Euler Number using Fluid Velocity Calculator

✖Fluid Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area.ⓘ Fluid Velocity [v_fluid]			+10% -10%
✖Change in Pressure is defined as the difference between final pressure and initial pressure. In differential form it is represented as dP.ⓘ Change in Pressure [dP]			+10% -10%
✖Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.ⓘ Density of Fluid [ρ_Fluid]			+10% -10%

✖Euler Number represents the non dimensional relationship between pressure drop and momentum in fluid flow.ⓘ Euler Number using Fluid Velocity [E_u]

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Formula

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Euler Number using Fluid Velocity

Formula

`"E"_{"u"} = "v"_{"fluid"}/(sqrt("dP"/"ρ"_{"Fluid"}))`

Example

`"13.82558"="128m/s"/(sqrt("105Pa"/"1.225kg/m³"))`

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Euler Number using Fluid Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid))
E_u = v_fluid/(sqrt(dP/ρ_Fluid))
This formula uses 1 Functions, 4 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

Euler Number - Euler Number represents the non dimensional relationship between pressure drop and momentum in fluid flow.
Fluid Velocity - (Measured in Meter per Second) - Fluid Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area.
Change in Pressure - (Measured in Pascal) - Change in Pressure is defined as the difference between final pressure and initial pressure. In differential form it is represented as dP.
Density of Fluid - (Measured in Kilogram per Cubic Meter) - Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.

STEP 1: Convert Input(s) to Base Unit

Fluid Velocity: 128 Meter per Second --> 128 Meter per Second No Conversion Required
Change in Pressure: 105 Pascal --> 105 Pascal No Conversion Required
Density of Fluid: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_u = v_fluid/(sqrt(dP/ρ_Fluid)) --> 128/(sqrt(105/1.225))

Evaluating ... ...

E_u = 13.8255801566034

STEP 3: Convert Result to Output's Unit

13.8255801566034 --> No Conversion Required

FINAL ANSWER

13.8255801566034 ≈ 13.82558 <-- Euler Number

(Calculation completed in 00.020 seconds)

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Created by Himanshu

Indian Institute of Technology, Madras (IIT Madras), Chennai, Tamil Nadu, India

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Euler Number using Fluid Velocity Formula

Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid))
E_u = v_fluid/(sqrt(dP/ρ_Fluid))

What is the significance of Euler Number?

Euler number has significance in cavitation i.e. when the pressure drops low enough to vapor pressure but it is less important unless the pressure drops low enough to vapor pressure cause cavitation in liquids.

What is the use of Euler Number?

The Euler Number is a dimensionless value used for analyzing fluid flow dynamics problems where the pressure difference between two points is important.

How to Calculate Euler Number using Fluid Velocity?

Euler Number using Fluid Velocity calculator uses Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid)) to calculate the Euler Number, Euler Number using Fluid Velocity is named after Leonhard Euler (1707-1783) and is defined as the ratio of inertial force to the pressure force. Euler Number is denoted by E_u symbol.

How to calculate Euler Number using Fluid Velocity using this online calculator? To use this online calculator for Euler Number using Fluid Velocity, enter Fluid Velocity (v_fluid), Change in Pressure (dP) & Density of Fluid (ρ_Fluid) and hit the calculate button. Here is how the Euler Number using Fluid Velocity calculation can be explained with given input values -> 1.382558 = 128/(sqrt(105/1.225)).

FAQ

What is Euler Number using Fluid Velocity?

Euler Number using Fluid Velocity is named after Leonhard Euler (1707-1783) and is defined as the ratio of inertial force to the pressure force and is represented as E_u = v_fluid/(sqrt(dP/ρ_Fluid)) or Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid)). Fluid Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area, Change in Pressure is defined as the difference between final pressure and initial pressure. In differential form it is represented as dP & Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.

How to calculate Euler Number using Fluid Velocity?

Euler Number using Fluid Velocity is named after Leonhard Euler (1707-1783) and is defined as the ratio of inertial force to the pressure force is calculated using Euler Number = Fluid Velocity/(sqrt(Change in Pressure/Density of Fluid)). To calculate Euler Number using Fluid Velocity, you need Fluid Velocity (v_fluid), Change in Pressure (dP) & Density of Fluid (ρ_Fluid). With our tool, you need to enter the respective value for Fluid Velocity, Change in Pressure & Density of Fluid 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 Euler Number?

In this formula, Euler Number uses Fluid Velocity, Change in Pressure & Density of Fluid. We can use 1 other way(s) to calculate the same, which is/are as follows -

Euler Number = Pressure Force/Inertia Force

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