Chapter $2$

$(10$ points$)$ Measuring tank levels.

a$.$ Your large manufacturing plant uses oil to lubricate bearings on the machines via automatic oilers. The oil is stored in a large cylindrical tank in the plant's basement, and you are responsible for scheduling refills with your supplier. The tank is covered to prevent contamination of the oil, so you can't see inside to know when the level is getting low but a small vent maintains atmospheric pressure in the headspace. You know that if the oil runs out, all the bearings on the machine will be destroyed, the company will lose production time in addition to the cost of replacing all the parts, and your boss is going to be very unhappy with you. To monitor the oil level, you plan to install a sensitive pressure gauge at the bottom of the tank where the outlet is$.$ The tank is $10$ feet tall, and you want to know when the oil level reaches $3$ feet to allow time to order more oil before it runs out. At what pressure in psi $($gauge$)$ should you order more oil? The tank diameter is $6$ feet and the density of the oil is $57\mathrm{.}6l\frac{b_m}{f}{t}^3.$

b$.$ Today you had the tank filled. Once it is completely full, you check the pressure gauge you installed, and you read a pressure of $10$ psig. Does this value make sense? Explain what you will tell your boss $($show a calculation$)$ and what you recommend doing next.