Analyzing a Multifluid Manometer with EES
Reconsider the multifluid manometer discussed in Example 1-7 and replotted in Fig. 1-66. Determine the air pressure in the tank using EES.
Also determine what the differential fluid height h_3 would be for the same air pressure if the mercury in the last column were replaced by seawater with a density of 1030 kg/m^3.
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
PI + rw*g*hl + 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 \text{Pa} \cong 130 \text{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 “h3 = 0.35” by “P1 = 129647″ and “rm = 13600” by “rm = 1030,” and clicking on the calculator symbol. It gives
h_3 = 4.62 in
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 [in]; h3 = 0.35 [m]
rw = 1000 [kg/m^3]; roil = 850 [kg/mA3]; rm = 13600 [kg/m^3]
P1 + rw*g*h1 + roil*g*h2 – rm*g*h3 = Patm