Hands-on exercise: the stress tensor of a tub of water

To complete this exercise you will need a lab assistant and the following supplies:

• A 2 or 3 liter tub filled with water.

• A square piece of stiff cardboard not more than a third as wide as the tub on a side.

• A marking pen with waterproof ink.

Fill the tub with water. Let it sit at rest on a table or counter. In your mind's eye, imagine Euclidean coordinate system axes for the tub, with the z axis in the vertical direction, and the x and y axes in the horizontal directions in a right-handed orientation relative to the z axis. These coordinate axes will be referred to as the tub frame.

Using the waterproof pen, draw a large round mark on one side of the cardboard. This will represent the direction normal to the surface of the cardboard. On the same side of the cardboard, draw two arrows, each of which is parallel to one side of the square piece of cardboard. These are the two directions tangential to the surface of the cardboard.

Leaving the tub of water at rest, insert the cardboard into the water so that the normal to the surface points in the positive x direction according to the tub frame. One of the arrows on the surface of the cardboard should be pointing in the positive y direction in the tub frame.