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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Formula

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Density Ratio with Similarity Constant having Slenderness Ratio

Formula

`"ρ"_{"ratio"} = (("γ"+1)/("γ"-1))*(1/(1+2/(("γ"-1)*"K"^2)))`

Example

`"1.864571"=(("1.1"+1)/("1.1"-1))*(1/(1+2/(("1.1"-1)*("1.396rad")^2)))`

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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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Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Hypersonic Flow and Disturbances » Density Ratio with Similarity Constant having Slenderness Ratio

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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PSG College of Technology (PSGCT), Coimbatore

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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)

Density Ratio with Similarity Constant having Slenderness Ratio Formula

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, The Density ratio with similarity constant having slenderness ratio formula is defined as the interrelationship between the specific heat ratio and similarity constant of hypersonic flow. 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 -> 1.865213 = ((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?

The Density ratio with similarity constant having slenderness ratio formula is defined as the interrelationship between the specific heat ratio and similarity constant of hypersonic flow 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?

The Density ratio with similarity constant having slenderness ratio formula is defined as the interrelationship between the specific heat ratio and similarity constant of hypersonic flow 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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