Boltzmann Constant for Cylindrical Blast 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 [y_sp]

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✖The Boltzmann Constant 1 is the Boltzmann constant used for cylindrical blast waves in hypersonic blast theory.ⓘ Boltzmann Constant for Cylindrical Blast Wave [k_b1]

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Formula

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Boltzmann Constant for Cylindrical Blast Wave

Formula

`"k"_{"b1"} = ("y"_{"sp"}^(2*("y"_{"sp"}-1)/(2-"y"_{"sp"})))/(2^((4-"y"_{"sp"})/(2-"y"_{"sp"})))`

Example

`"0.417963"=(("0.4")^(2*("0.4"-1)/(2-"0.4")))/(2^((4-"0.4")/(2-"0.4")))`

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Download Hypersonic Equivalence Principle and Blast-Wave Theory Formulas PDF

Boltzmann Constant for Cylindrical Blast Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

Boltzmann Constant = (Specific Heat Ratio^(2*(Specific Heat Ratio-1)/(2-Specific Heat Ratio)))/(2^((4-Specific Heat Ratio)/(2-Specific Heat Ratio)))
k_b1 = (y_sp^(2*(y_sp-1)/(2-y_sp)))/(2^((4-y_sp)/(2-y_sp)))
This formula uses 2 Variables

Variables Used

Boltzmann Constant - The Boltzmann Constant 1 is the Boltzmann constant used for cylindrical blast waves in hypersonic blast theory.
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.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 0.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_b1 = (y_sp^(2*(y_sp-1)/(2-y_sp)))/(2^((4-y_sp)/(2-y_sp))) --> (0.4^(2*(0.4-1)/(2-0.4)))/(2^((4-0.4)/(2-0.4)))

Evaluating ... ...

k_b1 = 0.417962690610264

STEP 3: Convert Result to Output's Unit

0.417962690610264 --> No Conversion Required

FINAL ANSWER

0.417962690610264 ≈ 0.417963 <-- Boltzmann Constant

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Hypersonic Equivalence Principle and Blast-Wave Theory » Cylindrical Blast Wave » Boltzmann Constant for Cylindrical Blast Wave

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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Verified by Rushi Shah

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

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< 8 Cylindrical Blast Wave Calculators

Modified Pressure Equation for Cylindrical Blast Wave

Go Pressure = [BoltZ]*Freestream Density*sqrt(pi/8)*Diameter*sqrt(Drag Coefficient)*(Freestream Velocity for Blast Wave^2)/Distance from X-Axis

Pressure Ratio for Blunt Cylinder Blast Wave

Go Pressure Ratio for Blunt Cylinder Blast Wave = 0.8773*[BoltZ]*Mach Number^2*sqrt(Drag Coefficient)*(Distance from X-Axis/Diameter)^(-1)

Boltzmann Constant for Cylindrical Blast Wave

Go Boltzmann Constant = (Specific Heat Ratio^(2*(Specific Heat Ratio-1)/(2-Specific Heat Ratio)))/(2^((4-Specific Heat Ratio)/(2-Specific Heat Ratio)))

Pressure for Cylindrical Blast Wave

Go Pressure for Blast Wave = Boltzmann Constant*Freestream Density*((Energy for Blast Wave/Freestream Density)^(1/2))/(Time Required for Blast Wave)

Modified Radial Coordinate Equation for Cylindrical Blast Wave

Go Radial Coordinate = 0.792*Diameter*Drag Coefficient^(1/4)*sqrt(Distance from X-Axis/Diameter)

Simplified Pressure Ratio for Blunt Cylinder Blast Wave

Go Pressure Ratio = 0.0681*Mach Number^2*sqrt(Drag Coefficient)/(Distance from X-Axis/Diameter)

Modified Energy for Cylindrical Blast Wave

Go Modified Energy for Blast Wave = 0.5*Freestream Density*Freestream Velocity^2*Diameter*Drag Coefficient

Radial Coordinate of Cylindrical Blast Wave

Go Radial Coordinate = (Energy for Blast Wave/Freestream Density)^(1/4)*Time Required for Blast Wave^(1/2)

Boltzmann Constant for Cylindrical Blast Wave Formula

What is Boltzmann constant?

The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas

How to Calculate Boltzmann Constant for Cylindrical Blast Wave?

Boltzmann Constant for Cylindrical Blast Wave calculator uses Boltzmann Constant = (Specific Heat Ratio^(2*(Specific Heat Ratio-1)/(2-Specific Heat Ratio)))/(2^((4-Specific Heat Ratio)/(2-Specific Heat Ratio))) to calculate the Boltzmann Constant, The Boltzmann constant for cylindrical blast wave formula is defined as is the interrelation of specific heat ratio, used for the studying the cylindrical blast wave. Boltzmann Constant is denoted by k_b1 symbol.

How to calculate Boltzmann Constant for Cylindrical Blast Wave using this online calculator? To use this online calculator for Boltzmann Constant for Cylindrical Blast Wave, enter Specific Heat Ratio (y_sp) and hit the calculate button. Here is how the Boltzmann Constant for Cylindrical Blast Wave calculation can be explained with given input values -> 0.034885 = (0.4^(2*(0.4-1)/(2-0.4)))/(2^((4-0.4)/(2-0.4))).

FAQ

What is Boltzmann Constant for Cylindrical Blast Wave?

The Boltzmann constant for cylindrical blast wave formula is defined as is the interrelation of specific heat ratio, used for the studying the cylindrical blast wave and is represented as k_b1 = (y_sp^(2*(y_sp-1)/(2-y_sp)))/(2^((4-y_sp)/(2-y_sp))) or Boltzmann Constant = (Specific Heat Ratio^(2*(Specific Heat Ratio-1)/(2-Specific Heat Ratio)))/(2^((4-Specific Heat Ratio)/(2-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.

How to calculate Boltzmann Constant for Cylindrical Blast Wave?

The Boltzmann constant for cylindrical blast wave formula is defined as is the interrelation of specific heat ratio, used for the studying the cylindrical blast wave is calculated using Boltzmann Constant = (Specific Heat Ratio^(2*(Specific Heat Ratio-1)/(2-Specific Heat Ratio)))/(2^((4-Specific Heat Ratio)/(2-Specific Heat Ratio))). To calculate Boltzmann Constant for Cylindrical Blast Wave, you need Specific Heat Ratio (y_sp). With our tool, you need to enter the respective value for Specific Heat Ratio 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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