# Euler Number

on . Posted in Dimensionless Numbers

Euler number, abbreviated as Eu, a dimensionless number, used in fluid dynamics problems.  It is different than the constant that carries the same name, the Euler Number.  Euler Number is used for analyzing flow where the differential pressure between two points is important.  Fundamentally, it is the relationship between local pressure drop caused by a restriction and and the volumetric kinetic energy in the flow stream.  The number is a method of characterizing the energy losses in the flow stream.  When friction losses equal zero, as in a perfect flowstream, the Euler number is zero.

## Euler number formula

$$\large{ Eu = \frac{ \Delta p }{ \rho \; U^2 } }$$

### Euler Number - Symbol for Eu

$$\large{ Eu = \frac{ \Delta p }{ \rho \; U^2 } }$$

 pressure change, Δp density, ρ characteristic velocity, U

### Euler Number - Solve for Δp

$$\large{ \Delta p = Eu \; \rho \; U^2 }$$

 Euler number, Eu density, ρ characteristic velocity, U

### Euler Number - Solve for ρ

$$\large{ \rho = \frac{ \Delta p }{ Eu \; U^2 } }$$

 pressure change, Δp Euler number, Eu characteristic velocity, U

### Euler Number - Solve for U

$$\large{ U = \sqrt{ \frac{ \Delta p }{ Eu \; \rho } } }$$

 pressure change, Δp Euler number, Eu density, ρ

Symbol English Metric
$$\large{ Eu }$$ = Euler number $$\large{ deminsionless }$$
$$\large{ \Delta p }$$ =  pressure change $$\large{\frac{lbf}{in^2}}$$ $$\large{\frac{N}{m^2}}$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ U }$$ = characteristic velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ Tags: Pressure Equations