For an ideal gas in equilibrium, the rate of collisions with the container wall and velocity distribution of particles hitting the container wall can be calculated based on naive kinetic theory, and the results can be used for analyzing effusive flow rates, which is useful in applications such as the gaseous diffusion method for isotope separation.
Assume that in the container, the number density (number per unit volume) is  and that the particles obey Maxwell's velocity distribution:
Then for a small area  on the container wall, a particle with speed  at angle  from the normal of the area , will collide with the area within time interval , if it is within the distance  from the area . Therefore, all the particles with speed  at angle  from the normal that can reach area  within time interval  are contained in the tilted pipe with a height of  and a volume of .
The total number of particles that reach area  within time interval  also depends on the velocity distribution; All in all, it calculates to be:
Integrating this over all appropriate velocities within the constraint  yields the number of atomic or molecular collisions with a wall of a container per unit area per unit time:
This quantity is also known as the "impingement rate" in vacuum physics. Note that to calculate the average speed  of the Maxwell's velocity distribution, one has to integrate over.
The momentum transfer to the container wall from particles hitting the area  with speed  at angle  from the normal, in time interval  is:Integrating this over all appropriate velocities within the constraint  yields the pressure (consistent with Ideal gas law):If this small area  is punched to become a small hole, the effusive flow rate will be: 
Combined with the ideal gas law, this yields
The above expression is consistent with Graham's law.
To calculate the velocity distribution of particles hitting this small area, we must take into account that all the particles with  that hit the area  within the time interval  are contained in the tilted pipe with a height of  and a volume of ; Therefore, compared to the Maxwell distribution, the velocity distribution will have an extra factor of :
with the constraint . The constant  can be determined by the normalization condition  to be , and overall: