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Exact Density Ratio Formula

GoDensity Ratio when Mach Becomes Infinite 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{(Y + 1) \cdot {(M \cdot (\sin (β)))}^{2}}{(Y - 1) \cdot {(M \cdot (\sin (β)))}^{2} + 2}

ρ_ratio - Density Ratio?Y - Specific Heat Ratio?M - Mach Number?β - Wave Angle?

Exact Density Ratio Example

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Here is how the Exact Density Ratio equation looks like with Values.

Here is how the Exact Density Ratio equation looks like with Units.

Here is how the Exact Density Ratio equation looks like.

2.6193 = \frac{(1.6 + 1) \cdot {(8 \cdot (\sin (0.286)))}^{2}}{(1.6 - 1) \cdot {(8 \cdot (\sin (0.286)))}^{2} + 2}

2.6193 = \frac{(1.6 + 1) \cdot {(8 \cdot (\sin (0.286rad)))}^{2}}{(1.6 - 1) \cdot {(8 \cdot (\sin (0.286rad)))}^{2} + 2}

2.6193 = \frac{(1.6 + 1) \cdot {(8 \cdot (\sin (0.286)))}^{2}}{(1.6 - 1) \cdot {(8 \cdot (\sin (0.286)))}^{2} + 2}

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Exact Density Ratio Solution

Follow our step by step solution on how to calculate Exact Density Ratio?

FIRST Step Consider the formula

ρ ratio = \frac{(Y + 1) \cdot {(M \cdot (\sin (β)))}^{2}}{(Y - 1) \cdot {(M \cdot (\sin (β)))}^{2} + 2}

Next Step Substitute values of Variables

∴

ρ ratio = \frac{(1.6 + 1) \cdot {(8 \cdot (\sin (0.286rad)))}^{2}}{(1.6 - 1) \cdot {(8 \cdot (\sin (0.286rad)))}^{2} + 2}

Next Step Prepare to Evaluate

∴

ρ ratio = \frac{(1.6 + 1) \cdot {(8 \cdot (\sin (0.286)))}^{2}}{(1.6 - 1) \cdot {(8 \cdot (\sin (0.286)))}^{2} + 2}

Next Step Evaluate

∴

ρ ratio = 2.61928491735577

LAST Step Rounding Answer

∴

ρ ratio = 2.6193

Exact Density Ratio Formula Elements

Variables

Functions

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: Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Heat Ratio

Mach Number

Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Wave Angle

Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.

Symbol: β

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Wave Angle

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.

Syntax: sin(Angle)

Other Formulas to find Density Ratio

Go Density Ratio when Mach Becomes Infinite

ρ ratio = \frac{Y + 1}{Y - 1}

Other formulas in Oblique Shock Relation category

Go Wave Angle for Small Deflection Angle

β = \frac{Y + 1}{2} \cdot (θ d \cdot \frac{180}{π}) \cdot \frac{π}{180}

Go Coefficient of Pressure Derived from Oblique Shock Theory

C p = 2 \cdot {(\sin (β))}^{2}

Go Parallel Upstream Flow Components after Shock as Mach Tends to Infinite

u2 = V 1 \cdot (1 - \frac{2 \cdot {(\sin (β))}^{2}}{Y - 1})

Go Perpendicular Upstream Flow Components behind Shock Wave

v2 = \frac{V 1 \cdot (\sin (2 \cdot β))}{Y - 1}

How to Evaluate Exact Density Ratio?

Exact Density Ratio evaluator 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 evaluate 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 evaluate Exact Density Ratio using this online evaluator? To use this online evaluator for Exact Density Ratio, enter Specific Heat Ratio (Y), Mach Number (M) & Wave Angle (β) and hit the calculate button.

FAQs on Exact Density Ratio

What is the formula to find Exact Density Ratio?

The formula of Exact Density Ratio is expressed as Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2). Here is an example- 2.619285 = ((1.6+1)*(8*(sin(0.286)))^2)/((1.6-1)*(8*(sin(0.286)))^2+2).

How to calculate Exact Density Ratio?

With Specific Heat Ratio (Y), Mach Number (M) & Wave Angle (β) we can find Exact Density Ratio using the formula - Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Density Ratio?

Here are the different ways to Calculate Density Ratio-

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

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Exact Density Ratio Formula

​GoDensity Ratio when Mach Becomes Infinite Formula

Exact Density Ratio Example

Exact Density Ratio Solution

Exact Density Ratio Formula Elements

Other Formulas to find Density Ratio

Other formulas in Oblique Shock Relation category

How to Evaluate Exact Density Ratio?

FAQs on Exact Density Ratio

Variable Name

GoDensity Ratio when Mach Becomes Infinite Formula