Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 1, Problem 9P

A storage tank contains a liquid at depth y, where y = 0 when the tank is half full. Liquid is withdrawn at a constant low rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3 Q sin 2 ( t ) .

Chapter 1, Problem 9P, A storage tank contains a liquid at depth y, where y=0 when the tank is half full. Liquid is

FIGURE P1.9

Equation (1.13) can be written for this system as

d ( A y ) d t = 3 Q sin 2 ( t ) Q ( change in volume ) = ( inflow ) ( outflow )

or, since the surface area A is constant

d y d t = 3 Q A sin 2 ( t ) Q A

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  m 2  and  Q = 450  m 3 /d . Assume that the initial condition is y = 0 .

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