Density Ratio with Similarity Constant having Slenderness Ratio Calculator

✖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%
✖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%

✖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.ⓘ Density Ratio with Similarity Constant having Slenderness Ratio [ρ_ratio]

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Density Ratio with Similarity Constant having Slenderness Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2)))
ρ_ratio = ((γ+1)/(γ-1))*(1/(1+2/((γ-1)*K^2)))
This formula uses 3 Variables

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

ρ_ratio = 1.86457146481159

STEP 3: Convert Result to Output's Unit

1.86457146481159 --> No Conversion Required

FINAL ANSWER

1.86457146481159 ≈ 1.864571 <-- Density Ratio

(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

Density Ratio with Similarity Constant having Slenderness Ratio Formula

LaTeX Go

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

What is similarity constant?

Similarity parameters mean some independent dimensionless parameter groups that represent the quantitative characteristics of physical similarity.

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

Density Ratio with Similarity Constant having Slenderness Ratio calculator uses Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2))) to calculate 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 calculate Density Ratio with Similarity Constant having Slenderness Ratio using this online calculator? To use this online calculator for Density Ratio with Similarity Constant having Slenderness Ratio, enter Specific Heat Ratio (γ) & Hypersonic Similarity Parameter (K) and hit the calculate button. Here is how the Density Ratio with Similarity Constant having Slenderness Ratio calculation can be explained with given input values -> 1.864571 = ((1.1+1)/(1.1-1))*(1/(1+2/((1.1-1)*1.396^2))).

FAQ

What is Density Ratio with Similarity Constant having Slenderness 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 and is represented as ρ_ratio = ((γ+1)/(γ-1))*(1/(1+2/((γ-1)*K^2))) or Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2))). 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 & 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.

How to calculate Density Ratio with Similarity Constant having Slenderness 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 is calculated using Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2))). To calculate Density Ratio with Similarity Constant having Slenderness Ratio, you need Specific Heat Ratio (γ) & Hypersonic Similarity Parameter (K). With our tool, you need to enter the respective value for Specific Heat Ratio & Hypersonic Similarity Parameter and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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