Temperature Ratio for Unsteady Expansion Wave 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%

✖Temperature ratio is the ratio of temperatures at different instances of any process or environment.ⓘ Temperature Ratio for Unsteady Expansion Wave [T_ratio]

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Formula

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Temperature Ratio for Unsteady Expansion Wave

Formula

`"T"_{"ratio"} = (1-(("γ"-1)/2)*("u'"/"c"_{"speed"}))^2`

Example

`"0.985186"=(1-(("1.6"-1)/2)*("8.5kg·m²"/"343m/s"))^2`

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Temperature Ratio for Unsteady Expansion Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Temperature Ratio - Temperature ratio is the ratio of temperatures at different instances of any process or environment.
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

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

Evaluating ... ...

T_ratio = 0.985186465673316

STEP 3: Convert Result to Output's Unit

0.985186465673316 --> No Conversion Required

FINAL ANSWER

0.985186465673316 ≈ 0.985186 <-- Temperature Ratio

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Hypersonic Inviscid Flow » Expansion Waves » Temperature Ratio for Unsteady Expansion Wave

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< 5 Expansion Waves Calculators

Density before Shock Formation for Expansion Wave

Go Density behind Shock = Stagnation pressure ahead of shock/(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds))

New Pressure after Shock Formation, Subtracted to Velocity for Expansion Wave

Go Pressure = Density ahead of shock*(1-((Specific Heat Ratio-1)/2)*(Normal velocity/Old Speed of Sound))^(2*Specific Heat Ratio/(Specific Heat Ratio-Time in seconds))

Pressure Ratio for Unsteady Waves with Subtracted Induced Mass Motion for Expansion 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 for Expansion Waves

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

Temperature Ratio for Unsteady Expansion Wave

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

Temperature Ratio for Unsteady Expansion Wave Formula

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

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 Temperature Ratio for Unsteady Expansion Wave?

Temperature Ratio for Unsteady Expansion Wave calculator uses Temperature Ratio = (1-((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^2 to calculate the Temperature Ratio, Temperature ratio for unsteady expansion wave 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. Temperature Ratio is denoted by T_ratio symbol.

How to calculate Temperature Ratio for Unsteady Expansion Wave using this online calculator? To use this online calculator for Temperature Ratio for Unsteady Expansion Wave, enter Specific Heat Ratio (γ), Induced Mass Motion (u') & Speed of Sound (c_speed) and hit the calculate button. Here is how the Temperature Ratio for Unsteady Expansion Wave calculation can be explained with given input values -> 0.985186 = (1-((1.6-1)/2)*(8.5/343))^2.

FAQ

What is Temperature Ratio for Unsteady Expansion Wave?

Temperature ratio for unsteady expansion wave 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 T_ratio = (1-((γ-1)/2)*(u'/c_speed))^2 or Temperature Ratio = (1-((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^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, 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 Temperature Ratio for Unsteady Expansion Wave?

Temperature ratio for unsteady expansion wave 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 Temperature Ratio = (1-((Specific Heat Ratio-1)/2)*(Induced Mass Motion/Speed of Sound))^2. To calculate Temperature Ratio for Unsteady Expansion Wave, 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.

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