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Exact Pressure Ratio Formula

GoPressure Ratio when Mach becomes Infinite Formula

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The Pressure Ratio is the comparison of pressures before and after an oblique shock wave, indicating changes in fluid dynamics during hypersonic flow. Check FAQs

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

r_p - Pressure Ratio?Y - Specific Heat Ratio?M - Mach Number?β - Wave Angle?

Exact Pressure Ratio Example

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

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

Here is how the Exact Pressure Ratio equation looks like.

17.8742 = 1 + 2 \cdot \frac{1.6}{1.6 + 1} \cdot ({(8 \cdot \sin (0.5))}^{2} - 1)

17.8742 = 1 + 2 \cdot \frac{1.6}{1.6 + 1} \cdot ({(8 \cdot \sin (0.5rad))}^{2} - 1)

17.8742 = 1 + 2 \cdot \frac{1.6}{1.6 + 1} \cdot ({(8 \cdot \sin (0.5))}^{2} - 1)

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Exact Pressure Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r p = 1 + 2 \cdot \frac{1.6}{1.6 + 1} \cdot ({(8 \cdot \sin (0.5rad))}^{2} - 1)

Next Step Prepare to Evaluate

∴

r p = 1 + 2 \cdot \frac{1.6}{1.6 + 1} \cdot ({(8 \cdot \sin (0.5))}^{2} - 1)

Next Step Evaluate

∴

r p = 17.8742476458087

LAST Step Rounding Answer

∴

r p = 17.8742

Exact Pressure Ratio Formula Elements

Variables

Functions

Pressure Ratio

The Pressure Ratio is the comparison of pressures before and after an oblique shock wave, indicating changes in fluid dynamics during hypersonic flow.

Symbol: r_p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Pressure Ratio

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.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Heat Ratio

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.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Wave Angle

The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.

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 Pressure Ratio

Go Pressure Ratio when Mach becomes Infinite

r p = \frac{2 \cdot Y}{Y + 1} \cdot {(M \cdot \sin (β))}^{2}

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 Pressure Ratio?

Exact Pressure Ratio evaluator uses Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1) to evaluate the Pressure Ratio, Exact Pressure Ratio formula is defined as a dimensionless quantity that characterizes the compression of a flow across an oblique shock wave, providing a crucial parameter in the analysis of high-speed fluid flows and their applications in aerospace engineering. Pressure Ratio is denoted by r_p symbol.

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

FAQs on Exact Pressure Ratio

What is the formula to find Exact Pressure Ratio?

The formula of Exact Pressure Ratio is expressed as Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1). Here is an example- 17.87425 = 1+2*1.6/(1.6+1)*((8*sin(0.5))^2-1).

How to calculate Exact Pressure Ratio?

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

What are the other ways to Calculate Pressure Ratio?

Here are the different ways to Calculate Pressure Ratio-

Pressure Ratio=(2*Specific Heat Ratio)/(Specific Heat Ratio+1)*(Mach Number*sin(Wave Angle))^2

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Exact Pressure Ratio Formula

​GoPressure Ratio when Mach becomes Infinite Formula

Exact Pressure Ratio Example

Exact Pressure Ratio Solution

Exact Pressure Ratio Formula Elements

Other Formulas to find Pressure Ratio

Other formulas in Oblique Shock Relation category

How to Evaluate Exact Pressure Ratio?

FAQs on Exact Pressure Ratio

Variable Name

GoPressure Ratio when Mach becomes Infinite Formula