Thrust on a Rocket

Using Bernoulli’s Equation, we can compute the thrust on a rocket.

Consider a chamber of cross-sectional area filled with a gas of density . There is a small hole at the bottom with cross sectional area . We want to find the speed at which the gas leaves the chamber, .

Let us rewrite Bernoulli’s Equation accordingly:

Where is the pressure inside the chamber and is the atmospheric pressure just outside the chamber.

For a gas, the density is usually so small we can neglect variation in pressure due to height. Removing that gives us:

Rearranged for we get:

We will assume Continuity of mass flow so that:

If the hole is so small that is much much smaller than , then that means is much much larger than . We can neglect in the equation. Thus, is:

If the chamber is the exhaust change of a rocket, the thrust on the rocket is . In a period of time , the change in mass .

Using our original equation: