Euler Number Calculator

Understanding Euler Number Calculator

The Euler number relates pressure forces to inertial forces and is used to characterize losses in fluid flow systems.

How to use this calculator

1. Enter the pressure drop \(\Delta p\) in the units used by your problem.
2. Enter the fluid density \(\rho\).
3. Enter the flow velocity \(v\).
4. Read the Euler number \(Eu\) from the calculator and compare it across similar flows.

The formula explained

This calculator uses \(Eu = \frac{\Delta p}{\rho v^2}\) to measure pressure drop relative to the fluid's density and speed. Because the result is dimensionless, it is useful for comparing different flow conditions directly.

• Eu = Euler number, a dimensionless pressure drop
• \(\Delta p\) = pressure drop across the system
• \(\rho\) = fluid density
• v = fluid velocity

Step by step method

1. Write down the pressure drop \(\Delta p\), density \(\rho\), and velocity \(v\).
2. Square the velocity to get \(v^2\).
3. Multiply \(\rho\) by \(v^2\), then divide \(\Delta p\) by that product.
4. Check that the final value has no units.

Worked example

Problem. A fluid has a pressure drop of \(\Delta p = 500\) Pa, density \(\rho = 1000\) kg/m\(^3\), and velocity \(v = 2\) m/s. Find the Euler number.

1. Compute \(v^2 = 2^2 = 4\).
2. Compute \(\rho v^2 = 1000 \times 4 = 4000\).
3. Compute \(Eu = \frac{500}{4000} = 0.125\).

Tips and common mistakes

• Make sure the pressure drop, density, and velocity are all in compatible units, because the calculator assumes the formula is used consistently.
• Do not forget to square the velocity, since using \(v\) instead of \(v^2\) gives the wrong result.

Frequently asked questions