formula - Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2))).

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