Question

If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how many cubic feet of oil were leaving the pipe each second? Each day?

Answer 1

This is a matter of Amount = Rate  times  time.

First, find the area of the circular opening.  A = pi (r^2).  Here,

A = pi(10.5 inches)^2.

To obtain the volume of water that flows out of the pipe per second, multiply this area by the 30 inches per second rate.

That comes out to a volume per second of  Volume rate = pi*(10.5 inches)^2 * 30 inches per second:

Volume rate = 3.14(110.25 in^2)(30 inches/sec)
                     = 10390.8 cubic inches per second

Convert this result to cubic feet per second.  Recall that 1 cubic foot = (12 inches)^3, or 1728 cubic inches / 1 cubic foot.

Thus, 10390.8 cubic inches per second comes out to

           10390.8 cubic inches
           ----------------------------   =   Just over 6 cubic feet per sec.
               1728 cu. inches
                ---------------------
                  1 cu. ft

How many sec in 1 day?    1 day = 24 hours
                                             1 hour = 60 minutes
                                             60 seconds = 1 minute

Figure out how many seconds there are in 1 day, and then multiply your result by 6 cu. ft. / sec.