## Sunday, April 27, 2014

### The Four By Sixteen Rule for Pipe Flow

There are dozens, if not hundreds, of quick-and-easy methods to estimate the required size for process and mechanical equipment.  This article addresses a very fast, easy, and accurate method to determine pipe size in a process plant.   The method requires no calculator, no spreadsheet, as it can be done mentally.  It is especially useful for sitting in a meeting and answering a question that may be posed, or quickly verifying a statement made by another in the meeting.

The method is one I call "Four by Sixteen", or the 4x16 Rule.   I have never seen this anywhere published, but perhaps it is.

The basic concept for the 4x16 Rule is, at a flowing velocity of 7 feet per second through a pipe of circular cross-section (most pipes), 4,000 gallons per minute will flow through a 16-inch diameter pipe.  A flowing velocity of 7 feet per second is generally considered optimum, or close to optimum for pipe in a process plant where velocity is provided by a pump. (see caveats below)

Engineers can quickly compute that 4,000 gpm in a 16 inch diameter pipe will provide less than 7 feet per second.  The flow is actually 6.38 feet per second.  However, with 16 inch pipe, the outer diameter is 16 inches, and wall thickness is approximately one-quarter inch, leaving an inner diameter of 15.5 inches.   For the 15.5 inch ID, the flowing velocity is 6.8 feet per second, very close to the optimum of 7.

From this, we can easily determine the pipe size required for other flow rates.  This is based on the property of pipes, that if one doubles the diameter, four times the flow results for the same flowing velocity.  This also works in reverse, if one halves the pipe diameter, only one-fourth the flow results.  Using numbers, an 8 inch pipe is half of the 16 inch, therefore the flow will be one-fourth of 4,000 gpm, or 1,000 gpm.

What happens if we want to double the flow from above, for example, we want 2,000 gpm?  For this, we use a rough approximation for the square root of 2, that approximation being 1.4.  The pipe size for 2,000 gpm is then the 8 inch pipe times 1.4, or 11.2 inches.  We generally round up to even numbers for pipe sizes, therefore a 12 inch pipe would be selected.

This works in the upward direction quite easily, too, so that a 32 inch pipe will carry 4 times that of a 16 inch, or 4 times 4,000 gpm or 16,000 gpm.   Or, we can use the 1.4 factor to compute the diameter required for a doubled flow, from 4,000 to 8,000 gpm.  The 16 inch pipe is multiplied by 1.4, resulting in 22.4 inch pipe.  This would be rounded down to 22 because it is so very close to 22 inch and would not be rounded up to 24 inches.

How does one multiple 1.4 times a number in one's head?   An example shows this:  take the 8 inch pipe from above, then multiply 8 by 0.4 to give 3.2.  Then add 3.2 to 8, to provide 11.2.

This method is also very useful for validation checks on computer output.  Experience has shown that computers should be trusted only after very thorough and careful validation.

A few caveats for the 4x16 Rule.  As stated earlier, this is for process plant piping where 7 feet per second is the accepted optimum.  That optimum is for standard pipe, typically made from mild carbon steel and non-corrosive fluids at 500 pounds per square inch pressure, or less.   For substantially different conditions, for example stainless steel piping at much higher pressures, a detailed economic analysis is required to determine the optimum flowing velocity.

Also, for petroleum pipelines, the flowing velocity is a bit higher, for example the Alaska Pipeline was designed for flow of approximately 10  16 feet per second.  The Alaska Pipeline is a 60-  48-inch pipe with a design flow of 3 million barrels per day.  With the pipe having 60 48 inch OD and half-inch thick walls, as I recall (now verified), the flow is 87,300 gallons per minute at a flowing velocity of 10.2 16 feet per second.  (note: corrections to the TAPS calculations based on a faulty memory, not 60 inch but 48 inch diameter-  RES)

In hopes that this article helps the various process engineers, in whose shoes I also once walked.

Update: 4/28/2014:  This same procedure works quite well for SI units, also.  The starting point is a 400 mm ID pipe, carrying 16 cubic meters per minute, at a flowing velocity of 2.1 meters per second (same as 7 feet per second).  -- end update --  Roger

Update 2: 5/12/2014 - A similar procedure for heat exchangers is shown -- see link.  -- end update --  Roger

UPDATE: 5-31-2015 - pipeline calculation above is corrected for 48 inch rather than 60 inch diameter -  end update

Roger E. Sowell, Esq.
Marina del Rey, California