Flow Velocity Upstream of Sound Wave Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Governing Equations and Sound Wave

Normal Shock Wave

Oblique Shock and Expansion Waves

✖Sound Speed Downstream refers to the speed of sound in a medium after passing through a sound wave or disturbance.ⓘ Sound Speed Downstream [a₂]			+10% -10%
✖Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave.ⓘ Sound Speed Upstream [a₁]			+10% -10%
✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave.ⓘ Flow Velocity Downstream of Sound [u₂]			+10% -10%

✖Flow Velocity Upstream of Sound represents the velocity of a fluid flow or airflow before being influenced by a sound wave.ⓘ Flow Velocity Upstream of Sound Wave [u₁]

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Formula

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Flow Velocity Upstream of Sound Wave

Formula

`"u"_{"1"} = sqrt(2*(("a"_{"2"}^2-"a"_{"1"}^2)/("γ"-1)+"u"_{"2"}^2/2))`

Example

`"79.95655m/s"=sqrt(2*((("31.90m/s")^2-("12m/s")^2)/("1.4"-1)+("45m/s")^2/2))`

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Flow Velocity Upstream of Sound Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
u₁ = sqrt(2*((a₂^2-a₁^2)/(γ-1)+u₂^2/2))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Flow Velocity Upstream of Sound - (Measured in Meter per Second) - Flow Velocity Upstream of Sound represents the velocity of a fluid flow or airflow before being influenced by a sound wave.
Sound Speed Downstream - (Measured in Meter per Second) - Sound Speed Downstream refers to the speed of sound in a medium after passing through a sound wave or disturbance.
Sound Speed Upstream - (Measured in Meter per Second) - Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.
Flow Velocity Downstream of Sound - (Measured in Meter per Second) - Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave.

STEP 1: Convert Input(s) to Base Unit

Sound Speed Downstream: 31.9 Meter per Second --> 31.9 Meter per Second No Conversion Required
Sound Speed Upstream: 12 Meter per Second --> 12 Meter per Second No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required
Flow Velocity Downstream of Sound: 45 Meter per Second --> 45 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

u₁ = sqrt(2*((a₂^2-a₁^2)/(γ-1)+u₂^2/2)) --> sqrt(2*((31.9^2-12^2)/(1.4-1)+45^2/2))

Evaluating ... ...

u₁ = 79.9565507009901

STEP 3: Convert Result to Output's Unit

79.9565507009901 Meter per Second --> No Conversion Required

FINAL ANSWER

79.9565507009901 ≈ 79.95655 Meter per Second <-- Flow Velocity Upstream of Sound

(Calculation completed in 00.004 seconds)

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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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

Flow Velocity Upstream of Sound Wave Formula

On what factors does the speed of sound depends?

The speed of sound in a medium is determined by a combination of the medium's rigidity (or compressibility in gases) and its density. The more rigid (or less compressible) the medium, the faster the speed of sound. The greater the density of a medium, the slower the speed of sound.

How to Calculate Flow Velocity Upstream of Sound Wave?

Flow Velocity Upstream of Sound Wave calculator uses 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)) to calculate the Flow Velocity Upstream of Sound, The Flow Velocity Upstream of Sound Wave refers to the velocity of the fluid along the streamline ahead of the sound wave, this formula calculates the velocity of the adiabatic flow along the streamline ahead of the sound wave. Flow Velocity Upstream of Sound is denoted by u₁ symbol.

How to calculate Flow Velocity Upstream of Sound Wave using this online calculator? To use this online calculator for Flow Velocity Upstream of Sound Wave, enter Sound Speed Downstream (a₂), Sound Speed Upstream (a₁), Specific Heat Ratio (γ) & Flow Velocity Downstream of Sound (u₂) and hit the calculate button. Here is how the Flow Velocity Upstream of Sound Wave calculation can be explained with given input values -> 76.19055 = sqrt(2*((31.9^2-12^2)/(1.4-1)+45^2/2)).

FAQ

What is Flow Velocity Upstream of Sound Wave?

The Flow Velocity Upstream of Sound Wave refers to the velocity of the fluid along the streamline ahead of the sound wave, this formula calculates the velocity of the adiabatic flow along the streamline ahead of the sound wave and is represented as u₁ = sqrt(2*((a₂^2-a₁^2)/(γ-1)+u₂^2/2)) or 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)). Sound Speed Downstream refers to the speed of sound in a medium after passing through a sound wave or disturbance, Sound Speed Upstream refers to the speed of sound in a medium before passing through a sound wave, The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow & Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave.

How to calculate Flow Velocity Upstream of Sound Wave?

The Flow Velocity Upstream of Sound Wave refers to the velocity of the fluid along the streamline ahead of the sound wave, this formula calculates the velocity of the adiabatic flow along the streamline ahead of the sound wave is calculated using 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)). To calculate Flow Velocity Upstream of Sound Wave, you need Sound Speed Downstream (a₂), Sound Speed Upstream (a₁), Specific Heat Ratio (γ) & Flow Velocity Downstream of Sound (u₂). With our tool, you need to enter the respective value for Sound Speed Downstream, Sound Speed Upstream, Specific Heat Ratio & Flow Velocity Downstream 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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