Isentropic Compressibility for given Density and Speed of Sound Calculator

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✖The Density of a material is defined as mass per unit volume of a given object.ⓘ Density [ρ]			+10% -10%
✖The Speed of Sound is defined as speed of the dynamic propagation of sound waves.ⓘ Speed of Sound [a]			+10% -10%

✖Isentropic Compressibility is the fractional change in volume of the fluid element per unit change in pressure when no heat is added or taken away and frictional and dissipative effects are ignored.ⓘ Isentropic Compressibility for given Density and Speed of Sound [𝜏_s]

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Isentropic Compressibility for given Density and Speed of Sound

Formula

`"𝜏"_{"s"} = 1/("ρ"*"a"^2)`

Example

`"0.069387cm²/N"=1/("1.225kg/m³"*("343m/s")^2)`

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Isentropic Compressibility for given Density and Speed of Sound Solution

STEP 0: Pre-Calculation Summary

Formula Used

Isentropic Compressibility = 1/(Density*Speed of Sound^2)
𝜏_s = 1/(ρ*a^2)
This formula uses 3 Variables

Variables Used

Isentropic Compressibility - (Measured in Square Meter per Newton) - Isentropic Compressibility is the fractional change in volume of the fluid element per unit change in pressure when no heat is added or taken away and frictional and dissipative effects are ignored.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material is defined as mass per unit volume of a given object.
Speed of Sound - (Measured in Meter per Second) - The Speed of Sound is defined as speed of the dynamic propagation of sound waves.

STEP 1: Convert Input(s) to Base Unit

Density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic 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

𝜏_s = 1/(ρ*a^2) --> 1/(1.225*343^2)

Evaluating ... ...

𝜏_s = 6.93866102229721E-06

STEP 3: Convert Result to Output's Unit

6.93866102229721E-06 Square Meter per Newton -->0.0693866102229721 Square Centimeter per Newton (Check conversion here)

FINAL ANSWER

0.0693866102229721 ≈ 0.069387 Square Centimeter per Newton <-- Isentropic Compressibility

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology (IIT), Bombay

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Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< 18 Governing Equations and Sound Wave Calculators

Speed of Sound Downstream of Sound Wave

Go Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))

Speed of Sound Upstream of Sound Wave

Go Sound Speed Upstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Downstream of Sound^2-Flow Velocity Upstream of Sound^2)/2+Sound Speed Downstream^2/(Specific Heat Ratio-1)))

Flow Velocity Downstream of Sound Wave

Go Flow Velocity Downstream of Sound = sqrt(2*((Sound Speed Upstream^2-Sound Speed Downstream^2)/(Specific Heat Ratio-1)+Flow Velocity Upstream of Sound^2/2))

Flow Velocity Upstream of Sound Wave

Go Flow Velocity Upstream of Sound = sqrt(2*((Sound Speed Downstream^2-Sound Speed Upstream^2)/(Specific Heat Ratio-1)+Flow Velocity Downstream of Sound^2/2))

Ratio of Stagnation and Static Pressure

Go Stagnation to Static Pressure = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(Specific Heat Ratio/(Specific Heat Ratio-1))

Critical Pressure

Go Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure

Stagnation Temperature

Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)

Speed of Sound

Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)

Ratio of Stagnation and Static Density

Go Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))

Critical Density

Go Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))

Mayer's Formula

Go Specific Gas Constant = Specific Heat Capacity at Constant Pressure-Specific Heat Capacity at Constant Volume

Ratio of Stagnation and Static Temperature

Go Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2

Critical Temperature

Go Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)

Isentropic Compressibility for given Density and Speed of Sound

Go Isentropic Compressibility = 1/(Density*Speed of Sound^2)

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Speed of Sound given Isentropic Change

Go Speed of Sound = sqrt(Isentropic Change)

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Isentropic Change across Sound Wave

Go Isentropic Change = Speed of Sound^2

Isentropic Compressibility for given Density and Speed of Sound Formula

Isentropic Compressibility = 1/(Density*Speed of Sound^2)
𝜏_s = 1/(ρ*a^2)

What is Isentropic Compressibility?

Compressibility is the fractional change in volume of the fluid element per unit change in pressure. If no heat is added to or taken away from the fluid element, and if friction is ignored, the compression of the fluid element takes place isentropically, defined as the isentropic compressibility.

How to Calculate Isentropic Compressibility for given Density and Speed of Sound?

Isentropic Compressibility for given Density and Speed of Sound calculator uses Isentropic Compressibility = 1/(Density*Speed of Sound^2) to calculate the Isentropic Compressibility, The Isentropic Compressibility for given Density and Speed of Sound formula is a measure of how the density of a fluid changes with pressure under adiabatic conditions. Isentropic Compressibility is denoted by 𝜏_s symbol.

How to calculate Isentropic Compressibility for given Density and Speed of Sound using this online calculator? To use this online calculator for Isentropic Compressibility for given Density and Speed of Sound, enter Density (ρ) & Speed of Sound (a) and hit the calculate button. Here is how the Isentropic Compressibility for given Density and Speed of Sound calculation can be explained with given input values -> 740.6069 = 1/(1.225*343^2).

FAQ

What is Isentropic Compressibility for given Density and Speed of Sound?

The Isentropic Compressibility for given Density and Speed of Sound formula is a measure of how the density of a fluid changes with pressure under adiabatic conditions and is represented as 𝜏_s = 1/(ρ*a^2) or Isentropic Compressibility = 1/(Density*Speed of Sound^2). The Density of a material is defined as mass per unit volume of a given object & The Speed of Sound is defined as speed of the dynamic propagation of sound waves.

How to calculate Isentropic Compressibility for given Density and Speed of Sound?

The Isentropic Compressibility for given Density and Speed of Sound formula is a measure of how the density of a fluid changes with pressure under adiabatic conditions is calculated using Isentropic Compressibility = 1/(Density*Speed of Sound^2). To calculate Isentropic Compressibility for given Density and Speed of Sound, you need Density (ρ) & Speed of Sound (a). With our tool, you need to enter the respective value for Density & 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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