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Table of Contents:

**E n ≈ [(2 2 ^{n+2} * (2n)!) / π^{2n+1} ] * [ 1 - ( 1/3^{2n+1} ) + ( 1/5^{2n+1} ) - ... ]**

**Where,**

n = Given large number.

Euler Number refers to the dimensional number used in calculation of fluid flow. The Euler Number expresses the relationship between local pressure drop and kinetic energy per volume.

The Euler Number is used to characterize losses in the flow between a local pressure and the kinetic energy per volume where a perfect frictionless flow corresponds to an Euler Number of 1.

**Example:**

Calculate the Euler number for the given details.

Large Number (n) = 5

**Solution:**

**Apply Formula:**

E n ≈ [(2 2n+2 * (2n)!) / π^{2n+1} ] * [ 1 - ( 1/3^{2n+1} ) + ( 1/5^{2n+1} ) - ... ]

En ≈ [(2 2*5+2 * (2*5)!) / π^{2*5+1} ] * [ 1 - ( 1/3^{2*5+1} ) + ( 1/5^{2*5+1} ) - ... ]

**En ≈ 50521**