Algebra of fluids: Stokes Law and Coriolis Equation. Disclosure 24
In the previous Disclosure blog (XXIII) we started a series of contribution about application of algebra and the explanation of some biological phenomenons, with the explanation of Laffer Curve and Rolle Theorem.
In this new edition we are going to apport information, though the explanation of Stokes Law and Coriolis equation about the application of fluids study and its relationship with biological facts.
Stokes Law (George Gabriel Stokes 1851) is a particular application about the Navier- Stokes laws for the study of friction forces., that affect the spherical bodies in low velocity movement inside a viscous fluid specially in laminar fluids with low Reynolds Lumber. In a general way the Stokes Law is formuled as:
Fr = 6 (pi)Rnv
R= radius of sphere
η= viscosity of the fluid.
For its application in biology it has an special interest the variant related to particles in falling vertically in a viscous fluid by its own weight. The falling velocity or sedimentation velocity can be calculated equalling friction weight with apparent weight of the particle in the fluid and the formula is as follows:
Vs= falling velocity of particles (limit velocity)
g= gravity acceleration
ρp = density of particles
ρf = density of fluids
η= viscosity of the fluid
This formula is fundamental to explain the variations in sedimentation velocity of red blood cells, caused by viscosity changes in the blood serum, that is held in tumour, parasitic, inflammatory or infectious processes. Can also vary according size of erythrocytes by effect of the altitude or composition change in a closed atmosphere.
Coriolis Equation (Gaspard-Gustave Coriolis 1836) describes the force that acts on a body in movement placed in a system in rotation. This equation obtains the value of the Coriolis Force with the following expression:
Fc = 2m (W x V)
m= mass of the body
v=velocity of the body in the rotation system
w= angular velocity with reference in a inertial system.
This force has a vectorial character and is perpendicular to the direction of rotation axis and the movement direction of the body from the system in rotation and is the result of interaction of a tangential component, and is the result of the interaction of a tangential component, due to interaction of radial component of the body movement and another radial component due to the tangential component of the body movement. As consequence the movement made by these bodies is spiral.
The more visible form of Coriolis forces can be observed in the turn of the storms and hurricanes, Foucault Pendle and in the thermohilian current of oceanic waters (specially in the visible part of Kuro Shivo current in Pacific and currents of Gulf’s in Atlantic and their influence in weather) there are other biological manifestations related with embryologic development, trabeculas bones in force lines or all that spiral form of biologic origin. There is also influence of Coriolis forces in bone pathology related with torsion to right or left in cranial bones, known as campilognatia, and that present torsion to one or the other sense in relation to the hemisphere they are developed.