You have a cylindrical tank with a 2 m diameter. At the bottom of the tank,...

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You have a cylindrical tank with a 2 m diameter. At the bottom of the tank, there is a 5 cm diameter drain pipe with a valve. When the valve is fully open, the flow through the drain pipe depends on the height of the liquid inside the tank, h, according to the equation: Q = gh 8 where g is the gravity acceleration, h is the liquid level of the tank in m, and d is the diameter of the pipe. The level of liquid changes over time depending on the differential equation dh dt = -40 D where D is the diameter of the tank, and you assume no water is added. a) If the tank is filled with water to a level of 2.6 m and then the valve is opened, how long (in minutes) will it take for the liquid to reach a level of 0.4 m inside the tank? c) What will be the level of the water in the tank after 0, 10, 20, 30, and 40 minutes? You have a cylindrical tank with a 2 m diameter. At the bottom of the tank, there is a 5 cm diameter drain pipe with a valve. When the valve is fully open, the flow through the drain pipe depends on the height of the liquid inside the tank, h, according to the equation: Q = gh 8 where g is the gravity acceleration, h is the liquid level of the tank in m, and d is the diameter of the pipe. The level of liquid changes over time depending on the differential equation dh dt = -40 D where D is the diameter of the tank, and you assume no water is added. a) If the tank is filled with water to a level of 2.6 m and then the valve is opened, how long (in minutes) will it take for the liquid to reach a level of 0.4 m inside the tank? c) What will be the level of the water in the tank after 0, 10, 20, 30, and 40 minutes?