TORRICELLI’S LAW

PRERNA FOR IAS

TORRICELLI’S LAW

1. Definition of Torricelli’s Law

Torricelli’s Law states that the speed of a liquid flowing out of a small hole in a container is equal to the speed that an object would gain if it freely fell through a height equal to the depth of the liquid above the hole. This law was proposed by the Italian scientist Evangelista Torricelli and is based on Bernoulli’s Principle. It explains the relationship between the height of the liquid and the speed of efflux. The law is widely used in fluid mechanics to study the behavior of flowing liquids in tanks, reservoirs, pipes, and other hydraulic systems.

2. Formula of Torricelli’s Law

The mathematical expression of Torricelli’s Law is:

v = √(2gh)

where v is the speed of efflux, g is the acceleration due to gravity (9.8 m/s²), and h is the vertical height of the liquid above the hole. The formula shows that the speed of the liquid depends only on the depth of the liquid and gravity. As the height increases, the speed of efflux also increases. This equation is derived using Bernoulli’s theorem and is similar to the formula for the velocity of a freely falling object. It is fundamental in fluid dynamics.

3. Main Points of Torricelli’s Law

Torricelli’s Law highlights several important facts about liquid flow. The speed of efflux depends only on the height of the liquid above the opening. A greater liquid depth produces a greater speed of outflow. The speed is independent of the shape, size, or design of the container. The law is derived from Bernoulli’s Principle, which relates pressure, velocity, and energy in flowing fluids. As the liquid level falls, the speed of efflux decreases because the height decreases. This principle helps engineers design water tanks, fountains, dams, and fluid transport systems efficiently and accurately.

4. Main Illustration of Torricelli’s Law