Two vertical, cylindrical tanks, each 10 m high, are installed side-by-side in a tank farm, their...

   

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Two vertical, cylindrical tanks, each 10 m high, are installed side-by-side in a tank farm, their bottoms at the same level. The tanks are connected at their bottoms by a horizontal pipe 2 meters long, with pipe inside diameter 0.03 m. The first tank (1) is full of oil and the second tank (2) is empty. Moreover, tank 1 has a cross-sectional area twice that of tank 2. The first tank also has another outlet (to atmosphere) at the bottom, composed of a short horizontal pipe 2 m long, 0.03-m diameter. Both of the valves for the horizontal pipes are opened simultaneously. What is the maximum oil level in tank 2? Assume laminar flow in the horizontal pipes, and neglect kinetic, entrance-exit losses. Problem 3: Solve the following first order equations: (A) dx =sin (ax) 2 (B) dx y = y3 Problem 4: Solve the following second order equation: dy 4/2 + (2/2) - ( 4 ) dx2 dy dx = 0 = 0; y(1) = 2; y'(1): y'(1) = -1 This is a tricky problem. (1) You will substitute y = x*v(x); (2) Once you finish simplifying after this substitution, you will substitute x = exp(t); and (3) Once you finish simplifying after this substitution, you will substitute dv/dt = p(v). Then you will see the way to finally solve it using the ODE method Two vertical, cylindrical tanks, each 10 m high, are installed side-by-side in a tank farm, their bottoms at the same level. The tanks are connected at their bottoms by a horizontal pipe 2 meters long, with pipe inside diameter 0.03 m. The first tank (1) is full of oil and the second tank (2) is empty. Moreover, tank 1 has a cross-sectional area twice that of tank 2. The first tank also has another outlet (to atmosphere) at the bottom, composed of a short horizontal pipe 2 m long, 0.03-m diameter. Both of the valves for the horizontal pipes are opened simultaneously. What is the maximum oil level in tank 2? Assume laminar flow in the horizontal pipes, and neglect kinetic, entrance-exit losses. Problem 3: Solve the following first order equations: (A) dx =sin (ax) 2 (B) dx y = y3 Problem 4: Solve the following second order equation: dy 4/2 + (2/2) - ( 4 ) dx2 dy dx = 0 = 0; y(1) = 2; y'(1): y'(1) = -1 This is a tricky problem. (1) You will substitute y = x*v(x); (2) Once you finish simplifying after this substitution, you will substitute x = exp(t); and (3) Once you finish simplifying after this substitution, you will substitute dv/dt = p(v). Then you will see the way to finally solve it using the ODE method