The objective of this project is to design a float valve to control flow of water to a tank. Consider a horizontal rectangular duct of height h = 10 cm and width b connected to a large reservoir as shown. The water elevation in the reservoir is H = 5 m. Water flows from the reservoir to the tank on the left through the duct. A float valve is to be used to stop the flow when the level of water rises in the tank. The valve consists of the gate ABC in which the AB section is inclined at angle 30 and the section BC is vertical. The ABC gate is hinged at A and has a total mass of 2kg. The float valve also consists of a floating ball which is solidly attached to gate ABC with the arm EB which has a 45 angle as shown when the valve is closed. As the level of water in the tank increases, the floating ball rises causing the gate ABC to close the duct. The dimensions of the tank is h x Ix b where h = 20 cm and = 30 cm. The width of the tank and duct (normal to page) is b = 10 cm. The ball can be considered plastic with specific gravity of 0.129. water reservoir H C Th/2 B 45% A E 30 D tank h width = b 4 a) Floating part design (70%): Determine the diameter of the floating ball, D, and the arm length EB considering these constraints: (1) the tank needs to be filled up to the maximum level possible but not exceeding h, and (2) the floating component dimensions should fit within the tank and the results should practically make sense. Show with a drawing/sketch, including all dimensions, to justify that these constraints are satisfied. b) Time to fill the tank (%10): If the flow velocity inside the duct is V = 2gH (where g is the gravity acceleration), calculate how long it takes to fill the tank with water up to the intended height.