Chapter 4, Problem 4.31P

A dilute aqueous solution of H₂SO₄ (Solution A) is to be mixed with a solution containing 90.0 wt% H₂SO₄ (Solution B) to produce a 75.0 wt% solution (Solution C).

The flow rate and concentration of Solution A change periodically, so that it is necessary to adjust the flow rate of Solution B to keep the product H₂SO₄ concentration constant.

Flowmeters A and B have linear calibration plots of mass flow rate (m) versus meter reading (/?),

which pass through the following points:
Flowmeter A:	mA = 150 lbn,/h, wa = 500 lbm/h.	«a = 25 «a = 70
Flowmeter B:	riiB = 200 lbm/h, mB= 800 lbm/h.	Rb = 20 /?B = 60

The analyzer calibration is a straight line on a semilog plot of %H₂SO₄(x) on a logarithmic scale versus meter reading (/?,) on a linear scale. The line passes through the points (x = 20%, R_x= 4.0) and (x = 100%./?, = 10.0).

1. Calculate the flow' rate of Solution B needed to process 300 lb_m/h of 55% H₂SO₄ (Solution A), and the resulting flow rate of Solution C. (The calibration data are not needed for this part.)
2. Derive the calibration equations for /ha(#a). «ib(^b), andx(/?_v). Calculate the values of R\, Ru, and R_xcorresponding to the flow rates and concentrations of Part (a).
3. The process technician's job is to read Flowmeter A and the analyzer periodically, and then to adjust the flow rate of Solution B to its required value. Derive a formula that the technician can use for R_bin terms of R_Aand R_x, and then check it by substituting the values of Part (a).