question about volume and size

[saltyesq]

Hi, this is a little off topic, but I am setting up a fish tank and need help with some math.

I was told that I was wrong by someone on the fishboards who had it all mathmatically layed out and I really don't understand it.

I have a 1.5" pipe which can't be reduced.

so I was thinking to split the pipe into two 3/4 inch pipes.

now looking at this, if I took two 3/4 inch pipes, that equals 1.5" But this person said that the total volume of water would be significantly less than the water coming out of the 1.5" pipe.

is this true?

thanks, Mike

[Epsilon=One]

...I took two 3/4 inch pipes, that equals 1.5" But this person said that the total volume of water would be significantly less than the water coming out of the 1.5" pipe.

is this true?Draw two 3/4 inch circles inside of a 1.5" circle. Then, you make your decision.

[HallsofIvy]

Epsilon=One's response was very good. Two circles of diameter 3/4" will fit nicely inside a circle of diameter 3/2" with room left over!

More arithmetically, the cross section area of 3/4" diameter pipe is pi(3/8)^2= (9/64)pi so two such pipes would have area (9/32)pi. The cross section of a 1 1/2= 3/2" diameter pipe is pi(3/4)^2= (9/16)pi, twice as large as the two 3/4" pipes together. At constant water speed, the volume of water through the pipe is proportional to the cross section area so the volume for the 3/2" pipe will be twice that of the two 3/4" pipes.

The problem is that the area of a circle depends on the SQUARE of the diameter. If a circle has 1/2 the diameter of another, it has only (1/2)^2= 1/4 the area. Two such circles will still have only 1/2 the area of the larger circle.

You could replace the 3/2" pipe with FOUR 3/4" pipes.