Problem 4. Two circular cylinders partially filled with water and connected at their bases by a tube as shown below are at rest. Cylinder 1 has radius of 10cm, cylinder 2 has radius of 30cm. Water volume is 1,000 cm³ and the tube contains water, yet the volume of the water in the tube is negligible. Gravity acts in the -y direction. a. Sketch the surfaces of the water in the outlined cylinder pair below that is labeled (a) and explain on subsequent pages the location and shape of the surface of the water in the two cylinders. (a) 10cm y 30cm Next, sketch the surfaces of the water in outlined cylinder pairs (b) to (e) below, and explain on subsequent pages the location and shape of the eventual steady-state surface of the water in the two cylinders when they are accelerating: b. +1 ms² in x. c. -1 ms² in x. d. +1 ms² in y. e. -1 ms² in y.

A long solid cylinder of radius 0.8 m hinged at point A is used as an automatic gate, When the water level reaches 5 m, the gate opens by turning about the hinge at point A. Determine (a) the hydrostatic force acting on the cylinder and its line of action when the gate opens and (b) the weight of the cylinder per m length of the cylinder.