Momentum thrust

As developed from the equation for conservation of momentum (Ref 27), the thrust, F, on a rocket motor is... 

By accelerating the gaseous combustion products through the exhaust nozzle, a thrust is imparted to the nozzle and motor case. This thrust is determined by the time rate-of-change of the total momentum of the bounded fluid, as indicated by the expression... 

The initial momentum of the jet must also be considered, as it is significant. An effective nozzle diameter can be determined to account for this momentum since sprinkler discharges lose momentum when they strike the droplet dispersal plate. This effective diameter can be found by measuring the initial thrust (Fa) of the spray. Consequently, another group follows as... 

An application for multiplexed diode-laser sensors with a potentially large impact is for measurements of important parameters at several locations in a gas turbine combustion system. In this example, illustrated schematically in Fig. 24.1, the multiplexed diode lasers are applied for simultaneous absorption measurements in the inlet, combustion, afterburner, and exhaust regions. For example, measurements of O2 mass flux at the inlet may be determined at the inlet from Doppler-shifted O2 absorption lineshapes near 760 nm. Measurements of gas temperature and H2O concentrations in the combustion and afterburner regions may be determined from H2O lineshape measurements near 1.4 pm. Finally, measurements of velocity, temperature, and species concentrations (e.g., CO, CO2, unburned hydrocarbons) may be recorded in the exhaust for the determination of momentum flux (component of thrust) and combustor emissions. 

One assumes a propulsion engine operated in the atmosphere, as shown in Fig. 1.3. Air enters in the front end i, passes through the combustion chamber c, and is expelled from the exit e. The heat generated by the combustion of an energetic material is transferred to the combustion chamber. The momentum balance to generate thrust F is represented by the terms ... 

Ducted rockets are intermediate between solid rockets and liquid ramjets in their propulsion characteristics. The propulsive force of soHd rockets is generated by the combustion of propellants composed of oxidizer and fuel components. Thus, no additional fuels or oxidizers need to be introduced from the atmosphere into the rocket motor. The momentum change of the exhaust gas from the nozzle attached to the aft-end of the combustion chamber is converted into the thrust for propulsion. On the other hand, the propulsive force of Hquid ramjets is generated by the combustion of a liquid hydrocarbon fuel with air introduced from the atmo-sphere.Ii] jjjg incoming air is compressed by a shock wave formed at the air-intake attached to the front end of the combustor. The air taken in from the atmosphere serves only as the oxidizer for the ramjets. The thrust is created by the momentum difference between the exhaust gas from the combustor and the air taken in from the atmosphere. 

Referring to Fig. 1.3, the momentum entering the air-intake is given by rhj> and that exiting from the nozzle is given by (m -i- m v. The thmst created by the momentum change is fundamentally represented by Eq. (1.62). When the air-intake and the nozzle attached to the ducted rocket are designed to obtain maximum thrust efficiency, the pressures at the front end of the air-intake and at the aft end of the nozzle become Pa = Pi = Pr> and then Eq. (1.62) is represented by... 

In any such engine performance analysis the thrust equation is the fundamental starting point. In general, the thrust exerted on a duct of arbitrary shape can be calculated from the momentum equation written in integrated form appropriate for one-dimensional problems. Following Figure n. A. 1., one has ... 

The high temperature gas generated in the combustion chamber of a rocket engine is expanded through a De Laval nozzle to convert a major portion of the enthalpy to mechanical thrust. The thrust F of a rocket engine is defined by the following conservation of momentum equation ... 

And then he trembles as the thrust of evolution, carried by its own momentum, passes the threshold where innocence ceases and an entirely new criterion of success and failure takes hold of the divine stake. The advent of man means the advent of knowledge and freedom, and with this supremely double-edged gift the... 

According to the z-component of the linear momentum equation, the thrust force from the impeller blade is balanced by the pressure difference over the pump [83] (p 423) ... 

The molecular pump functions in a fashion analogous to a diffusion pump. Instead of a molecule being diffused to the pump and then given a preferred direction by a momentum transfer from an oil vapour stream, the principle of the molecular drag pump is based on the directional velocity imparted to gss molecules which strike a fast moving surface. The overlapping of the directional velocity component with the thermal velocity component determines the overall velocity and the direction in which the particles are thrust away. If there is a second surface opposite the first, this process is repeated there. The undirected thermal movement of the gas molecules prior to collision with the moving surface is thus turned into a directed movement of the gas stream. 

---