of linear momentum can be formulated, in a generic way, on a differential basis
identical to that presented for the conservation of mass, that is:
F
! ¼
d
!
P
dt
!
system
ðA2:40Þ
where the linear moment, or quantity of movement of the system P
!
, is given by:
P
!
system ¼
Z
mass
ðsystemÞ
V
!
dm
ðA2:41Þ
where in the resulting force F
!
, includes all forces and surface F
!
S and volume, F
!
V :
Whence,
F
! ¼ F
!
S þ F
!
V
ðA2:42Þ
For an infinitesimal mass system dm, Newton’s 2nd Law can be expressed by:
d
!
F ¼ dm
d
!
V
dt
!
system
ðA2:43Þ
Equation (A2.43) can be generically developed for a fluid particle of infinitesimal
mass, dm:
d F
! ¼ dm
d V
!
dt
¼ dm u
@ V
!
@x
þ v
@ V
!
@y
þ x
@ V
!
dz
þ
@ V
!
@t
"
#
ðA2:44Þ
Fig. A2.6 Schematic showing static pressure distribution
and flow velocity in horizontal pipes of homogeneous
section (upper) and variable
(lower) (after Asimov 1993)
Annex A2: Basic Topics on Laws of Motion and Evaporation
351