Bathtub Dynamics Simulation

This simulation has three models. Model1 shows constant inflow and outflow into a bathtub. Model 2 shows constant inflow and nonlinear outflow based on the quantity of water in the bathtub. Model 3 shows constant inflow and nonlinear outflow based on the quantity of water in the bathtub. However, Model 3 uses Torricelli's law to calculate the flow rate based on physical principles. It's an important principle in fluid dynamics and is closely related to Bernoulli's principle. 

Torricelli’s Law states that the speed (velocity) at which a fluid exits a hole in a container under the influence of gravity is given by:

v = √(2gh)

where g is the acceleration due to gravity (9.81 m/s²) and h is the vertical distance from the fluid surface to the hole.

This relationship comes from the conservation of energy: the fluid's potential energy is converted into kinetic energy as it exits. The law assumes an ideal fluid (incompressible and non-viscous), no energy losses, and that the hole is small compared to the height of the fluid, so the velocity at the surface of the fluid can be ignored.

The volumetric flow rate can then be found using the formula:

Q = A × v

where Q is the flow rate, A is the area of the hole, and v is the efflux velocity. This principle is used in applications ranging from hydrodynamics to practical situations like draining tanks or bathtubs.