
The integrals in Equation 1.7 can be approximated by assuming F
1
(t) and F
0
(t) are constant over the
interval t to t þDt (see Figure 1.4). Hence,
ð
tþDt
t
F
1
(t)dt F
1
(t)Dt (1:8)
ð
tþDt
t
F
0
(t)dt F
0
(t)Dt (1:9)
Equations 1.8 and 1.9 are reasonable approximations provided Dt is small. Substituting Equations
1.8 and 1.9 into Equation 1.7 yields
DV F
1
(t)Dt F
0
(t)Dt (1:10)
Substituting Equations 1.5, 1.6, and 1.10 into Equation 1.4 gives
AH( t þ Dt) AH(t) þ[F
1
(t) F
0
(t)]Dt (1:11)
) A[H(t þ Dt) H(t)] [F
1
(t) F
0
(t)]Dt (1:12)
) A
DH
Dt
F
1
(t) F
0
(t)(1:13)
where DH is the change in liquid level over the interval (t, t þDt). Note that DH=Dt is the average ...