Question

______ is the square root of the ratio of the inertia force to the pressure force
1. Reynolds number
2. Mach’s number
3. Euler’s number
4. Froude’s number

Answer 1

Correct Answer - Option 3 : Euler’s number

Explanation:

Forces encountered in flowing fluids include those due to inertia, viscosity, pressure, gravity, surface tension, and compressibility. These forces can be written as follows:

• Reynolds Number (Re)
• Euler Number (Eu)
• Froude Number (Fr)
• Mach Number (M)
• Weber Number (We)

Reynolds number: 

It is the ratio of inertia force to the viscous force.

\({R_e} = \frac{{\rho VD}}{\mu }\)

Used in the application of pipe flow.

Euler's Number: 

It is defined as the ratio of the square root of the inertia force to the pressure force.

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

It finds in an application of Closed pipe flow, cavitation in a pipe, etc.

Froude Number: 

It is defined as the ratio of the square root of the inertia force to the gravity force.

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

V = velocity of water flowing through the pipe

LC = Characteristics length of the pipe

It finds its application in Free surface flows such as flow over spillways, weirs.

• Sluices, channels, etc

Mach Number: 

It is defined as the ratio of the square root of the inertia force to the elastic force.

\({M_c} = \frac{V}{{\sqrt {\frac{k}{\rho }} }}\)

It finds its application in water hammer problem, compressible flows, Aerodynamic testing, etc.