- 23 Aug 09, 16:47#145360Thrust is a mechanical force which is generated through the reaction of accelerating a mass of gas, as explained by Newton's third law of motion. A gas or working fluid is accelerated to the rear and the engine and *insert mechanical device here* are accelerated in the opposite direction.
From Newton's second law of motion, we can define a force F to be the change in momentum of an object with a change in time. Momentum is the object's mass m times the velocity V. So, between two times t1 and t2, the force is given by:
F = ((m * V)2 - (m * V)1) / (t2 - t1)
If we are dealing with a solid, keeping track of the mass is relatively easy; the molecules of a solid are closely bound to each other and a solid retains its shape. But if we are dealing with a fluid (liquid or gas) and particularly if we are dealing with a moving fluid, keeping track of the mass gets tricky. For a moving fluid, the important parameter is the mass flow rate. Mass flow rate is the amount of mass moving through a given plane over some amount of time. Its dimensions are mass/time (kg/sec, slug/sec, ...) and it is equal to the density r times the velocity V times the area A. Aerodynamicists denote this parameter as m dot (m with a little dot over the top).
m dot = r * V * A
*The "dot" notation is used a lot by mathematicians, scientists, and engineers as a symbol for "d/dt", which means the variable changes with a change in time. For example, we can write Newton's second law as either
F = d(mv)/dt or F = (mv)dot
So "m dot" is not simply the mass of the fluid, but is the mass flow rate, the mass per unit time.*
Since the mass flow rate already contains the time dependence (mass/time), we can express the change in momentum across the propulsion device as the change in the mass flow rate times the velocity. We will denote the exit of the device as station "e" and the free stream as station "0". Then
F = (m dot * V)e - (m dot * V)0
A units check shows that on the right hand side of the equation:
mass/time * length/time = mass * length / time^2
This is the dimension of a force. There is an additional effect which we must account for if the exit pressure p is different from the free stream pressure. The fluid pressure is related to the momentum of the gas molecules and acts perpendicular to any boundary which we impose. If there is a net change of pressure in the flow there is an additional change in momentum. Across the exit area we may encounter an additional force term equal to the exit area Ae times the exit pressure minus the free stream pressure. The general thrust equation is then given by:
F = (m dot * V)e - (m dot * V)0 + (pe - p0) * Ae
Normally, the magnitude of the pressure-area term is small relative to the m dot-V terms.
there are two possible ways to produce high thrust. One way is to make the engine flow rate (m dot) as high as possible. As long as the exit velocity is greater than the free stream, entrance velocity, a high engine flow will produce high thrust. A large amount of air is processed each second, but the velocity is not changed very much. The other way to produce high thrust is to make the exit velocity very much greater than the incoming velocity. A moderate amount of flow is accelerated to a high velocity in these engines.
Cars can produce thrust, F1 cars do not.
