DISCOVER

# How to Calculate Flow Rates in a Gravity Flow Concrete Pipe

Updated February 21, 2017

Nonpressurized, gravity-flow concrete pipes are widely used in drainage systems to carry nonpotable water to treatment facilities. Flow occurs as the result of gravity acting on the water as the pipes continuously slope downward while traversing horizontal distances. The concrete pipe industry has produced accepted formulas and data that enable system designers to calculate many concrete pipe parameters including flow rates.

Define the concrete pipe flow rate application example. Assume a 24-inch diameter concrete pipe with an n value of 0.013 (n is the concrete roughness factor, which ranges from 0.10 to 0.013 for concrete). The higher the roughness factor, the coarser the inner surfaces of the pipe. The downward slope rate of the pipe is 2 per cent. If the water level inside the pipe is 18 inches, you can calculate the flow rate for the pipe.

Select the flow formula for this example. The American Concrete Pipe Association recommends the Manning Formula. This formula is Q = 1.486/n x A x R^2/3 x S^1/2", where Q is the flow rate in cubic-feet-per-second, n is Manning roughness coefficient (see Step 1), A is the cross-sectional flow area in square feet (see Steps 3 and 4), and R is the hydraulic radius of the pipe in feet (see Steps 3 and 5). S is slope fraction = slope per cent/100 per cent.

Determine the coefficient values for calculating the A and R parameters in the Manning Formula by consulting Figure 1- Relative Velocity and Flow in Circular Pipe for Any Design Depth or Flow (graph top of Page 6) in the American Concrete Pipe Association data for partial flow. To use Figure 1, calculate the Depth of Flow Factor by dividing the specified 18-inch water depth by the 24-inch pipe diameter for a result of 0.75. Locate 0.75 on the Depth of Flow axis on the left side of the graph between 0.7 and 0.8. Follow the 0.75 value horizontal line to the right to the curve for Area of Flow, A. The coefficient value at this point is approximately 0.83. Continue along the line to the Hydraulic Radius, R curve where the coefficient value will be 1.22. Note these two values to use in Steps 4 and 5.

Calculate the A parameter value by multiplying the 0.83 A(partial) coefficient times the full area A(full), which would be the 24-inch diameter^2 d x pi/4 = 452.16 square-inches x 0.83 = 375.29 square inches/144 square-inches/square foot or A(partial) = 2.61 square feet.

Calculate the R parameter for the formula by taking the R(partial) coefficient of 1.22 from Figure 1 times the R(full) value of 24 inches/12 inches/foot = 2 feet X pi = 6.28 feet X 1.22 = 7.66 feet.

Substitute all known values by into the formula Q = 1.486/n x A x R^2/3 X S^1/2 to calculate the flow rate in cubic feet per second. In this example, Q = 1.484/0.013 X 2.61 X 7.66^2/3 X 0.02^1/2 = 114.3 X 2.61 X 3.89 X 0.1414 = 164.12 cubic-feet/second.

Convert cubic-feet/second to gallons per minute (gpm) using the standard conversion factor of 7.48 gallons-per-cubic foot. 164.12 cubic-feet/second x 7.48 gallons/cubic-foot X 60 seconds/minute = 73,657 gpm. This flow rate would drain the average residential in-ground pool (13,500 gallons) in about 11 seconds.

#### Tip

Use concrete pipes with rougher internal finishes to moderate flows with greater slopes.

#### Warning

Have drain and sewer pipe calculations checked by a licensed professional to prevent full-pipe overflow events that may contaminate potable water sources.

#### Things You'll Need

• Scientific calculator
• Concrete pipe industry technical data