A storage tank contains a liquid at depth y, where y = 0 when the tank...

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A storage tank contains a liquid at depth y, where y = 0 when the tank is half full. Liquid is withdrawn at a rate that depends on the depth of the liquid. The contents are resupplied at a sinusoidal rate. For this case, the differential equation for depth can be written as dy 3 sin dt A sin ²(t)- a(1+y)¹.5 A where A = 1200 m², Q = 400 m³/d, and a = = 160. 1.1. Use Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 2.5 d. Assume that the initial condition is y = 0. Perform all the calculations by hand. 1.2. Write a MATLAB program that uses Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 0.5 d. Assume that the initial condition is y = 0. Comment on the accuracy of this approach compared with the hand written approach. Offer reasons for any differences. A storage tank contains a liquid at depth y, where y = 0 when the tank is half full. Liquid is withdrawn at a rate that depends on the depth of the liquid. The contents are resupplied at a sinusoidal rate. For this case, the differential equation for depth can be written as dy 3 sin dt A sin ²(t)- a(1+y)¹.5 A where A = 1200 m², Q = 400 m³/d, and a = = 160. 1.1. Use Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 2.5 d. Assume that the initial condition is y = 0. Perform all the calculations by hand. 1.2. Write a MATLAB program that uses Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 0.5 d. Assume that the initial condition is y = 0. Comment on the accuracy of this approach compared with the hand written approach. Offer reasons for any differences.

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