Problem 3
30 Points
You are working at a chemical production plant, where there is a large reaction tank that is at-
tempting to generate a gas from out of a base liquid. The system arrangement is shown in the
Figure provided with this problem. Specifically, the base liquid (of density PB) is filled in the tank./nI ho
hg
GAS PRESSURE METER
GAS
Pg PRESSURE
ELUTE (PE)
OIL (P.)
BASE (₂)
4
RELIEF VALVE
MANOMETER READING
L₁
FIXED / CONTROL
PRESSURE P
MANOMETER FLUID (Pm)
View mo
after which the reactions occur and a layer of elute of density pg is formed with a thickness of
hg. Below this elute layer is an oil layer of density po and height ho. The base liquid fills the
remaining space up to a height hg. The top of the chamber where the gas collects has an attached
pressure gauge that reads the gas pressure Pg, and a relief valve that has an opening pressure P.
However, if the pressure keeps building and the valve malfunctions, you need a manual override
(otherwise things may explode!). As an engineer you have designed a simple manometer to read
out and monitor the gas pressure P, as shown. Your objective is if the gas pressure read out from
the manometer exceeds 10 percent of the valve opening pressure and the valve is not open yet, you
will manually open the valve. You keep the end of manometer at a fixed constant pressure Pa, and
you ignore the contributions to the pressure from the fixed pressure gauge fluid. You are able to
read out the manometer fluid (density pf) heights on both ends of the manometer. Determine an
expression for the manometer readings at which point you will check for whether valve needs to be
manually opened.
Note: We have structured this as a design type problem without sub-parts explicitly carved out for
the problem. However, you will receive partial credits for the major steps. So definitely break the
problem down into the major steps that you need to accomplish to get to the final answer, and
ensure that you have presented all of these steps to show your work.
Fig: 1
Fig: 2
