There is a tank shaped like a square box with all sides 3 m

There is a tank shaped like a square box, with all sides 3 m in length (see sketch on the right). One of the side walls is movable: it can swing outwards from a hinge at the base. That wall is help upright by a horizontal rope at the top of the tank (3 m above the tank bottom). The tank is full of water to a depth of 2 m and the moveable wall is upright. The water is at 15.6 degree C, so gamma = 9.80 kN/m^3. (a) What is the force acting on the movable wall due to hydrostatic pressure? (b) Where does that force act? (c) What is the tension in the rope? (d) Now imagine that a 1 in thick layer of oil (gamma = 8.95kN/m^3) is added on top of the water. What is the tension in the rope?

Solution

a) Pressure acting on the movable wall = 9.80 x 2 = 19.6 kN/m².

b) Force acts at the center of pressure = 1 + 2/2 = 2 m below from top of the wall.

c) Say , tension is the rope is T kN.

Now take a moment about hinge at equilibrium , T x 3 - 19.6 x 2 x 3 x 1 = 0

Or, T = 39.2 kN.

d) If oil is top of the water then pressure on the wall = 19.6 + 8.95 x 1 = 28.55 kN/m2.

So, new tension in the rope is Tn.

Moment equation at equilibrium about hinge , Tn x 3 - 19.6 x 2 x 3 x 1 - 8.95 x 3 x 1 x 0.5 = 0

Or, Tn = 43.675 kN.