A storage tank contains a liquid at depth y where y = 0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Q sin (). Equation can be written for this system as d(Ay) = 3Qsin (1) – d(t) Q (change in = (inflow) – (outflow) volume since the surface area A is constant sin²(t) A dy d(t) 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 = 1200 m² and Q = 500 m³/d. Assume that the initial condition is y = 0.

A storage tank contains a liquid at depth y where y = 0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Q sin (). Equation can be written for this system as d(Ay) = 3Qsin (1) – d(t) Q (change in = (inflow) – (outflow) volume since the surface area A is constant sin²(t) A dy d(t) 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 = 1200 m² and Q = 500 m³/d. Assume that the initial condition is y = 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Perform the given problem solving on Finite Divided Difference or Euler's method. Show the step-by-step solution with the numerical model, table of results, and graph of the model.

Problem Exercise
A storage tank contains a liquid at depth y where y = 0 when
the tank is half full. Liquid is withdrawn at a constant flow rate Q
to meet demands. The contents are resupplied at a sinusoidal rate
3Q sin?().
y
Equation can be written for this system as
d(Ay)
= 3Q sin (1) –
d(t)
change in
(inflow) – (outflow)
volume
since the surface area A is constant
dy
= 3 sin?(t
d(t)
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 = 1200 m² and
Q = 500 m³/d. Assume that the initial condition is y = 0.
%3D

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