ERT 321 Process Control & Dynamics TUTORIAL 2 Anis Atikah binti Ahmad

I. M. Appelpolscher has acquired considerable knowledge of pneumatic control valves over the years. In particular, he knows that the flow characteristic of a “quick opening” valve is which is one reason they also called “square root” valves. Appelpolscher reasons that, if there is a need for a quick opening valve, there may be a need for a slow-opening valve as well. He conjectures that it probably would have the flow characteristic of and decides to build and test such valve. Plot f versus for his “square” valve. Does your plot resemble any other known valve characteristic? Calculate how does the gain of Appelpolscher’s valve (i.e; change in f versus change in lift) compare numerically with linear and quick-opening valves at values of = 0, 0.5 and 1.

c) If Appelpolscher wants a valve that will provide a maximum flow rate of 1024 gpm with a pressure drop across the valve of 64 psi using a liquid of specific gravity = 1, calculate the value of valve coefficient, Cv d) For a pneumatic valve, the lift is related to the air pressure signal p applied to the topworks, which varies between 3 and 15 psig. Develop an expression for in terms of p. e) With particular Cv that you have calculated in part c) and lift expression that you have developed in part d), express the relation between flow rate q and The air pressure signal p, and The liquid pressure drop developed across the value ∆Pv. Check the relation to make sure it gives reasonable values of q for various choices of p and ∆Pv.

(a) Plot f versus for his “square” valve. Does your plot resemble any other known valve characteristic? 0.00 0.20 0.04 0.45 0.40 0.16 0.63 0.60 0.36 0.77 0.80 0.64 0.89 1.00

(a) The slow opening valve resembles an equal percentage valve characteristic.

Figure 9.8 Control valve characteristics. 12

(b) Gain Linear Slow-opening Quick-opening Linear 1 Quick open 0.707 0.5 Slow open 2 The largest gain for quick opening is at , while the largest for slow opening is at . A linear valve has constant gain.

(c) Maximum flow is found when

(d) Expression for and p When p = 3 psig When p =15 psig output input

e) Expression of q in terms of: The air pressure signal p, and The liquid pressure drop developed across the value ∆Pv. Since then,

(e) p=3psig, q=0 for all ΔPv p=15psig, when