The first thing I did was to draw up a table of developed dynamic probe pressure versus velocity, and to do that, I found this dynamic pressure calculator on the internet:
Hint, for the program to work, Java script needs to be enabled on your computer.
To use the calculator, first enter the density of the fluid. Change the default value from (1,000 for water) to 0.0765 for air at 59 degrees Fahrenheit. Then click on imperial units (from the default SI units).
You can then enter the air velocity into the second field, and the software will calculate the developed dynamic probe pressure.
For instance enter 250 feet per second. And it will tell you that your velocity probe will develop 14.3 inches of water. At 500 feet per second the probe pressure will be 57.2 inches of water.
This is particularly interesting, in that it follows an exact inverse square law, the same as the orifice formula does for an orifice flow bench.
In other words:
Zero pressure = zero velocity (and zero orifice flow)
One quarter full pressure = half reference velocity (and half reference flow)
Full pressure = full scale reference velocity (and full scale reference flow).
The inverse square law velocity scale on a velocity probe manometer would look identical to the flow sale on a sloping manometer in an orifice bench, because it follows the exact same mathematical law.
A bit more thinking along these lines has led to a rather interesting and exciting discovery. There are many manufacturers around the world producing low cost digital voltmeter modules, both LED and liquid crystal versions, and these invariably use the same type of "chip" to make them work. Here is an example of a typical commercial LED voltmeter module:
I have come up with a very simple and very accurate way to make these digital display modules display with a perfect inverse square law. In other words, you feed in a voltage exactly proportional to measured differential pressure, (from a pressure transducer) and the display will read correctly in either feet per second velocity, or CFM flow directly in the corrected units.
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edit:
Further testing has shown that while this modification provides a smooth curve that at first glance appears to be an inverse square law, it is not a true inverse square law function, only an approximation. What fooled me was that it does produces the exact numbers at both ends, and right in the middle of the range, but it introduces a type of "S" distortion into the curve.
It reads low in the the low part of the range, correct in the middle, and slightly high at the upper end of the scale. Unfortunately the error is significant enough to sink this whole idea. I only discovered the problem after very carefully checking many more data points. More details about this later in the thread (top of page four).
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These modules invariably use either the Intersil ICL7106 (LED type) or the ICL7107 (liquid crystal type), but otherwise they work exactly the same way. To make these modules display in inverse square law, all that is required to do this are two resistors that have an EXACT 3:1 resistance ratio, and cross coupling the pressure input signal to the reference input of the chip.
Some suggested values for the two resistors might be 10k/30k, 11k/33k, 12k/36k, or 13/39k 1% metal film type.
The display module always reads 1,000 x input voltage at the chip, divided by the reference voltage at the chip.
Zero input voltage (zero pressure) displays "000" (chip i/p 0mV, chip ref 50mV) (reads 000)
+25mV input (quarter pressure) displays "250" (chip i/p +18.75mV, chip ref 75mV) (reads 250)
+100mV input (full scale pressure) displays "500" Chip i/p 75mV, chip ref 150mV) (reads 500)
That is with the reference voltage fixed at -50mV
By changing the fixed reference voltage, or the input voltage range, full scale readings other than "500" can readily be obtained, (up to "1999") but the inverse square law still always remains correct.
