Adapted from Luyben and Luyben (1997).

(a) Calculate the gain of an orifice plate and differential pressure transmitter for flow rates of 10, 50, 75 and 90% of full scale,

(b) Calculate the gains of linear, equal-percentage, and square root control valves at the same operating points assuming constant pressure drop over the valve.

(c) For each type of valve, calculate the overall gain of the valve and sensor-transmitter system at each operating point using the results in (a) and (b). Which combination yields the most nearly linear characteristics over the range 10% to 90% of full-scale flow?

(d) Evaluate the validity of the assumptions made in this analysis; that is, to what extent would the conclusions from part (c) be expected to apply to the real situation of an orifice plate placed in series with a control valve?

Notes

(i) The gain of an orifice plate and differential pressure transmitter is Kt = dPt)dq

Where Pt = transmitter output

q = flow rate

(ii) The gain of a control valve (constant pressure drop across the valve) is Kv = dp/dP

Where q = flow rate

P = pressure applied to the valve.

(iii) The valve lift is proportional to P.