1 (35)

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Problem 2.26PP
A laboratory experiment in the flow of water through two tanks is sketched in Fig. Assume that 
Eq. describes flow through the equal-sized holes at points A, B, or C.
(a) With holes at B and C. but none at A, write the equations of motion for this system in terms of 
h1 and h2. Assume that when /?2 = 10 cm, the outflow is 200 g/min.
(b) At h1 = 30 cm and h2= ^0 cm, compute a linearized model and the transfer function from 
pump flow (in cubic-centimeters per minute) to h2.
(c) Repeat parts (a) and (b) assuming hole B is closed and hole A is open. Assume that h3 = 20 
cm, h i > 20 cm, and h2 20 cm, and h2 
J ? s 3 0 g ^c m 2
30g ^cm
Step 3 of 5
(b)
Consider the following nonlinear equation from above information.
(5)
(6)
Consider the linearized equation.
(7)
..........(8 )
Substitute equation (7) and equation (8) in equation (5). 
1 /— 7Z— 7:— r— i
Substitute 30 cm for 10 cm for Aj,, 100 cm2 for A, 1 for /?, IQOQcip/sfC ̂ for g and 30 for R 
in equation (9).
Sh,= -̂ (1)(I0O0)(30+5*i-1O-5^)h(1)(100)(30)'
s k = - 2 ^ f i + - L t f k — L t f t V J - K’ 30i, 40 ’ 40 100 "
(1)(100)
( 10)
Consider the total inflow equation.
W ^ = W ^ + S W ...... (11)
Consider the value of nomina! Inflow Is '̂ Iven below 
10
= y > ^ c m V s e c
Substitute equation (11) in equation (10). 
1 - - L a A . l + - L ( » ' + ^ » ')
’ 3 0 l, 40 ’ 40 lo o ' ” ’
.(12)
Substitute y -v ^ c m ’ /sec for in equation (12).
S k — —