This section is from the book "House Drainage And Sanitary Plumbing", by William Paul Gerhard. Also available from Amazon: House Drainage and Sanitary Plumbing.
With various Grades, and for Lots of different sizes, capable of discharging 2 inches of rain per hour when running three-fourths full.
Robert Moore, C. E., St. Louis. Mo.

The quantity of rain to be discharged will be, under the same suppositions as above, 2 x 60 x .2755 acres = 33.06 cub. ft, per minute. For a drain, running 3/4 full, the table gives the necessary diameter = 5 1/4 inches.
For a convenient graphical exhibit of the relation between inclination, size, velocity and discharge of drains and sewers see the author's "Diagram for Sewer Calculations," 1881, N. Y.
The foregoing explanations have, I believe, sufficiently proved that no house drain needs to be larger than six inches under ordinary circumstances, while in most cases a 4-inch pipe will fully answer the purpose. Any increase of size would tend to be a detriment rather than a benefit.
 
Continue to: