Solution Found!
A pneumatic control valve is used to adjust the flow rate
Chapter 9, Problem 9.5(choose chapter or problem)
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.
Questions & Answers
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)