Pressure Ratio for Unsteady Waves 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%
✖Induced Mass Motion, added mass or virtual mass is the inertia added to a system because an accelerating or decelerating body must move some volume of surrounding fluid as it moves through it.ⓘ Induced Mass Motion [u']			+10% -10%
✖The speed of sound is defined as the dynamic propagation of sound waves.ⓘ Speed of Sound [c_speed]			+10% -10%

✖Pressure Ratio is ratio of final to initial pressure.ⓘ Pressure Ratio for Unsteady Waves [r_p]

⎘ Copy

👎

Formula

✖

Pressure Ratio for Unsteady Waves

Formula

`"r"_{"p"} = (1+(("γ"-1)/2)*("u'"/"c"_{"speed"}))^(2*"γ"/("γ"-1))`

Example

`"1.040294"=(1+(("1.6"-1)/2)*("8.5kg·m²"/"343m/s"))^(2*"1.6"/("1.6"-1))`

Calculator

LaTeX

Reset

👍

Download Hypersonic Flow Formula PDF

Pressure Ratio for Unsteady Waves Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1))
r_p = (1+((γ-1)/2)*(u'/c_speed))^(2*γ/(γ-1))
This formula uses 4 Variables

Variables Used

Pressure Ratio - Pressure Ratio is ratio of final to initial pressure.
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.
Induced Mass Motion - (Measured in Kilogram Square Meter) - Induced Mass Motion, added mass or virtual mass is the inertia added to a system because an accelerating or decelerating body must move some volume of surrounding fluid as it moves through it.
Speed of Sound - (Measured in Meter per Second) - The speed of sound is defined as the dynamic propagation of sound waves.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Induced Mass Motion: 8.5 Kilogram Square Meter --> 8.5 Kilogram Square Meter No Conversion Required
Speed of Sound: 343 Meter per Second --> 343 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_p = (1+((γ-1)/2)*(u'/c_speed))^(2*γ/(γ-1)) --> (1+((1.6-1)/2)*(8.5/343))^(2*1.6/(1.6-1))

Evaluating ... ...

r_p = 1.04029412393728

STEP 3: Convert Result to Output's Unit

1.04029412393728 --> No Conversion Required

FINAL ANSWER

1.04029412393728 ≈ 1.040294 <-- Pressure Ratio

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Hypersonic Inviscid Flow » Shock Dynamics and Aerodynamic Shape » Pressure Ratio for Unsteady Waves

Credits

Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 10+ Shock Dynamics and Aerodynamic Shape Calculators

Pressure Ratio for Unsteady Waves

Go Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Ratio of New and Old Temperature

Go Temperature Ratio across Shock = (1+((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2)

Grid Point Calculation for Shock Waves

Go Grid Points = (Distance from X-Axis-Body shape in hypersonic flow)/Local Shock-detachment Distance

Mach Wave behind Shock

Go Mach Number behind shock = (Freestream Velocity-Local Shock Velocity for Mach Wave)/Speed of Sound

Local Shock Velocity Equation

Go Local Shock Velocity = Speed of Sound*(Mach Number-Mach Number ahead of shock)

Mach Wave behind Shock with Mach Infinity

Go Mach Number ahead of shock = Mach Number-Local Shock Velocity/Speed of Sound

Nose Radius of Cylinder-Wedge

Go Radius = Local Shock-detachment Distance/(0.386*exp(4.67/(Mach Number^2)))

Nose Radius of Sphere Cone

Go Radius = Local Shock-detachment Distance/(0.143*exp(3.24/(Mach Number^2)))

Detachment Distance of Cylinder Wedge Body Shape

Go Local Shock-detachment Distance = Radius*0.386*exp(4.67/(Mach Number^2))

Detachment Distance of Sphere Cone Body Shape

Go Local Shock-detachment Distance = Radius*0.143*exp(3.24/(Mach Number^2))

Pressure Ratio for Unsteady Waves Formula

Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1))
r_p = (1+((γ-1)/2)*(u'/c_speed))^(2*γ/(γ-1))

What is an induced mass motion?

In fluid mechanics, added mass or virtual mass is the inertia added to a system because an accelerating or decelerating body must move (or deflect) some volume of surrounding fluid as it moves through it.

How to Calculate Pressure Ratio for Unsteady Waves?

Pressure Ratio for Unsteady Waves calculator uses Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1)) to calculate the Pressure Ratio, The Pressure ratio for unsteady waves formula is defined as the interrelation between specific heat ratio, speed of sound during the unsteady waves, and induced mass motion at an arbitrary point inside the wave. Pressure Ratio is denoted by r_p symbol.

How to calculate Pressure Ratio for Unsteady Waves using this online calculator? To use this online calculator for Pressure Ratio for Unsteady Waves, enter Specific Heat Ratio (γ), Induced Mass Motion (u') & Speed of Sound (c_speed) and hit the calculate button. Here is how the Pressure Ratio for Unsteady Waves calculation can be explained with given input values -> 1.040294 = (1+((1.6-1)/2)*(8.5/343))^(2*1.6/(1.6-1)).

FAQ

What is Pressure Ratio for Unsteady Waves?

The Pressure ratio for unsteady waves formula is defined as the interrelation between specific heat ratio, speed of sound during the unsteady waves, and induced mass motion at an arbitrary point inside the wave and is represented as r_p = (1+((γ-1)/2)*(u'/c_speed))^(2*γ/(γ-1)) or Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1)). 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, Induced Mass Motion, added mass or virtual mass is the inertia added to a system because an accelerating or decelerating body must move some volume of surrounding fluid as it moves through it & The speed of sound is defined as the dynamic propagation of sound waves.

How to calculate Pressure Ratio for Unsteady Waves?

The Pressure ratio for unsteady waves formula is defined as the interrelation between specific heat ratio, speed of sound during the unsteady waves, and induced mass motion at an arbitrary point inside the wave is calculated using Pressure Ratio = (1+((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-1)). To calculate Pressure Ratio for Unsteady Waves, you need Specific Heat Ratio (γ), Induced Mass Motion (u') & Speed of Sound (c_speed). With our tool, you need to enter the respective value for Specific Heat Ratio, Induced Mass Motion & Speed of Sound and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search