Pipe Pig

When oil refinery operations change it is common that the previous product of a pipe must be cleared before a new previous product can pass through. To clean a pipe, "engineers" place a tight-fitting rubber plug, called a Pig into one end of the pipe then using compressed nitrogen they force the pig it through the pipe and into the holding tank. The plug pushes the previous product out, leaving the pipe clean.

A pipe, 500 meters long, leads to a collecting tank. The product density is 48 lbm/cubic foot. Prior to the event a "Pig" is held secure in the extreme left end of the pipe, restrained by a pin. Our event commences when the pin is pulled. Assume commencing at that instant (t = 0+), the plug is pushed to the right at 0.8 ft/s.

Will the tank overflow?
♦ Before any manner of cleaning starts, we check to make sure the tank will not overflow. To calculate the greatest second depth of oil in the tank we take the mass of oil as the system. Initially the oil resides in the tank and pipe. Finally, oil is in the tank, only. As the Pig enters the tank, the greatest depth occurs.

(1)The mass is the same later as it was before.
Change occurred in a finer detail."

The system mass of a "closed system" is the same "later" as it was "before." The "change" here is the location and shapes changes of the system. We put the masses in their volume configurations.

(2)The mass equation when mass is constant, applies to
considerations of changes of space of the mass."

The mass equation when mass is constant, applies to considerations of changes of space of the mass. Application of the numbers permits a calculation of the second depth of product in the tank.

(3) 3

Seven meters is greater than 16.3 feet. The tank will not overflow.

Calculate the speed at which the level of oil rises in the tank.
♦ The system is all of the oil. The mass of the system is:

(4) 4

We chose a "closed system" approach. The system mass will be constant.

(5) 5

Numbers can be applied now.

(6) 6

The mass equation works for changing shaped and boundary velocity relationships. Use the equation wisely - avoid senseless algebra.