Pressure loss form:
ΔP ¼τA=A’ ð 1 : 64 Þwhere, A is wall areaðÞ¼ 2 Πrl and A’is cross-sectional flow areaðÞ¼Πr^2 ,ris
radius of the pipe,lis flow length.
Replacing (1.63)in(1.64)
ΔP¼fρU^2 A=2A’¼fρU^2 : 2 Πrl= 2 Πr^2
¼fρU^2 :ðÞðl=r 1 : 65 ÞHead lossform:
Replacing (1.6)in(1.63)
Δh¼fρU^2 :ðÞ¼l=rgρ fU^2 l=rg ð 1 : 66 Þ- Coriolis effect: Inertial frame and particle motion
It is inertial force acting upon bodies relative to a rotating reference frame. For
example, if a particle rolls on a static disc as illustrated in Fig.1.9, by the virtue of
inertia, it appears to move in a straight line to the observer in the same frame of
reference. When the disc starts to rotate then the particle is still moving in the
straight line if observed by someone standing in an inertial frame of reference
outside of the rotating disc. However, if the observer is standing on the rotating disc
in the non-inertial reference frame, then the particle will look like following a
curved path, such that the particle is resisting in the change of its final destination by
the virtue of inertia. Thus we can say thatthe Coriolis effect is in contrast to the
normal inertia which resists the change in body’s motion, whereas in this effect
body resists the change in displacement. It is crucial in inertial microfluidics where
plasma can be separated from whole blood and cells of different sizes can be
separated from each other. The direction of fluids in specific channels in centrifugal
microfluidics as a function of inertial forces and Coriolis effect can also be
achieved.
The Coriolis effect can be expressed
Fc¼m:ac ð 1 : 67 Þwhere,
Fc is Coriolis force, m is mass of the fluidic plug or particle,acis angular
acceleration.
Since,
ac¼2Uω ð 1 : 68 Þwhere,
24 C.K. Dixit