Calculus
Activity:
Torricelli’s Law
Posted on May 26, 2008
Topic: Applications of Integration
In this activity, students develop and use differential equations which support their learning of both Torricelli’s Law for falling liquids and projectile motion. Using multiple representations, students derive the defining formulas, beginning with the velocity of escaping liquid through to the trajectory path of that fluid.
Select your product
Downloads
Select Teacher or Student files from the drop down menu. Click on the file type you want to download.
Downloaded: 701
Activity Key Steps:
In this activity, 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 derive and explore these relationships using differential equations.
Students use the principle of conservation of energy, to discuss that potential energy possessed by water is to the top of the tank, the kinetic energy as it leaves through the tap, and then equate these to derive the common form for Torricelli’s Law, as shown.
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.