Chapter 8, Problem 8.15P

Interpretation Introduction

Interpretation: The relation between the flow and height of the float in a tube for a rotameter is to be derived by force balance.

Concept introduction: A Rotameter is a variable area meter in which the pressure drop is constant and the area changes as the flow rate through the rotameter changes. They are used for both liquid and gas flow measurements. At the equilibrium condition of the rotameter, the drag force just balances the gravitational force.

  $\begin{array}{l}{\text{F}}_{\text{g}}\text{=}{\text{F}}_{\text{D}}\\ \text{mg}\text{=}{\text{C}}_{\text{D}}\text{ρ}\frac{{\text{u}}^{\text{2}}}{\text{2}}\text{A}\mathrm{.......}\text{(1)}\end{array}$

In the above formula, the notations used are,

F_g = Gravitational force

F_D = Drag force

m = Mass of the float

g = Acceleration due to gravity

A = Area of the float

  $\text{ρ}$ = Density of the fluid

  ${\text{C}}_{\text{D}}$ = Drag coefficient

u = Local velocity at sharp edge