GRIM -WebPilot wrote:Hi GRIM,
I am glad to read you are enjoying the thread.
Flow lags pressure by 90° or pressure leads flow by 90°.
This is a property of an RL circuit excited by a sinusoidal voltage in electricity/electronics.
I have always found the resemblance of the jet pipe to a transmitting antenna fascinating. I used to use a simple wire as an antenna for low-power ham transmitters (this is known as a "Zep" antenna, since it is exactly what was used on the great Zeppellins of another era). Its length is precisely set for the frequency you're using, i.e. the antenna is "resonant" at that exact frequency. Here's how it works (you may already know this, but it may be new to some):
The transmitter sources RF alternating current swings in its output stage. However, at the farthest point of the antenna, it is impossible for current to flow in the wire, because it terminates at a porcelain or glass insulator. At the nearest point of course, there is almost zero resistance at the frequency in question, and current can flow at whatever rate the final stage can deliver. So, as the final stage current swings high, there is increasing flow at the near point into the wire. The charge represented by that current accumulates in the wire! However, the accumulation is greatest at the far point (the insulated end where current is zero) and nil at the near point (where there is no resistance). In between, the current tapers off and the net charge increases from near point to far point. The charge is represented at any point in the wire at a given moment in time as a particular voltage.
At the moment in the cycle where the transmitter stops pumping current (the current graph crosses the zero point of the sine curve), it has delivered all the charge it can, and at this moment of the cycle, the far end of the wire has been pumped up to maximum voltage, and there is zero current in the entire wire! The voltage is greatest at the far end and, at this moment, graphs as a quarter of a sine curve with a zero value at the near end.
The transmitter now crosses into the negative part of the current cycle (it begins to "sink" current), and the charge in the wire now acts as a high voltage "generator" feeding the near point. As the current at the near point increases over time, this charge is drained with current building at the near point but still zero (naturally) at the far point. The near point has no capability of holding charge, so its voltage is always zero. The charge in the wire decreases over the next quarter of the cycle until it is exhausted. At the moment when the voltage / charge of the entire wire is zero, maximum current is attained at the near point (this current is "negative", i.e. opposite to the maximum current we started out with at the beginning of the cycle). The whole process now repeats with charge and current reversed from what we saw before.
When you graph it out, the voltage along the wire is always a quarter sine curve (we might say 90 degrees) which is farthest from zero at the insulated far end, and always zero at the near end. The current graphs as exactly the opposite, maximized at the near end and always zero at the far end. But, at the moment of maximum current, the voltage all along the wire is zero -- and at the moment of maximum voltage, the current in the entire wire is zero. The curves simply rise and fall as partial sine curves of varying magnitude (like the side view of a jump rope being worked by two kids, if you could only see half its length). If we look at the charge in the wire as feeding the near point current, there is indeed a "90 degree lag" between voltage and current (i.e. between pressure and flow).
The frequency of resonance of such an antenna is determined by only two factors: the length of the wire and the speed of light. Unlike our pulsejets, the swings are always perfect sine curves, because all accidentally generated harmonics in the transmitter are rigorously suppressed before the signal gets to the antenna.
L Cottrill
