Euler Number Calculator - Physics

Euler Number Calculator – Physics

Euler Number Calculator is a mathematical tool that is used to find the Euler number by using the change in pressure in the flow of the fluid, its density, and the velocity of the fluid in the steady flow. It also finds other terms such as (pressure, density, and velocity) by putting the values of the remaining terms.

What is Euler Number in physics?

In physics, Euler numbers play an important role to find the dimensional number of the fluid in its steady flow. The euler number shows the relationship between the kinetic energy and dropness of the pressure in flow.

It is also used to determine the losses of flow rate due to friction of the surface under kinetic energy and the specific pressure of the fluid that corresponded to the Euler number.

Formula:

The mathematical formula for the Euler number is stated as.

E_u = Δp / ρV²

It’s arranged to find the value of pressure.

Δp = E_u ρV²

To find the value of velocity it becomes.

V² = Δp / ρ E_u

V = √Δp / ρ E_u

To find the value of Density it becomes.

ρ = Δp / E_uV²

Where,

• Δp = change in Pressure of the fluid
• ρ = Density of the flowing fluid
• V = velocity of the fluid
• E_u = Euler number of the fluid

How to evaluate the Euler number:

Here we solved some examples in detail to explain the working of the tool.

Example 1:

Find the Euler number of the fluid if it flows with a pressure of 64, the density of a fluid is 4, and its flows with a velocity of 2 m/s².

Solution:

Step 1:

Write the data from the question carefully.

Δp = change in Pressure = 64,                        ρ = Density of fluid = 4,

V = velocity of fluid = 2,                                   E_u = Euler number =?

Step 2:

Write the formula of the Euler number in detail.

E_u = Δp / ρV²

Where,

Δp = change in Pressure of the fluid, ρ = Density of the flowing fluid

V = velocity of the fluid,                       E_u = Euler number of the fluid

Step 3:

Put the data in the above formula carefully and simplify.

Δp = 64, ρ = 4, V = 2

E_u = Δp / ρV²

E_u = 64 / [(4)(2)²]

E_u = 64 / (4 × 4)

E_u = 64 / 16

E_u = 4

Example 2:

Find the value of density of the fluid if it flows with an Euler number 14, the pressure of a fluid is 224, and its flows with a velocity of 3 m/s².

Solution:

Step 1:

Write the data from the question carefully.

Δp = change in Pressure = 224,                      ρ = Density of fluid =?,

V = velocity of fluid = 3,                                   E_u = Euler number = 14

Step 2:

Write the formula of the Euler number in detail.

ρ = Δp / E_uV²

Where,

Δp = change in Pressure of the fluid, ρ = Density of the flowing fluid

V = velocity of the fluid,                       E_u = Euler number of the fluid

Step 3:

Put the data in the above formula carefully and simplify.

Δp = 224,  E_u = 14, V = 3

ρ = Δp / E_uV²

ρ = 224 / [(14)(3)²]

ρ = 224 / (14 × 9)

ρ = 224 / 126

ρ = 1.78 (kg/m³)

Example 3:

Find the value of pressure of the fluid if it flows with an Euler number 4, the density of a fluid is 24, and its flows with a velocity of 5 m/s².

Solution:

Step 1:

Write the data from the question carefully.

Δp = change in Pressure = ?,                           ρ = Density of fluid = 24,

V = velocity of fluid = 5,                                   E_u = Euler number =4

Step 2:

Write the formula of the Euler number in detail.

Δp = E_u ρV²

Where,

Δp = change in Pressure of the fluid, ρ = Density of the flowing fluid

V = velocity of the fluid,                       E_u = Euler number of the fluid

Step 3:

Put the data in the above formula carefully and simplify.

 E_u = 4, ρ = 24, V = 5

Δp = E_u ρV²

Δp = 4 × 24 × (5)²

Δp = 4 × 24 × 25

Δp = 2400 (Pascal)