Which of the following is dimension less number?

I. Froude's number

II. Euler's number 

Explanation:

Dimensionless Numbers: Dimensionless numbers are quantities without any physical units and are used in various fields of engineering and physics to describe the relative effects of different physical phenomena.

• Froude's Number (I): This is a dimensionless number defined as the ratio of the inertial forces to the gravitational forces. It is used to characterize the flow of fluids, particularly in open channels and ship hydrodynamics. 

\({F_r} = \frac{V}{{\sqrt {gL_C} }}\)

V = velocity of water flowing through the pipe and LC = Characteristics length of the pipe

• Euler's Number (II): This is another dimensionless number defined as the ratio of the pressure forces to the inertial forces within a fluid flow. It is used in fluid dynamics 

\({E_u} = \frac{V}{{\sqrt {\frac{P}{\rho }} }}\)

Both Froude's number and Euler's number are dimensionless numbers.