Page 357 - Bird R.B. Transport phenomena

Table 11.4-1 Equations of Change for Pure Fluids in Terms of the Fluxes

Eq. Special form In terms of D/Dt Comments

Cont. — Table 3.5-1 For p — constant, simplifies to
(A) (V • v) = 0

Motion General T] + Table 3.5-1 For т = 0 this becomes Euler's
(B) equation

Approximate p— = -Vp - [V- T] + pg - pgP(T - т) 11.3-2 Displays buoyancy term

(C)

Energy In terms of D(K + U + Ф) -(V • q) - (V • pv) - (V • [T • v]) Exact only for Ф time independent
Dt
K+ 11 + Ф (D)

D(K+U)
In terms of •q)- (V • pv) (V • [T • v]) + p(v • g)
Dt
£+ U (E)

In terms of - ( v [V-T]) + p ( v g ) Table 3.5-1 From equation of motion
(F)

In terms of v) - (T:VV) 11.2-2 Term containing (V • v) is zero for
U (G) constant p

Dp
In terms of p^--(V.q)- (T:V v) + — 11.2-3 H=U+ {pip)
H (H)

In terms of - T | -j, j (V • v) - (T:VV) For an ideal gas Т(др/дТ) () = p
C v and T (I)

£ DT _ In p\ Dp
In terms of ( V # } 11.2-5 For an ideal gas {d In pld In T) = 1
p
In T) Dt
p
C pand T (J)