Non-inertial Control Volume

Non-inertial Control Volume

Rocket engine

Rocket engine works on the principle of jet propulsion.

• The gases constituting the jet are produced by the combustion of a fuel and appropriate oxidant carried by the engine. Therefore, no air is required from outside and a rocket can operate satisfactorily in a vacuum. 
  
• A large quantity of oxidant has to be carried by the rocket for its operation to be independent of the atmosphere.
  
• At the start of journey, the fuel and oxidant together form a large portion of the total load carried by the rocket.
  
• Work done in raising the fuel and oxidant to a great height before they are burnt is wasted.
  
• Therefore, to achieve the efficient use of the materials, the rocket is accelerated to a high velocity in a short distance at the start. This period of rocket acceleration is of practical interest.

Fig 11.10   A Control Volume for a Rocket Engine

Let    be the rate at which spent gases are discharged from the rocket with a velocity u relative to the rocket (Fig. 11.10) Both  and u are assumed to be constant.

Let M and V be the instantaneous mass and velocity (in the upward direction) of the rocket. The control volume as shown in Fig. 11.10 is an accelerating one. Therefore we have to apply Eq. (10.18b) as the momentum theorem of the control volume. This gives

	(11.22)

where ΣF is the sum of the external forces on the control volume in a direction vertically upward. If p_e and p_a be the nozzle exhaust plane gas pressure and ambient pressure respectively and D is the drag force to the motion of the rocket, then one can write

(11.23)

Where, A_e is outlet area of the propelling nozzle. Then Eq. (11.22) can be written as

In absence of gravity and drag, Eq (11.23) becomes