Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:О
О
VC
Transcribed Image Text:1.9 A storage tank (Fig. P1.9) contains a liquid at
depth y where y = 0 when the tank is half full. Liquid is with-
drawn at a constant flow rate Q to meet demands. The contents
are resupplied at a sinusoidal rate 3Q sin² (t). Equation (1.14)
can be written for this system as
d(Ay)
dt
change in
volume
=
=
3Q sin² (1) -
or, since the surface area A is constant
=
(inflow) - (outflow)
dy 3—sin² (1) - Q
dt
A
A
Q
Page 16
Use Euler's method to solve for the depth y from t = 0 to 10 d
with a step size of 0.5 d. The parameter values are A = 1250 m²
and Q = 450 m³/d. Assume that the initial condition is y
3
= 0.
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