Pipe and cistern

Question

15 pipes each having the same diameter can fill a cistern in 12 minutes.How Long will it take for 6 pipes,each with double the original diameter,to fill the same cistern at the same speed of the flow?

Answer 1

R is the diameter of the original pipe.

The length or height of the cylinder shaped pipes are assumed to be the same, k, a fixed number constant.

15 pipes fill the cistern in 12 minutes.

15 pipes fill 1/12 of the cistern per minute.

1 pipe fills 1/180 of the cistern per minute.

1 pipe with radius R fill 1/180 of the cistern per minute.

The volume of the pipe is k * pi * R^2

= k * pi * (D/2)^2 <---- radius is half of the diameter

= k * pi * D^2/4

when the diameter is doubled:

= k * pi * (2D)^2/4

= k * pi * 4D^2/4

= k * pi * D^2

which is 4 times the original volume.

So if 1 pipe with radius R fill 1/180 of the cistern per minute

the new, larger pipe with DOUBLE the DIAMETER can fill the cistern

4 times as fast.

THe new work-rate is therefore 4 times the original.

1 larger pipe with twice the diameter fills 4 * 1/180 = 4/180 = 2/90 = 1/45 of the cistern per minute.

6 of these larger pipes will fill 6 * 1/45 = 6/45 = 2/15 of the cistern per minute.

So it will take 6 of the larger pipes to 15/2 minutes to fill the cistern.

That is exactly 15/2 = 7 and 1/2 = 7.5 minutes = 7 minutes and 30 seconds