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Q: Can any one give me a simple formula for changing volume flow steam into mass flow steam? Our steam is superheated, and we have pressure and temperature recording.
A: You can find the superheated steam tables in Appendix A.5b (on page 1,353) in Volume 1 of my Instrument Engineers’ Handbook.
A: When automating the conversion of volumetric dry steam flow to mass flow using pressure and temperature parameters, we use the gas laws. The gas law applies to superheated and dry steam over extended regions of pressure and temperature. It becomes the basis for making the conversion from volumetric to mass flow.
The value of the applicable gas constant can be derived from steam tables or charts for the pressure and temperature region of interest by picking one point in the center of the operating domain, and noting the values of v, P and T. Using this set of values, the gas constant, R = v * P/T, where v = specific volume of dry steam in volume per mass units; P = absolute pressure in force per unit area units; and T is the temperature in absolute temperature units.
Mass flow rate, m = V * P / ( R * T) where V = measured volumetric flow rate in volume per time units; P = measured dry steam pressure in absolute pressure units; R is the above derived gas constant in units compatible with the measurements; and T is the measured dry steam temperature in absolute temperature units. The pressure and temperature measurements may not be in absolute units. In that case, add the barometric pressure (in compatible units) to the measured gauge pressure, and 273 (in the case of a degree Centigrade or 460 in the case of a degree Fahrenheit measurement) to the measured value before the above-indicated computation is completed.
Any set of units that can be related to the steam table or steam chart in your library can be used.
By way of example, I will assume your steam temperature is 610 °F (610 + 460 = 1070 °R); your pressure is 86.0 psig; and your barometric pressure is 14.5 psia (86.0 + 14.5 = 100.5 psia steam pressure); your measured flow rate is 2.34 cu ft per second. You may ask, what is the flow rate in pounds of steam per second.
My steam table has no entry for 610 °F and 100.5 psia, but there is an entry for 600 °F and 100 psia. For that combination, the table shows the specific volume, v = 6.216 cu ft/lb. Using that data, gas constant R = v * P/T = 6.216 * 100/(600 + 460) = 0.5864 (cu ft/(sq.in.* °R)). With the gas constant, R, in hand, the mass rate m for your measured conditions may now be found: m = V * P / ( R * T) = 2.34 cu ft/sec * 100.5 psia /(0.5864*1070 °R) = 0.3784 lb/sec.
If the conditions change, and the volumetric flow rises to 10 cu ft/sec, while the pressure becomes 95 psig, and the temperature falls to 590 °F, then the mass flow rate becomes m = V * P / ( R * T) = 10 * (95 + 14.5)/(0.5864*(590 + 460)) = 10*109.5/(0.5864*1030) = 1.813 lb/sec. (Note the reuse of the gasconstant, R, derived at the beginning.)
Barometric pressure changes, as a fraction of the total process pressure, are small, and the barometric pressure used in calculations of this kind may be taken to be the average annual barometric pressure for the process location.
Steam tables are available for other units of measurement, such as pressure in bar, temperature in degrees Kelvin and specific volume in cu m/kg. Use the table that comes closest to matching your measurement units and use conversion constants for the misfits.
Otto Muller-Girard, PE, FISA
Q: What is the basis for fixing the acceptance criteria for an equipment under calibration?
A: During calibration, we ascertain the error by comparing the sensor output against a reference. (I intentionally use the term “error” instead of “accuracy” because I prefer the grammatically correct term, since a device is 1% accurate when it has 99% error.)
Otherwise, there are no “universal” criteria for calibration. As to the allowable maximum error, that is a function of the application. Personally, I like to use a reference that has an order of magnitude smaller error than the device being calibrated.
If you are a manufacturer of a device, you should inform the user of the maximum error that you guarantee not to succeed, namely the error as a percentage of the actual measurement. In addition, you should also state the rangeability over which the guaranteed error statement is guaranteed.
In addition, if the error limit is influenced by process- or installation-related factors (Reynolds number, straight pipe run requirement, viscosity limit, etc.), you should also state those limitations. For example, for a magnetic flow meter, you might say that the error limit (inaccuracy) is 1% of actual flow within the range of 10:1 if the process fluid is conductive and the flow velocity exceeds 0.5 fps.
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