Question 1.12: Analyzing a Multifluid Manometer with EES Reconsider the mul...

The pressure in a water tank is measured by a multifluid manometer. The air pressure in the tank and the differential fluid height h_{3} if mercury is replaced by seawater are to be determined using EES.
Analysis We start the EES program by double-clicking on its icon, open a new file, and type the following on the blank screen that appears (we express the atmospheric pressure in Pa for unit consistency):

g=9.81

Patm=85600

h1=0.1; h2=0.2; h3=0.35

rw=1000; roil=850; rm=13600

P1+rw*g*h1+roil*g*h2-rm*g*h3=Patm

Here P_{1} is the only unknown, and it is determined by EES to be

P_{1}=129647 Pa \cong 130 kPa

which is identical to the result obtained before. The height of the fluid column h_{3} when mercury is replaced by seawater is determined easily by replacing \text { "h3 }=0.35 \text { " by "P1 }=129647 \text { " and " } r m =13600 \text { " by " } r m =1030, " and clicking on the calculator symbol. It gives

h_{3}=4.62 m

Discussion Note that we used the screen like a paper pad and wrote down the relevant information together with the applicable relations in an organized manner. EES did the rest. Equations can be written on separate lines or on the same line by separating them by semicolons, and blank or comment lines can be inserted for readability. EES makes it very easy to ask “what if” questions, and to perform parametric studies, as explained in Appendix 3 on the DVD.

EES also has the capability to check the equations for unit consistency if units are supplied together with numerical values. Units can be specified within brackets [ ] after the specified value. When this feature is utilized, the previous equations would take the following form:

g=9.81 [m/s^2]

Patm=85600 [Pa]

h1=0.1 [m]; h2=0.2 [m]; h3=0.35 [m]

rw=1000 [kg/m^3]; roil=850 [kg/m^3]; rm=13600 [kg/m^3]

P1+rw*g*h1+roil*g*h2-rm*g*h3=Patm