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.

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

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

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