Calculuss II final went ok. There were two problems that I chose to leave until the end because I knew that they were difficult and would eat up all my time if I did them first
( Read more... )
I'm sure that you will get partial credit for making a serious effort toward solving the problem.
For the gas tank problem, what if you put a vertical plane lengthwise through the tank, such that the tank was split into two long halves? You would now have the two foot section split with two linear sides (the plane and the surface of the fluid -- forget the meniscus). You know that one side is two feet; you should be able to calculate the other from the information given for the tank. From there, find the curve, get drunk, and derive. Me, I would forget to multiply by two at the end.
For pumps, work = weight of fluid volume * height. You would need to know the density of the fluid, or assume the density of water at 62.4 pounds per cubic foot. The height would be the distance from the bottom of the feed tube in the tank to the ground + two feet. Assuming standard temp and pressure, there should be no difference in the work as the fluid level changes, unless the feeder tube is attached to a float so that it the height changes as the fluid level drops.
There was no equation given to represent the outside of the tank. I'm thinking you needed to have calculated the equation since it was a circle of of radius 10. In my moment of dumbness I forgot how to calculate the equation.
For the gas tank problem, what if you put a vertical plane lengthwise through the tank, such that the tank was split into two long halves? You would now have the two foot section split with two linear sides (the plane and the surface of the fluid -- forget the meniscus). You know that one side is two feet; you should be able to calculate the other from the information given for the tank. From there, find the curve, get drunk, and derive. Me, I would forget to multiply by two at the end.
For pumps, work = weight of fluid volume * height. You would need to know the density of the fluid, or assume the density of water at 62.4 pounds per cubic foot. The height would be the distance from the bottom of the feed tube in the tank to the ground + two feet. Assuming standard temp and pressure, there should be no difference in the work as the fluid level changes, unless the feeder tube is attached to a float so that it the height changes as the fluid level drops.
Reply
I didn't know you were a calculus genius!
Reply
:-P
Reply
Reply
Leave a comment