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# A pneumatic control valve is used to adjust the flow rate

ISBN: 9780470128671 148

## Solution for problem 9.5 Chapter 9

Process Dynamics and Control | 3rd Edition

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Problem 9.5

A pneumatic control valve is used to adjust the flow rate of a petroleum fraction (specific gravity = 0.9) that is used as fuel in a cracking furnace. A centrifugal pump is used to supply the fuel, and an orifice meter/differential pressure transmitter is used to monitor flow rate. The nominal fuel rate to the furnace is 320 gal/min. Select an equal percentage valve that will be satisfactory to operate this system. Use the following data (all pressures in psi; all flow rates in gal/min): (a) Pump characteristic (discharge pressure): P = (1 - 2.44 X 10-6q2)Pde where P de is the pump discharge pressure when the pump is dead ended (no flow). (b) Pressure drop across the orifice: 11P0 = 1.953 X 10-4q2 (c) Pressure drop across the furnace burners: 11Pb = 40 (d) R for the valve: 50 (e) Operating region of interest: 250 ,; q ,; 350 This design attempt should attempt to minimize pumping costs by keeping the pump capacity (related to Pde) as low as possible. In no case should 11Pvii1P8 be greater than 0.33 at the nominal flow rate. Show, by means of a plot of the installed valve characteristic (q vs. C), just how linear the final design is.

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Uses of the Equations of Motion • Very few exact solutions of the full equations: – Unidirectional laminar flows are one class of exact solutions. – Simple shapes: spheres, ellipsoids, tori, etc., have solutions. – Most problems not amenable to exact analytical solutions. – Linear vs. nonlinear mathematics. • Dimensional analysis: – Insights even without solving the equations. – Scaling for length, velocity, pressure, etc. • Computational (numerical) solution: – Modern digital computers and the rise of CFD. – Commercial CFD software. Special team projects during the week of the AICHE Annual Meeting (Nov. 9-13) CHE377 – Fall 2016 Digression: past projects in CHE377 • Build Geometry • Solve PDE Digre

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A pneumatic control valve is used to adjust the flow rate