8. An open tank has a vertical partition and on one side contains gasoline with density 700 kg/m³ at depth of 4 m, as shown in fig. (2.8). A rectangular gate that is 4 m high and 2 m wide and hinged at one end is located in the partition. Water is slowly added to the empty side of the tank. At what depth, (h) will the gate start to open. -Partition Stop Water Hinge Figure (2.8)

Problem 4.1 An incompressible liquid with density p is contained in a tank with rigid, vertical walls. The tank is open to the atmosphere on the top and divided into two sections, Side A and Side B. The height h of the liquid and the cross-sectional or foot-print area A on each side of the tank (area perpendicular to the coordinate h) is shown in the figure. There is a hole in the partition and the liquid can flow freely between the two sides. Assume that the system is the mass of liquid in both tanks. hA AA a) Draw a system diagram. b) Write an equation for the mass of the system, msys, in terms of the given information. One approach is to find mys, and msys, separately and then add them together to find msys. Your answer should only contain symbols. Ав c) Using your result from Part (a), calculate the first derivative of the system mass with respect to time: dmsys/dt. Your answer should include two derivatives dh/dt and dhp/dt. What is the physical meaning of these two terms and why…