1 Foundation of Fluid Mechanics
27
Fig. 1.29 Claude-Louis Navier (1785~1836, French mechanist)
Fig. 1.30 Simeon-denis Poisson (1781~1840, French scientist)
dv
dt
=
∂v
∂t
+ u
∂v
∂ x
+ v
∂v
∂ y
+ w
∂v
∂z
= f y −
1
ρ
∂ p
∂ y
+ ννv
dw
dt
=
∂w
∂t
+ u
∂w
∂ x
+ v
∂w
∂ y
+ w
∂w
∂z
= f z −
1
ρ
∂ p
∂z
+ ννw
where u, v, and w are the velocity components of the particle, respectively;
f x , f y , and f z are the unit mass forces acting on the particle; p is the pressure
acting on the particle; ν is the viscous coefficient of fluid motion; and is