Suppose the gas in the explosion chamber of a rocket ship is kept at density $\rho$  and a pressure $P_1$  and that it exudes from the chamber into empty space through an opening of area at one end of the rocket, find the thrust produced on the rocket ship:

The situation is somewhat contributed. But we assume that the instant gas exudes, it maintains its density in the chamber${\rho }_1$ . Then, applying Bernoulli’s theorem between interior of chamber where $v=0$  and the point of degree $\left(p=0\right)$  and neglecting gravitational energy in space, we get:

$0+\frac{1}{2}{\rho }_1{v}^2=P_1+0$

or $v=\sqrt{\frac{2P_1}{{\rho }_1}}$

Thrust = time rate of change of momentum. All particles exit with velocity $v$  and the mass of gas leaving per unit time is ${\rho }_{1}av$ .

Rate of change of momentum

$=\left({\rho }_{1}av\right)v={\rho }_{1}a{v}^2={\rho }_{1}a\frac{2P_1}{{\rho }_1}=2P_{1}a$