A spherical water tank of radius, R = 4 meters is emptied through a small circular...

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A spherical water tank of radius, R = 4 meters is emptied through a small circular hole of radius r = 0.02 meters at the bottom. The top of the tank is open to atmosphere. The instantaneous water level, h, (measured from the bottom of the tank, at the drain), in the tank can be determined from the solution of the following ODE: dh dt = r²√2gh 2hR-h² where g = 9.81 m/s², t is in seconds and h is in meters. a) If the initial water level (at t = 0 seconds) is h = 7m, find the water level of the tank after 6 hours, using Midpoint method with a step size of 1 hour (note: be consistent with the units). Give your answer correct to 4 decimal places. b) Based on your calculation in part (a), at least how many hours it takes to drain the water level below 4 meters? c) Use MATLAB's ode45 function to find the time it takes for the tank to drain completely (ie. h nearest 10 minutes (you need to use a step size of 10 minutes). = 0). Give your answer in minutes, correct to the Note: • you have to generate the full tspan vector (instead of just specifying the start and end values of the tspan), with a step size of 10 minutes and pass it to the ode45 function. ⚫ the height, h will become a complex value once it falls below 0 meters. A spherical water tank of radius, R = 4 meters is emptied through a small circular hole of radius r = 0.02 meters at the bottom. The top of the tank is open to atmosphere. The instantaneous water level, h, (measured from the bottom of the tank, at the drain), in the tank can be determined from the solution of the following ODE: dh dt = r²√2gh 2hR-h² where g = 9.81 m/s², t is in seconds and h is in meters. a) If the initial water level (at t = 0 seconds) is h = 7m, find the water level of the tank after 6 hours, using Midpoint method with a step size of 1 hour (note: be consistent with the units). Give your answer correct to 4 decimal places. b) Based on your calculation in part (a), at least how many hours it takes to drain the water level below 4 meters? c) Use MATLAB's ode45 function to find the time it takes for the tank to drain completely (ie. h nearest 10 minutes (you need to use a step size of 10 minutes). = 0). Give your answer in minutes, correct to the Note: • you have to generate the full tspan vector (instead of just specifying the start and end values of the tspan), with a step size of 10 minutes and pass it to the ode45 function. ⚫ the height, h will become a complex value once it falls below 0 meters.

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a To solve the differential equation using the Midpoint method with a step size of 1 hour we can fol... View the full answer