Calculating Gas Particle Effusion Rate Through Two Holes

[Grand]

Homework Statement

A gas effuses into a vacuum through a small hole of area A. The particles are then collimated by passing through a very small circular hole of radius a, in a screen a distance d from the first hole. Show that the rate at which particles emerge from the second hole is
$$\frac{1}{4}nA\left\langle v \right\rangle \frac{a^2}{d^2}$$,
where n is the particle density. We also assume that no collisions occur after the gas effuses through the first hole.

Homework Equations

We know that the effusion rate from the first hole is
$$\frac{1}{4}n\left\langle v \right\rangle$$
but I have no idea how to proceed.

The Attempt at a Solution

 

[member 553083]

I'm not sure how to begin. I understand that particles will be collimated by the small hole, but I don't know how to proceed from here.