The purpose of the sanitary drainage system is to remove effluent discharged from plumbing fixtures and other equipment to an approved point of disposal. In this article, I will review some information on drainage pipe systems including definitions, gravity flow in stacks drainage fixture units (DFUs), and horizontal pipe slope and sizing.

A sanitary drainage system generally consists of: horizontal branches; vertical stacks; a building drain inside the building, and 30 inches outside by IPC or 60 inches by CPC; and a building sewer from the building drain to the point of disposal.

A stack is a main vertical pipe that carries away discharge from within a facility of water closets and urinals (soil stack) or other water waste from equipment and non-sanitary fixtures (waste stack).

History of drainage sizing

Dr. Roy Hunter, at the National Bureau of Standards, is credited with developing the sizing method for drainage systems, which was originally proposed in 1923. Each fixture had two curves developed to identify the performance of the fixture. His 1940 report, “Building Materials and Structures,” featuring the famous Hunter’s Curve, can be found here: http://fire.nist.gov/bfrlpubs//build40/PDF/b40002.pdf.

The main curve discussed in the report is the Q/t curve. The other curve discussed is the T/t curve, which evaluates the probability of simultaneous use.

Flush valve (FV) and flush tank (FT) toilets will have a similar impact of the sanitary waste system, unlike the variance that they display on the water supply side. That is because a FT has the water stored in a tank, and the FV has to release the same amount of water through a bigger supply pipe. Also, low-flow fixtures have the same or similar peak flow rate, but for slightly less time than would higher flush volume fixtures. 

The two curves develop a DFU value. We assign DFU values to fixtures to represent their load-producing effect on the plumbing system. Each fixture is assigned a DFU value. That value is used to size the drainage system. A fixture unit is a measure of potential flow and pipe sizing is still subject to probability. The fixture unit values were designed for application in conjunction with the probability of simultaneous use of fixtures to establish the maximum permissible drainage loads expressed in fixture units rather than in gallons per minute of drainage flow. 

A DFU does not necessarily equate to a specific flow rate, but it is basically based on the amount of flow one would expect from a lavatory. This led to assigning a fixture unit value to represent the degree to which a fixture loads a system when used at the maximum assumed flow and frequency. 
For devices that provide continuous or semi-continuous flow into the drainage system, such as sump pumps, ejectors, and air-conditioning equipment, a value of 2 fixture units can be assigned for each gpm (L/s) of flow. 

We design our waste and sanitary drainage systems to run half-full. Of course the pipe is 100 percent “full,” but half is required for air to allow for the movement of air within the system. Half-full flow also prevents a reversal of flow in the drains, which would push the effluent up into the branch piping, and possibly cause flooding at drains or fixtures, or at least loss of the trap seal. The piping is sized based on maximum DFU discharge, but half-full flow will rarely, if ever, occur. Assuming that we design it properly and it is installed, maintained, and used properly and as intended.

Pitch or slope

Drains must be pitched to maintain a velocity of 2 feet per second or greater. The minimum velocity is designed to keep the solids in suspension. The minimum pitch is ¼ inch per foot (2 percent) for sizes 1-½-inch and 2-inch drains, and 1/8 inch per foot (1 percent) for larger drains. Some codes vary and require ¼ inch per foot for 3-inch and smaller.

The pitch of any horizontal line must be uniform. There is no maximum pitch in a piping system. The most extreme pitch is vertical. We call that a stack. 

Sizing

We use DFUs. It is not generally, but sometimes, necessary to use GPM values. Count the DFUs. The fixture unit values can be found in code books, just like the water supply fixture units. Make sure that you are using the correct code and the correct version. It is not always the latest version, but depends on the Authority Having Jurisdiction (AHJ). We do not have to convert these units to GPM for the basic sizing of the waste piping.

We now refer to charts that show the maximum number of DFUs that can be connected to a given pipe size. Note these four instances of addressing various system configurations:

 

• Any horizontal fixture branch
• One stack of three stories or fewer
• More than three stories in height: Total for stack
• More than three stories in height: Total at one story or branch interval

When sizing horizontal branch, determine the number of fixture units. Determine the fixture drain size based on trap size. Establish the minimum pipe size.

Flow in a stack only occupies 7/24 of the stack area. There is not a tight spiral of flow. This keeps the flow channel open. Sizing charts are based on this maximum flow. Remember that both Dawson and Hunter, in entirely independent investigations, came to the conclusion that slugs of water, with their accompanying violent pressure fluctuations, did not occur until the stack flowed ¼  to 1/3 full. Most model codes have based their stack loading tables on a value of r = ¼ or 7⁄24.

A connection from a branch to a stack must be sized to prevent the backup of flow. A branch cannot exceed the capacity of the stack at the given floor. Branches have special sizing limitations to avoid interruption of flow.

Branch interval

Branch interval is a distance along a soil or waste stack corresponding to a story height, but not less than 8 feet, within the horizontal branches from one floor or story of a structure are connected to the stack.

When stack sizing for three branch intervals, first determine the number of fixture units discharging into the stack. Stack must be as large as largest branch connecting. Next, determine the number of fixture units discharging into the stack. Determine the number of fixture units discharging into each branch interval. Stack must be as large as largest branch connecting.

While we can have up to 160 DFU on a 4-inch branch, we are only allowed 90 DFU in one branch interval, on a 4-inch stack, of more than three stories. This means that we would have to increase the stack size to 6 inches, if we have more than 90 DFUs on branch lines within any branch interval. Be careful, because this can sneak up on you and you can have an undersized stack. Note that the “Building Sewer” or “Building Drain” has slightly different numbers.

When the sheet of water spiraling down the stack reaches the bend at the base of the stack, it turns at approximately right angles into the building drain. Flow enters the horizontal drain at a relatively high velocity compared to the velocity of flow in a horizontal drain under uniform flow conditions. The velocity of the water flowing along the building drain and sewer decreases slowly then increases suddenly as the depth of flow increases and completely fills the cross section of the drain. 

This phenomenon is called a “hydraulic jump.” After the hydraulic jump occurs and water fills the drain, the pipe tends to flow full until the friction resistance of the pipe, retarding the flow to that of uniform flow conditions. That means that air can be trapped in the pipe, which interferes with flow and creates water hammer and other issues.

The critical distance at which the hydraulic jump may occur varies from immediately at the stack fitting to 10 times the diameter of the stack downstream. Less hydraulic jump occurs if the horizontal drain is larger than the stack.

Stacks and offsets

Refer to the following figure for an example of a high-rise stack with some offsets. Read all of the annotations to get a better understanding of how the offsets affect the sizes.

Building drain sizing

The “Building Drain” and “Building Sewer” have slightly different numbers. When sizing, first determine the number of fixture units. Next, determine the pitch of the pipe. Finally, establish the minimum pipe size. 

David E. DeBord, CPD, FASPE, GPD, LEED AP BD+C, ARCSA AP, CFPS, is director of Plumbing and Fire Protection Engineering at dbHMS. He is also the Vice President of Education for the American Society of Plumbing Engineers (ASPE). He can be reached at ddebord@dbHMS.com.