The height H of water in a tank, whose cross-sectional area is A, is a function of time t due to an inflow qin and an outflow qout. The governing differential equation arises from a mass balance as where qin and qout are the volume flow rates, and the density of water is taken as constant. The initial height, at t = 0, is zero. Compute the time taken for the height to rise to 2 m. The area A is given as 0.03 m2, and qin = 6 × 10−4 m3/s. The outflow is given by qout = × Hm /s − 3 10 4 3 . Solve this problem by the fourth-order Runge–Kutta method. What is the height attained at steady state, and how long does it take to reach this value?
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