ООVC 1.9 A storage tank (Fig. P1.9) contains a liquid atdepth y where y = 0 when the tank is half full. Liquid is with-drawn at a constant flow rate Q to meet demands. The contentsare resupplied at a sinusoidal rate 3Q sin² (t). Equation (1.14)can be written for this system asd(Ay)dtchange involume==3Q sin² (1) -or, since the surface area A is constant=(inflow) - (outflow)dy 3—sin² (1) - QdtAAQPage 16Use Euler's method to solve for the depth y from t = 0 to 10 dwith a step size of 0.5 d. The parameter values are A = 1250 m²and Q = 450 m³/d. Assume that the initial condition is y3= 0.

ddt(Ay)=Qsin2⁡(t)−QSince A is constant .So dydt=3QAsin2⁡(t)−QAHere A=1250m2 and Q=450m3/d.Thus…

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College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.4: Graphs Of Logarithmic Functions

Problem 60SE: Prove the conjecture made in the previous exercise.

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Question

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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