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Gravity pipe calculation

In this blog I will present sizing of gravity underground pipes. Sizing gravity underground pipes is more on a civil side, but because of simplicity it can be performed by piping designer. Calculation of gravity underground pipes will be conducted using rational method for the layout given in the figure below. Note that rational method is limited to watersheds 200 acres or smaller.
1-undergroung-gravity-pipe2-undergroung-gravity-pipe
Note that maximum paved area and maximum travel path for one catch basin is specified in a design criteria. Normally, the design criteria specified 10 years return period having time of concentration equal to storm duration. Some projects might require 20 years, but the most common data for plant is 10 years return period.
Sizing lateral for paved (slab) area (potentially oily water)
Step 1
Obtain rainfall intensity for 2 years period return and 24 hours rainfall. Hydrology data or rainfall intensity (precipitations) is given for geographical location in form of graphs, maps or equations, depending of country. Usually rainfall intensity can be found visiting Hydrology institute website or another relevant institution (government site).
Figure below shows rainfall intensity given in the form of graph.
3-rainfall-intesity
Based on graph above, precipitation of 2.5 inches (63.5 mm) is obtained using the graph above and taking 2 years return period and 24 hours storm duration.
Step 2
Calculate time of concentration, for the paved area (A) having rainfall intensity of 2.5 inches (63.5 mm)
4-time-of-concetration
Note that time of concentration is calculated using Kinematic equation and roughness coefficient (n) for concrete surface is taken 0.013.
Step 3
Calculate flow for 1 inch (25.4 mm) precipitation. One inch precipitation is obtained using the graph above, taking 10 years return period and 1.2 minute storm duration (design condition-time of concentration equal to storm duration).
5-flow-calculation-underground-pipe
Run off coefficient (C) is taken 1.00 for plant paved area. Design specification will normally specified minimum firewater quantities that must be taken into consideration and usually it is in the range of 110 to 130 cubic meters per hour, depending of company standard. Since calculated flow of 4.9 cubic meters per hour is less than required firewater flow, firewater quantities will govern pipe design and it will be taken 110 cubic meters per hour in further calculation.
Step 4
Calculate velocity assuming 8″ steel pipe sch. 40, 1.5% slope and full flow condition.
6-manning-equation
Velocity is calculated using Manning equation where ManningĂ­s roughness coefficient (n) is taken 0.011 (steel pipe). Calculated velocity (1.198) for sewers must be in the range of 0.7 m/sec to 3.5 m/sec. Velocity greater than 3.5 m/sec will cause erosion and velocity smaller than 0.7 m/sec will cause deposition of fine particles in the pipe. Maximum flow thru pipe (124.09) must be greater than firewater requirement (110). Since both conditions (flow and velocity) are met, 8″ is adequate and it must be installed at slope of 1.5%. Note that minimum slope for water to run off is 1%. All coefficients (Runoff, ManningĂ­s roughness) used in above calculation should be specified in a design criteria as well as minimum pipe size for all sewers.
Sizing collector
Sizing collector (for paved area) will be performed in the same manner. Maximum flow thru collector pipe must be greater than firewater quantity (110). It should be noted that firewater quantity (110) is governing since it is larger than sum of all laterals flow (4.9×2=9.8).
Paved off area (storm water)
Same procedure will be applied for paved off area where tributary area (Aa) will be used. Tributary area will be estimated based on site map. Basically it is area from which water will be collecting into the ditch and that amount of water (Q) will be used for sizing a storm sewer and ditch. Runoff coefficient must be taken for the site condition. In the most cases calculated pipe size will be smaller than minimum required pipe sized specified in design criteria. Full explanation of Manning equation can be found on The Engineering Toolbox website.
Time of concentration has been calculated applying equation for sheet flow where longest travel path is limited to 150 ft. If longest travel path is greater than 150 feet, the total area might be sub-divided into smaller catchment areas having longest travel path less than 150 feet. Figure below is a site condition where sheet, shallow and channel flow occurs at the same time since longest travel path is greater than 150 feet.
7-rational-method
This case is beyond this scope because of its complexity. For this case, storm management analysis must be conducted by civil designer. Piping designer should always refer to design specification or customer design criteria, since there will more requirements than presented here, that must be met.