Biomedical Engineering Reference
In-Depth Information
v
θ
r
ω
θ
σ
r
θ
fixed
rod
liquid
sample
turning
cylindrical
crucible
aR
R
fixed
rod
L
roller
bearing
drive
shaft
FIGURE 14.31
Concentric cylinder viscometer.
the r direction (radially fromthe center to the edge of the vessel), and the theta direction (circum-
ferentially). This equation assumes that the density is a constant. A constant density assumes the
fluid to be incompressible, which is a realistic assumption formost liquids (such as blood) and is
unrealistic for most gases, which can compress at higher pressures.
1
r
@
@
r
1
r
@
u
y
@
y
þ
@
u
z
(
ru
r
Þþ
@
z
¼
0
:
Because mass is a scalar quantity, there is only one conservation of mass equation, although
there are three terms in that equation, relating the derivatives of the three orthogonal
velocities.
14.2.3 Fluid Momentum, the Equations of Motion, and the
Navier Stokes Equations
The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel
Stokes, describe the motion of viscous fluids such as liquids and gases and therefore the
