Hydrostatics

The speed of water flowing through a hole in a tank can be determined using the Torricelli’s law, which is derived from the principle of conservation of energy. The speed of the water flowing through the hole at a depth is given by the equation: Where: - is the acceleration due to gravity (approximately ), - is the height of the water above the hole. This formula is derived by equating the potential energy per unit volume of the water at depth to the kinetic energy per unit volume of the water exiting the hole. Thus, the speed of water flowing through the hole is .

When a string is stretched, the work done on the string is stored as potential energy. The work done in stretching the string is given by: Where: - is the force applied (load), - is the elongation (strain). Since the strain is proportional to the elongation , the work done is: Thus, the correct expression for the work done to stretch the string is .

Concept: Total pressure inside bubble:
• External pressure at depth =
• Excess pressure due to surface tension =

Step 1: Add pressures.