Induction System Volumetric Efficiency
There are two real world effects that determine how much fuel/air charge can get into the cylinder. The first is that air is compressible, the second is the dynamics (acceleration/deceleration) of the air. The compressibility of the air becomes a factor when the air enters the intake port around the intake valve. The intake port/valve forms a constriction, like the throat of a nozzle. Because air is compressible, it can only be pushed through a constriction so fast. Regardless of how much pressure you apply, the maximum velocity possible through the throat of a nozzle is a velocity equal to the speed of sound .
The same effect happens at the intake valve. The ratio of the typical velocity to the intake sonic velocity is called the inlet Mach index. From the science of fluid mechanics the controlling velocity in a compressible flow system is usually the intake valve opening. For a given cylinder and valve design, the inlet Mach index is proportional to the piston speed, and that the fuel/air charge flows in faster when the piston moves down faster. Of course, at some point the constriction of the valve opening starts to limit this. When the inlet Mach index exceeds 0.5 (intake velocity equal to half the speed of sound), the volumetric efficiency falls rapidly with increasing speed. Therefore, enginest are typically designed so that the inlet Mach index does not exceed 0.5 at the highest rated speed.
The effect of this constriction shows up as a pressure drop through the intake valve. Why don't we just open the intake valve further? Because when the valve is lifted a distance equal to 1/4 of its diameter, the area of a cylinder around the valve (that the fuel/air charge passes through, not the engine cylinder) is equal to the area of the valve face and intake port, ignoring the valve stem. Mathematically, the area of the cylinder is (2 r)(d/4). Since d = 2r, this evaluates to r2, which is the area of the intake port, the amount of additional flow through the intake port increases very slowly as the lift of the valve increases beyond 1/4 of the valve diameter.
Because of the dynamics of the fuel/air charge, the intake valve normally closes at some time after the piston passes bottom dead center. As the piston moves down, it draws the fuel/air charge into the cylinder. This movement builds up momentum in the intake manifold. When the piston reaches bottom dead center, the fuel/air charge is still flowing into the cylinder as a result of this residual momentum. Thus, at the speed desired for maximum torque, the intake valve closing is timed to correspond with the velocity of the fuel/air charge through the intake port dropping to zero. This closing will occur at some time after the piston has started the compression stroke, and will result in the maximum amount of fuel/air charge being drawn into the cylinder. This maximizes the volumetric efficiency, and maximizes the torque delivered to the crankshaft, ignoring friction effects. The angle of the crankshaft at the time the intake valve closes is called the intake valve closing angle.
So what effects does this later valve closing have at other speeds? At low speeds, the momentum built up in the intake manifold will be small, such that part of the fuel/air charge will be pushed back into the intake manifold as the piston starts up prior to the intake valve closing. At speeds above the speed for maximum torque, the constriction of intake valve opening will cause a pressure loss which will reduce the amount of fuel/air charge entering the cylinder. In either case, the amount of fuel/air charge in the cylinder is reduced, and thus the torque is reduced.
The design of the intake manifold also affects the amount of momentum built up in the flow of the fuel/air charge. The momentum of the fuel/air charge is the sum of the effect of standing waves built up from previous intake strokes keep in mind that any tube will have a resonant frequency and effect the transient wave caused by the current intake stroke. While the standing waves contribute to the overall effect, there are no sudden changes in the volumetric efficiency when the RPM of the engine is an even multiple of the natural frequency of the intake manifold.
Long, skinny intake manifold pipes give high volumetric efficiencies at low piston speeds because high momentum lots of velocity is built up in the pipe during the intake stroke. At high piston speeds, the small diameter of the intake pipe causes a constriction and the volumetric efficiency falls. Fat intake pipes show a maximum volumetric efficiency at intermediate piston speeds. However, at high piston speeds, the larger mass of the fuel/air charge in the fat intake pipe is slow to accelerate, and thus the volumetric efficiency falls off.
As the manifold pipes get shorter, the maximum gain in volumetric efficiency over having no intake manifold at all decreases. However, the gain you do get with shorter intake pipe happens over a greater range of piston speeds. Basically, it comes down to the intake manifold pipe should be designed according to the engine requirements. If you need high torque at slow piston speeds, use long skinny intake pipes. For high torque at intermediate piston speeds, use long fat intake pipes. For high torque over a wide range of piston speeds (i.e. a flat torque curve), use shorter intake pipes.