The trans-Alaskan pipeline spans 800 miles and moves millions of gallons of oil across Alaska every day. The amazing feat of engineering is possible due to the same physics that moves water into your house, waste into treatment facilities and medicine through IVs at the hospital. By understanding the relationship between flow rate and velocity, you'll be able to calculate the diameter of a pipe.
The equation for pipe diameter is the square root of 4 times the flow rate divided by pi times velocity. For example, given a flow rate of 1,000 inches per second and a velocity of 40 cubic inches per second, the diameter would be the square root of 1000 times 4 divided by 3.14 times 40 or 5.64 inches. Make sure your units are consistent.
