Calculus: Torricelli's Law

Students investigate Torricelli’s Law. This law describes the relationship between the velocity of fluid leaving a container under the force of gravity and the height of the fluid.

Students explore this relationship using differential equations.

Students then make a connection between the equation given by Torricelli’s law and a differential equation for the change in volume with respect to time. They identify all the relevant parameters and functions which apply to such a system, and how these relate to each other.

Students build a relationship between time and height, which leads to a formula for height with respect to time.

Students will describe this situation as a graphical representation of height vs. time. At the end of this activity, given a function that expresses the velocity or acceleration of a moving object as a function of time, students integrate to find a function that describes the displacement as a function of time.