process dynamics

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50288-9-6E AID: 59493 | 17/10/2017
(a)
Refer to Fig 9.8 in the textbook.
The flow characteristics of linear characteristics is .
The flow characteristics of square-root characteristics is .
The flow characteristics of square characteristics is .
Using excel a graph is drawn between f versus l for three different characteristics. The plot obtained is shown in Figure 1.
From the plot in Figure 1, the square valve curve is similar to the equal percentage curve in Fig 9.8.
Thus, the characteristics of square valve resemble the characteristics of equal percentage valve.
(b)
Consider the change in f to the change in l is the valve gain.
 	…… (1)
Calculate the gain of quick-opening valve.
Substitute for f in equation (1)
Calculate the gain of linear valve.
Substitute for f in equation (1)
The valve gains of quick-opening valve and linear valve are calculated for .
	Valve
	Valve Gain
	l=0
	l=0.5
	l=1
	Quick open
	
	
 
	0.707
	0.5
	Linear
	1
	1
	1
	1
The maximum gain for Quick open valve is at l=0.
The gain for linear valve is constant.
Thus, the valve gains of quick-opening valve and linear valve are calculated and compared.
(c)
Consider the design equation for sizing control valves.
	…… (2)
 is the valve coefficient
 is the flow characteristics
 is the pressure drop across the value
 is the specific gravity of the fluid
Substitute 1 for , 64 for and 1024 for q in equation (2).
The value of is determined when 
Rewrite the equation.
The value of is .
(d)
Consider the change in lift values to the applied pressure.
The values are at and at 
Write the expression for l in terms of p.
 
Thus, the expression relating l and p is .
(e)
The value of calculated in part (c) is 
Substitute 128 for and 1 for in equation (2).
For square valve, 
Substitute for l.
	…… (4)
The applied pressure varies between 3 and 15 psig.
Substitute 3 for p in equation (4).
For , for all values of 
Substitute 15 for p in equation (4).
For ,
For ,
Thus, the calculated values of q for various choices of p and are reasonably well within the limits.