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3/6/2014 5:42 PM | |
Joined: 3/28/2010 Last visit: 5/29/2020 Posts: 581 Rating: (141) |
Busting the myth: square root of the pressure drop value is not a flow rate Everyone knows the mantra - flow is the square root of the differential pressure, right? So here's the challenge. On a flow stand used for calibrating flow meters how can three different primary flow elements, an orifice plate, an averaging pitot tube and a venturi, each with its own inherent "characteristic", give an accurate, certified valid flow reading when the orifice plate drops 89.92"w.c., the averaging pitot tube drops 3.789"w.c. and a venturi drops 38.80"w.c. for exactly the same flow through exactly the same pipe? The square roots of three different values, 89.92, 3.789 and 38.80, do NOT equal the same number, yet the flow rate through a given pipe on my flow stand is the same for all three primary flow elements. For that matter, the pressure can be read out in different units on the same DP transmitter. 100.0" DP drop is the same as 249.17 mbar. The square root of 100.0" is not the same value as the square root for 249.17 mbar ! So tell me, how can square rooting the DP produce a flow value? None of the square root math works out ! ! ! Is square rooting the pressure drop to get a flow rate really a myth? No, it's not a myth, but square rooting the pressure drop is only part of the story of how the calculation is done. The part about 'percentage' is missing. The unspoken, 'insider' information is that the calculation for flow rate is NOT done on the pressure value itself, it is done on the percentage DP value as that percentage DP relates to the maximum flow rate at its associated DP drop value. The square root is extracted on the percent of maximum DP value, not the DP value itself. For instance, an orifice plate plate's sizing sheet states that the "max flow rate" of 400 gallons per minute has a DP of 89.92" w.c. 400 gpm is 100% of the flow rate for this orifice plate, process conditions and medium. 89.92"w.c. is 100% of the pressure drop for the process conditions and medium for this orifice plate. Let's see how a flow value is calculated for this orifice plate. What is the flow rate when the DP is 57.549" from an orifice plate that drops 89.92"w.c. at a maximum flow rate of 400 gpm? The DP value is 57.549" What percentage is 57.549" of the max DP at the maximum flow rate? 57.459/89.92 = 0.64 = 64% A DP of 57.549" is 64.0 % of 89.92". The square root is taken on 0.64 (the decimal version of 64%). Sq rt 0.64 = 0.80 The result, 0.80, is the percentage of the maximum flow rate. 0.80 = 80.0% of maximum flow rate 0.80 * 400 gpm = 320 gpm. Answer: A DP of 57.74" is 64% of the max DP (89.92") whose square root, 0.80 is 80% of the maximum flow rate (400 gpm) which is 320 gpm. As you can see, the square root is not extracted on the DP value of 89.92" or its corresponding value 223.98 mbar. Rather, the square root is extracted on the decimalized percentage value of the pressure drop with respect to the 100% DP value for the 100% flow rate value, as sized for that flow element. This resulting calculated square root, which is a percentage of the max flow rate, can be applied to the analog output or to the display value or the process value in a fieldbus transmitter. 80% of 4-20mA = 16.8mA Note that 64% of the maximum DP value produces a flow rate that is 80% of 'maximum flow rate' (for those process conditions, medium and primary flow element). That's the square root relationship. It's easy to understand that the square root of 64%, 0.64, is always the same value, 0.80, regardless of whether the DP is created by an orifice plate, an averaging pitot tube, a venturi, or any other differential pressure primary flow element. Again, it's the sizing calculation for the primary flow element that determines what that DP value is a "maximum flow rate" for given process conditions, medium, and the specific primary flow element. The calculation takes into account the characteristics of the primary flow element. By using a percentage of maximum DP/flow for calculation, three different primary flow elements can create three different DPs for exactly the same flow rate at the exactly the same process conditions, without messing with DP values or flow units. The result of the square root extraction is a still percentage value, which is applied as to 4-20mA analog output or used to scale the max flow rate value to get the instantaneous flow rate value for display or as a process value in a fieldbus transmitter. For reference, here are some even values for decimalized percentages and square roots: 100% decimalizes to 1.00 81% decimalizes to 0.81 64% decimalizes to 0.64 49% decimalizes to 0.49 36% decimalizes to 0.36 25% decimalizes to 0.25 16% decimalizes to 0.16 9% decimalizes to 0.09 4% decimalizes to 0.04 1% decimalizes to 0.01 200% decimalizes to 2.00 The square root of 1.00 is 1.00 The square root of 0.89 is 0.90 The square root of 0.64 is 0.80 The square root of 0.49 is 0.70 The square root of 0.36 is 0.60 The square root of 0.25 is 0.50 The square root of 0.16 is 0.40 The square root of 0.09 is 0.30 The square root of 0.04 is 0.20 The square root of 0.01 is 0.10 The square root of 2.0 is 1.414 |
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