Conversion formula for instrumentation

In an installation where differential pressure across an orifice plate is being used to infer volumetric flowrate, the flow is proportional to the square root of the differential pressure. That is why the square root function must be used to extract a linear flow signal.

To calculate flow rate: square root of percentage of pressure = percentage of max design flow

Example: design max flow = 1200mm (wc) DP pressure drop at 1,000 lpm

100% of 1200mm pressure = 1200mm; Sq rt of 1.00 = 1.00; 100% of max flow = 1,000 lpm
81% of 1200mm pressure = 972mm; Sq rt of 0.81 = 0.900; 90% of max flow = 900 lpm
50% of 1200mm pressure = 600mm; Sq rt of 0.50 = 0.707; 70.7% of max flow = 707 lpm
25% of 1200mm pressure = 400mm; Sq rt of 0.25 = 0.500; 50.0% of max flow = 500 lpm
20% of 1200mm pressure = 240mm; Sq rt of 0.20 = 0.447; 44.7% of max flow = 447 lpm
15% of 1200mm pressure = 192mm; Sq rt of 0.16 = 0.400; 40.0% of max flow = 400 lpm
10% of 1200mm pressure = 120mm; Sq rt of 0.10 = 0.316; 31.6% of max flow = 316 lpm
5% of 1200mm pressure = 60mm; Sq rt of 0.05 = 0.223; 22.3% of max flow = 223 lpm
1% of 1200mm pressure = 12mm; Sq rt of 0.01 = 0.100; 10.0% of max flow = 100 lpm

The quick check points I remember are:
25% of max pressure = 50% flow rate
50% of max pressure = ~ 70% flow rate

A GA for you.You did his simple math for him without being condesecending.

Square root flow scales? Like these from a durable old Brown? With ink stains from refilling the capillaries? Are there any Taylor Ful-Scopes or Bristol pr Foxboror Stabilogs still in operation?

And why is square root even an issue when all the current technology has something like this: