Gaussian plume models can be used in several fluid dynamics scenarios to calculate concentration distribution of solutes, such as a smoke stack release or contaminant released in a river. Gaussian distributions are established by Fickian diffusion, and follow a Gaussian (bell-shaped) distribution. For calculating the expected concentration of a one dimensional instantaneous point source we consider a mass  released at an instantaneous point in time, in a one dimensional domain along . This will give the following equation:
where  is the mass released at time  and location , and  is the diffusivity . This  equation makes the following four assumptions:
# The mass  is released instantaneously.
# The mass  is released in an infinite domain.
# The mass spreads only through diffusion.
# Diffusion does not vary in space.