Equation of Continuity for Compressible Fluids Calculator

✖Cross-Sectional Area at Point 2 is the area of cross section at a point 2.ⓘ Cross-Sectional Area at Point 2 [A₂]			+10% -10%
✖Velocity of the fluid at 2 is defined as the velocity of the flowing liquid at point 1.ⓘ Velocity of the fluid at 2 [V₂]			+10% -10%
✖Density 2 is defined as the density of the fluid at point 2.ⓘ Density 2 [ρ₂]			+10% -10%
✖Cross-Sectional Area at Point 1 is defined as the area of the section at point 1.ⓘ Cross-Sectional Area at Point 1 [A₁]			+10% -10%
✖Density 1 is defined as the density of the fluid at point 1.ⓘ Density 1 [ρ₁]			+10% -10%

✖Velocity of the fluid at 1 is defined as the velocity of the flowing liquid at a point 1.ⓘ Equation of Continuity for Compressible Fluids [V₁]

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Equation of Continuity for Compressible Fluids

Formula

`"V"_{"1"} = ("A"_{"2"}*"V"_{"2"}*"ρ"_{"2"})/("A"_{"1"}*"ρ"_{"1"})`

Example

`"3m/s"=("6m²"*"5m/s"*"700kg/m³")/("14m²"*"500kg/m³")`

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Equation of Continuity for Compressible Fluids Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2*Density 2)/(Cross-Sectional Area at Point 1*Density 1)
V₁ = (A₂*V₂*ρ₂)/(A₁*ρ₁)
This formula uses 6 Variables

Variables Used

Velocity of the fluid at 1 - (Measured in Meter per Second) - Velocity of the fluid at 1 is defined as the velocity of the flowing liquid at a point 1.
Cross-Sectional Area at Point 2 - (Measured in Square Meter) - Cross-Sectional Area at Point 2 is the area of cross section at a point 2.
Velocity of the fluid at 2 - (Measured in Meter per Second) - Velocity of the fluid at 2 is defined as the velocity of the flowing liquid at point 1.
Density 2 - (Measured in Kilogram per Cubic Meter) - Density 2 is defined as the density of the fluid at point 2.
Cross-Sectional Area at Point 1 - (Measured in Square Meter) - Cross-Sectional Area at Point 1 is defined as the area of the section at point 1.
Density 1 - (Measured in Kilogram per Cubic Meter) - Density 1 is defined as the density of the fluid at point 1.

STEP 1: Convert Input(s) to Base Unit

Cross-Sectional Area at Point 2: 6 Square Meter --> 6 Square Meter No Conversion Required
Velocity of the fluid at 2: 5 Meter per Second --> 5 Meter per Second No Conversion Required
Density 2: 700 Kilogram per Cubic Meter --> 700 Kilogram per Cubic Meter No Conversion Required
Cross-Sectional Area at Point 1: 14 Square Meter --> 14 Square Meter No Conversion Required
Density 1: 500 Kilogram per Cubic Meter --> 500 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V₁ = (A₂*V₂*ρ₂)/(A₁*ρ₁) --> (6*5*700)/(14*500)

Evaluating ... ...

V₁ = 3

STEP 3: Convert Result to Output's Unit

3 Meter per Second --> No Conversion Required

FINAL ANSWER

3 Meter per Second <-- Velocity of the fluid at 1

(Calculation completed in 00.004 seconds)

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Equation of Continuity for Compressible Fluids

Go Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2*Density 2)/(Cross-Sectional Area at Point 1*Density 1)

Equation of Continuity for Incompressible Fluids

Go Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2)/Cross-Sectional Area at Point 1

Cavitation Number

Go Cavitation number = (Pressure-Vapour Pressure)/(Mass Density*(Fluid Velocity^2)/2)

Turbulence

Go Turbulence = Density 2*Dynamic Viscosity*Fluid Velocity

Unstable Equilibrium of Floating Body

Go Metacentric Height = Distance between Point B and G-Distance between Point B and M

