Mumbai University > Civil Engineering > Sem 5 > Applied Hydraulics 1

Marks: 10M

Year: May 2016

Reynold's number:-

It is defined as the ratio of inertia force of flowing fluid and the viscous force of the fluid.

$R_e = \frac{F_i}{F_v} = \frac{\rho AV^2}{\mu \frac{V}{L}\times A } = \frac{\rho VL}{/mu}$

$\frac{V \times L}{(\mu / \rho)}$

$R_e = \frac{V \times L}{v} \hspace{2cm} (\because \frac{\mu}{\rho} = V = \text{kinematic viscosity})$

Fi = Interia force

Fv = Viscous force

Mach's number:-

Mach's number is defined as the square root of the interia force of a flowing fluid to the elastic force.

$M = \sqrt{\frac{Fi}{Fe}} = \sqrt{\frac{\text{Inertia force}}{\text{Elastic force}}}$

$M = \sqrt{\frac{\rho AV^2}{KXL^2}} = \sqrt{\frac{\rho \times L^2 \times V^2}{K \times L^2}} = \sqrt{\frac{V^2}{K \times \rho}} = \frac{V}{\sqrt{K \times \rho}}$

$M = \frac{V}{C}$