handbook of modern sensors

11
Flow Sensors
It’s a simple task to make a complex system,
It’s a complex task to make a simple system
11.1 Basics of Flow Dynamics
One of the fundamentals of physics is that mass is a conserved quantity. It cannot be
created or destroyed. In the absence of sources or sinks of mass, its quantity remains
constant regardless of boundaries. However, if there is influx or outflow of mass
through the boundaries, the sum of influx and efflux must be zero. Whatever mass
comes in, it must go out. When both are measured over the same interval of time, mass
entering the system (M in ) is equal to mass leaving the system (M out ) [1]. Therefore,
dM in
= dM out
. (11.1)
dt dt
In mechanical engineering, moving media whose flow is measured are liquids (water,
oil, solvents, gasoline, etc.), air, gases (oxygen, nitrogen, CO, CO 2 , methane CH 4 ,
water vapor, etc.).
In a steady flow, the velocity at a given point is constant in time. We can draw a
stream line through every point in a moving medium (Fig. 11.1A). In steady flow, the
line distribution is time independent. A velocity vector is tangent to a stream line in
every point z. Any boundaries of flow which envelop a bundle of stream lines is called
a tube of flow. Because the boundary of such a tube consists of stream lines, no fluid
(gas) can cross the boundary of a tube of flow and the tube behaves something like
a pipe of some shape. The flowing medium can enter such a pipe at one end, having
cross section A 1 and exit at the other through cross section A 2 . The velocity of a
moving material inside of a tube of flow will, in general, have different magnitudes
at different points along the tube.
The volume of moving medium passing a given plane (Fig. 11.1B) in a specified
time interval t is
= V ∫ ∫ x dA
t = = vdA, (11.2)
t