Biomedical Engineering Reference
In-Depth Information
Figure 2.6
Momentuminthe
x
-direction.
2.6 shows the inlet and outlet momentum in the
x
-direction, and Figure 2.7 repre-
sents the forces on the same fluid element.
Projecting all these forces on the
x
-direction, and using the mass conservation
equation, we obtain
¶
τ
Du
¶
σ
xy
x
ρ
= -
+
+
F
(2.8)
x
Dt
¶
x
¶
y
Normal stress and tangential stress are for most fluids (called Newtonian fluids)
given by the constitutive relations
Figure 2.7
Forcebalanceinthe
x
-direction.Normalstress
σ
x
,tangentialstress
τ
xy
,andbodyforces
perunitvolume
F
x
ona
D
x
D
y
element.
