Exact Density Ratio Calculator

✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows.ⓘ Specific Heat Ratio [Y]			+10% -10%
✖The Mach Number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.ⓘ Mach Number [M]			+10% -10%
✖The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.ⓘ Wave Angle [β]			+10% -10%

✖The Density Ratio is the comparison of the density of a fluid before and after passing through an oblique shock wave, indicating changes in flow properties.ⓘ Exact Density Ratio [ρ_ratio]

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Exact Density Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2)
ρ_ratio = ((Y+1)*(M*(sin(β)))^2)/((Y-1)*(M*(sin(β)))^2+2)
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Density Ratio - The Density Ratio is the comparison of the density of a fluid before and after passing through an oblique shock wave, indicating changes in flow properties.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows.
Mach Number - The Mach Number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.
Wave Angle - (Measured in Radian) - The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Mach Number: 8 --> No Conversion Required
Wave Angle: 0.5 Radian --> 0.5 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ_ratio = ((Y+1)*(M*(sin(β)))^2)/((Y-1)*(M*(sin(β)))^2+2) --> ((1.6+1)*(8*(sin(0.5)))^2)/((1.6-1)*(8*(sin(0.5)))^2+2)

Evaluating ... ...

ρ_ratio = 3.53280590108057

STEP 3: Convert Result to Output's Unit

3.53280590108057 --> No Conversion Required

FINAL ANSWER

3.53280590108057 ≈ 3.532806 <-- Density Ratio

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< Oblique Shock Relation Calculators

Parallel Upstream Flow Components after Shock as Mach Tends to Infinite

LaTeX Go Parallel Upstream Flow Components = Velocity of the fluid at 1*(1-(2*(sin(Wave Angle))^2)/(Specific Heat Ratio-1))

Perpendicular Upstream Flow Components behind Shock Wave

LaTeX Go Perpendicular upstream flow components = (Velocity of the fluid at 1*sin(2*Wave Angle))/(Specific Heat Ratio-1)

Wave Angle for Small Deflection Angle

LaTeX Go Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180

Coefficient of Pressure Derived from Oblique Shock Theory

LaTeX Go Pressure Coefficient = 2*(sin(Wave Angle))^2

Exact Density Ratio Formula

LaTeX Go

Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2)
ρ_ratio = ((Y+1)*(M*(sin(β)))^2)/((Y-1)*(M*(sin(β)))^2+2)

What is exact density ratio?

Higher density ratio 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

How to Calculate Exact Density Ratio?

Exact Density Ratio calculator uses Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2) to calculate the Density Ratio, Exact Density Ratio formula is defined as a measure of the compression of air across an oblique shockwave, which occurs when an object moves at supersonic speeds, and is used to determine the density of air behind the shockwave. Density Ratio is denoted by ρ_ratio symbol.

How to calculate Exact Density Ratio using this online calculator? To use this online calculator for Exact Density Ratio, enter Specific Heat Ratio (Y), Mach Number (M) & Wave Angle (β) and hit the calculate button. Here is how the Exact Density Ratio calculation can be explained with given input values -> 4.118812 = ((1.6+1)*(8*(sin(0.5)))^2)/((1.6-1)*(8*(sin(0.5)))^2+2).

FAQ

What is Exact Density Ratio?

Exact Density Ratio formula is defined as a measure of the compression of air across an oblique shockwave, which occurs when an object moves at supersonic speeds, and is used to determine the density of air behind the shockwave and is represented as ρ_ratio = ((Y+1)*(M*(sin(β)))^2)/((Y-1)*(M*(sin(β)))^2+2) or Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2). The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows, The Mach Number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium & The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.

How to calculate Exact Density Ratio?

Exact Density Ratio formula is defined as a measure of the compression of air across an oblique shockwave, which occurs when an object moves at supersonic speeds, and is used to determine the density of air behind the shockwave is calculated using Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2). To calculate Exact Density Ratio, you need Specific Heat Ratio (Y), Mach Number (M) & Wave Angle (β). With our tool, you need to enter the respective value for Specific Heat Ratio, Mach Number & Wave Angle 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 Density Ratio?

In this formula, Density Ratio uses Specific Heat Ratio, Mach Number & Wave Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Density Ratio = (Specific Heat Ratio+1)/(Specific Heat Ratio-1)

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