what size of pipe would be needed if 4 pipes must carry off the flow of a 12" pipe?

Question

Thanks in advance!

Answer 1

The flow through a circular pipe depends on the area of a cross-section of the pipe.  This is expressed as:

     A = pi*r²

 

Let d=diameter of one of the four pipes

 

To have the same cross-section area,

     4*(area of small pipe) = (area of 12” pipe)

     4*Pi*(d/2)² = Pi*(12/2)²

         d²= 36                    [cancel Pi; square d/2; cancel 4; square 6]

           d = 6               [take square root]

  Four 6” diameter pipes are required.

Answer 2

Hi Chad, to replace the volume of the 12" pipe by 4 pipes, we need to know the area of the 12" pipe.

 

Area = pi * r²

 

Area = 3.14 * 6², radius is equal to one-half of the diameter

 

Area = 3.14 * 36

 

Area = 113.1 square inches

 

Each of the 4 pipes will have to care one-quarter of the volume of the 12" inch pipe.

 

Divide 113.1 by 4 to determine how much each of the four pipes will have to carry.

 

Each pipe will have to carry 28.3 square inches of the volume.

 

Area = pi * r²

 

28.3 = 3.14 * r²

 

Divide by 3.14 gives:

 

r^{2 = 9}

 

r = 3

 

The diameter of a circle is equal to two times the radius.

 

d = 2 * r = 2 * 3 = 6", or the diameter of each of the four pipes would have to be 6" in diameter to carry the same amount as a 12" pipe.

 

Questions?

Answer 3

The issue here is to match the area of the big pipe to the total area of the four small pipes.

 

The area of circular openings is A = πr².

 

So to get the area of the big pipe, we would assume 12" refers to the diameter and take half of 12" because the radius of a circle is equal to half of the diameter.

Then substituting r=6" into the formula for area we get:

A_L=π(6'')²

A_L=π*36 inches squared

A_L=36π inches squared

 

Now lets take take one fourth of A_L to get the area of a small pipe.

We get A_s = (1/4)A_L

           A_s = (1/4)36π inches squared

           A_s = 9π inches squared

 

Since the area of a single small pipe is 9π inches squared we can use the area formula backwards to find the radius of a small pipe.

 

                       A_s = πr²

9π inches squared = πr^2            Next we will divide both sides by π

9π inches squared = πr^2            We get

 π                             π

 

9 inches squared   = r²                     Next we take the square root of both sides

      3 inches          = r                 Last, we double the radius to get the diameter

d = 2 * 3 ''

d = 6                                          We need four 6'' pipes to equal the flow rate of one 12'' pip.