Knudsen Number

Go Knudsen Number = Mean Free Path of Molecule/Characteristic Length of Flow

Kinematic Viscosity

Go Kinematic Viscosity of Liquid = Dynamic Viscosity of Fluid/Mass Density

Stagnation Pressure Head

Go Stagnation Pressure Head = Static Pressure Head+Dynamic Pressure Head

Weight Density given Specific Weight

Go Weight Density = Specific Weight/Acceleration due to Gravity

Weight

Go Weight of Body = Mass*Acceleration due to Gravity

Bulk Modulus given Volume Stress and Strain

Go Bulk Modulus = Volume Stress/Volumetric Strain

Vorticity

Go Vorticity = Circulation/Area of fluid

Specific Volume

Go Specific Volume = Volume/Mass

Sensitivity of Inclined Manometer

Go Sensitivity = 1/sin(Angle)

Equation of Continuity for Compressible Fluids Formula

Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2*Density 2)/(Cross-Sectional Area at Point 1*Density 1)
V₁ = (A₂*V₂*ρ₂)/(A₁*ρ₁)

Define Equation of Continuity.

The equation of continuity is simply a mass balance of a fluid flowing through a stationary volume element. It states that the rate of mass accumulation in this volume element equals the rate of mass in minus the rate of mass out.

How to Calculate Equation of Continuity for Compressible Fluids?

Equation of Continuity for Compressible Fluids calculator uses Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2*Density 2)/(Cross-Sectional Area at Point 1*Density 1) to calculate the Velocity of the fluid at 1, Equation of Continuity for compressible fluids is defined as the product of the cross-sectional area of the pipe and the velocity of the fluid at any given point along the pipe is constant. Velocity of the fluid at 1 is denoted by V₁ symbol.

How to calculate Equation of Continuity for Compressible Fluids using this online calculator? To use this online calculator for Equation of Continuity for Compressible Fluids, enter Cross-Sectional Area at Point 2 (A₂), Velocity of the fluid at 2 (V₂), Density 2 (ρ₂), Cross-Sectional Area at Point 1 (A₁) & Density 1 (ρ₁) and hit the calculate button. Here is how the Equation of Continuity for Compressible Fluids calculation can be explained with given input values -> 3 = (6*5*700)/(14*500).

FAQ

What is Equation of Continuity for Compressible Fluids?

Equation of Continuity for compressible fluids is defined as the product of the cross-sectional area of the pipe and the velocity of the fluid at any given point along the pipe is constant and is represented as V₁ = (A₂*V₂*ρ₂)/(A₁*ρ₁) or Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2*Density 2)/(Cross-Sectional Area at Point 1*Density 1). Cross-Sectional Area at Point 2 is the area of cross section at a point 2, Velocity of the fluid at 2 is defined as the velocity of the flowing liquid at point 1, Density 2 is defined as the density of the fluid at point 2, Cross-Sectional Area at Point 1 is defined as the area of the section at point 1 & Density 1 is defined as the density of the fluid at point 1.

How to calculate Equation of Continuity for Compressible Fluids?

Equation of Continuity for compressible fluids is defined as the product of the cross-sectional area of the pipe and the velocity of the fluid at any given point along the pipe is constant is calculated using Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2*Density 2)/(Cross-Sectional Area at Point 1*Density 1). To calculate Equation of Continuity for Compressible Fluids, you need Cross-Sectional Area at Point 2 (A₂), Velocity of the fluid at 2 (V₂), Density 2 (ρ₂), Cross-Sectional Area at Point 1 (A₁) & Density 1 (ρ₁). With our tool, you need to enter the respective value for Cross-Sectional Area at Point 2, Velocity of the fluid at 2, Density 2, Cross-Sectional Area at Point 1 & Density 1 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Velocity of the fluid at 1?

In this formula, Velocity of the fluid at 1 uses Cross-Sectional Area at Point 2, Velocity of the fluid at 2, Density 2, Cross-Sectional Area at Point 1 & Density 1. We can use 1 other way(s) to calculate the same, which is/are as follows -

Velocity of the fluid at 1 = (Cross-Sectional Area at Point 2*Velocity of the fluid at 2)/Cross-Sectional Area at Point 1

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