Question

2. Oil flows out a pipe at a rate of 12 cm3/sec which you are pouring into barrels for storage. The base diameter of the barrel is 52 centimeters and the height of the tank is 0.8 meters. At what rate is the depth of the oil in the tank changing when the radius of the top of the oil is 0.10 meters? How long will it take to fill up the barrel? Does the speed change if the barrel was an inverted cone instead of the same dimensions?

Answer 1

No the speed of filling the tank won't change because its volume will remain same and rate of filling is also same.

The speed of filling me varry if the inlet of the pipe is fed at the bottom of the barrel instead of top.

12cm3 sec. 7 1m -locm dhung dnt .8m = 80cm h .52m 52cm Rate of oil inflow = Adh dt An area of barrel at height to = 12 cm3/sec. 0 Now 2 d. 12 a height ho | An = π dy dia of barrel at 4 By interpolation dn = 52-42b 80 from ean 0 ② 4 - 12 ( 52-42 52.-42h ² dh 80 dt ta 8% 2704+ •27562512-28.665h) an = S 1244 44 180 + [2704 th +.091943 - 14-33256? E 21 6320 + 47040-91728 = 48+ T it - 11233.289 sec