Burt Rutan's White Knight and SpaceShip One, Photo Courtesy of Scaled Composites
Thermodynamics and Propulsion

10.2 Application of the Integral Momentum Equation to Rockets

Consider the rocket shown in Figure 10.3.

Figure 10.3: Control volume for application of momentum theorem to a rocket.
Image fig2MomentumRocket_web

$\displaystyle \sum F_x = T + A_e(p_0 - p_e), \qquad \vec{u}\cdot\vec{n} = 0 \textrm{ everywhere except } A_e$    

$\displaystyle T+A_e(p_0-p_e)=\rho u_e u_e A_e = \dot{m}u_e$    

$\displaystyle T = \dot{m} u_e + A_e(p_e-p_0)\qquad\textrm{Static thrust for a rocket engine}$