A pneumatic control valve is used to adjust the flow rate

Chapter 9, Problem 9.5

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QUESTION:

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):

\(P=(1-2.44 \times 10^{-6}q^2)P_{de}\)

where \(P_{de}\) is the pump discharge pressure when the pump is dead ended (no flow).
(b) Pressure drop across the orifice:

\(\Delta P_0=1.953 \times 10^{-4}q^{2}\)

(c) Pressure drop across the furnace burners:

\(\Delta P_b=40\)

(d) R for the valve: 50
(e) Operating region of interest:

\(250 \leq q \leq 350\)

This design attempt should attempt to minimize pumping costs by keeping the pump capacity (related to \(P_{de}\)) as low as possible. In no case should \(\Delta P_v/\Delta P_s\) be greater than 0.33 at the nominal flow rate. Show, by means of a plot of the installed valve characteristic \((q\ \mathrm {vs.}\ \ell)\), just how linear the final design is.

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QUESTION:

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):

\(P=(1-2.44 \times 10^{-6}q^2)P_{de}\)

where \(P_{de}\) is the pump discharge pressure when the pump is dead ended (no flow).
(b) Pressure drop across the orifice:

\(\Delta P_0=1.953 \times 10^{-4}q^{2}\)

(c) Pressure drop across the furnace burners:

\(\Delta P_b=40\)

(d) R for the valve: 50
(e) Operating region of interest:

\(250 \leq q \leq 350\)

This design attempt should attempt to minimize pumping costs by keeping the pump capacity (related to \(P_{de}\)) as low as possible. In no case should \(\Delta P_v/\Delta P_s\) be greater than 0.33 at the nominal flow rate. Show, by means of a plot of the installed valve characteristic \((q\ \mathrm {vs.}\ \ell)\), just how linear the final design is.

ANSWER:

 

Step 1 of 5

Let \(\Delta P_{v} / \Delta P_{s}=0.33\) at the nominal \(\bar{q}=320 \mathrm{gpm}\)

\(\Delta P_{s}  =\Delta P_{B}+\Delta P_{o} \)

\(=40+1.953 \times 10^{-4} q^{2}\)  …… (1)

Also,

\(\Delta P_{v}  =P_{D}-\Delta P_{s} \)

\( =\left(1-2.44 \times 10^{-6} q^{2}\right) P_{D E}-\left(40+1.953 \times 10^{-4} q^{2}\right)\)  …… (2)

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