A common device used to measure volumetric flow rate is the rotameter.
The rotameter consists of a transparent tapered tube with a float in
it. When the flow enters the rotameter, the float will rise to a position
where both the drag force and buoyant force will be balanced by its own weight. That is,
FD + FB = W
Solving for flow velocity, um,gives,
Note that um is the mean velocity passing through the annular
space between the float and the tube; Vb is the volume of
the float; ρb and ρf are
the density of the float and fluid, respectively; CD is the
drag coefficient; Afr is the projected area of the float;
and g is the acceleration of gravity.
The volumetric flow rate is then given by
Q = umAm
where Am is the area of the annular space.
The discussion of rotameters has taken into account the drag
force, which is due to viscous effects. Although this chapter is mainly
focused on discussion of incompressible and inviscid flow, for illustration
purposes, it is appropriate to introduce the flow measurement technique
using the rotameter here, which includes viscous drag effect (modeled as CD).