Hydraulic calculations for pipes, culverts and open channels are to be as follows.
(A) Gravity versus pressure flow for enclosed systems.
(1) Two design philosophies exist for sizing storm drains under the steady uniform flow assumption. The first is referred to as open channel, or gravity flow design, in which the water surface within the conduit remains open to atmospheric pressure. Pressure flow design, on the other hand, requires that the flow in the conduit be at a pressure greater than atmospheric. For a given flow rate, design based on open channel flow requires larger conduit sizes than those sized based on pressure flow. While it may be more expensive to construct storm drainage systems designed based on open channel flow, this design procedure provides a margin of safety by providing additional headroom in the conduit to accommodate an increase in flow above the design discharge. However, there may be situations where pressure flow design is desirable. For example, on some projects, there may be adequate headroom between the conduit and inlet/access hole elevations to tolerate pressure flow. In this case, a significant cost savings may be realized over the cost of a system designed to maintain open channel flow. Also, in some cases it may be necessary to use an existing system which must be placed under pressure flow to accommodate the proposed design flow rates. Under most ordinary conditions, it is recommended that storm drains be sized based on a gravity flow criteria at full flow or near full. Pressure flow design may be justified in certain instances. As hydraulic calculations are performed, frequent verification of the existence of the desired flow condition should be made. Storm drainage systems can often alternate between pressure and open channel flow conditions from one section to another. (From Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22, U.S. Department of Transportation Federal Highway Administration.)
(2) For gravity flow conditions, Manning’s formula shall be used as described below.
Q = (1.486)* A * (R2/3)* (S1/2)
n
Where:
Q = Discharge in cubic feet per second
A = Cross-sectional area of flow in square feet
n = Roughness Coefficient (see Table A)
R = Hydraulic radius (R = A/P) in feet
S = Slope in feet per foot
P = Wetted perimeter in feet
The hydraulic grade line shall be at least one foot below the throat of a curb inlet, and shall be below the throat of an area inlet, as long as this inlet is located on grade and has an overflow path to another area inlet. If no overflow path is available for the area inlet, the hydraulic grade line shall be at least 1 foot below the throat of the area inlet.
(3) In closed conduits flowing under pressure flow, the hydraulic grade line shall be calculated using the following equation:
p1/g + z1 = p2/g + z2 + hf +hm
Where:
p1/g = pressure head in the upstream system segment in feet
z1 = elevation of the system invert in the upstream system segment in feet
p2/g = pressure head in the downstream system segment in feet
z2 = elevation of the system invert in the downstream system segment in feet
hf = friction loss in the downstream system segment in feet
hm = minor system losses in the downstream segment in feet
(B) Pipe friction losses, hf, may be calculated by the Darcy Formula, the Hazen-Williams formula or the friction slope method.
(1) Darcy Formula. The most common expression for calculating head loss due to friction is the Darcy formula:
hf = f * L * v2
D * 2g
Where:
f = the friction factor, determined from the Moody friction factor chart
L = length of pipe in feet
v = velocity of flow at point of interest in feet per second
D = diameter of pipe in feet
2g = 64.4 feet per second per second
(2) Hazen-Williams Formula. Another method for finding the friction head loss is the Hazen-Williams formula. The Hazen-Williams formula gives good results for liquids that have kinematic viscosities around 1.2 EE-5 ft2/sec (corresponding to 60°F water). The Hazen-Williams formula should be used only for turbulent flow. The Hazen-Williams head loss is:
hf = 3.022 * v1.85 * L
(C1.85 * D1.165)
Where:
C = Loss coefficient, determined from H-W chart for various pipe materials
(3) Friction Slope Method. This formula is from the FHWA’s Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22.
hf = Sf * L = ((Q * n)/(1.486 * A * R 2/3))2 * L
Where:
Sf = friction slope, ft/ft, which is also the slope of the HGL
Minor losses, hm, shall be calculated by:
hm = k * v2
2g
Where:
k = Coefficient as shown in Table B
(4) Manual calculation. A step-by-step procedure for manual calculation of the EGL using the energy loss method is presented in § 7.5 of the Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22, U.S. Department of Transportation Federal Highway Administration. For most drainage systems, computer methods such as HYDRA or SWMM are the most efficient means of evaluating the EGL and designing the system elements.
(C) Culverts. Classified as having either entrance or outlet control. Either the inlet opening (entrance control) or friction loss within the culvert or backwater from the downstream system (outlet control) will control the discharge capacity.
(1) Entrance control. Entrance control occurs when the culvert is hydraulically short (when the culvert is not flowing full) and steep. Flow at the entrance would be critical as the water falls over the brink. If the tailwater covers the culvert completely (i.e., a submerged exit), the culvert will be full at that point, even though the inlet control forces the culvert to be only partially full at the inlet. The transition from partially full to full occurs in a hydraulic jump, the location of which depends on the flow resistance and water levels. If the flow resistance is very high, or if the headwater and tailwater levels are high enough, the jump will occur close to or at the entrance.
(2) Outlet control.
(a) If the flow in a culvert is full for its entire length, then the flow is said to be under outlet control. The discharge will be a function of the differences in tailwater and headwater levels, as well as the flow resistance along the barrel length.
(b) Alternatively, refer to the Federal Highway Administration website for these charts (www.fhwa.dot.gov/bridge/hec05.pdf). Download applicable design manuals, reports and FHWA hydraulics engineering such as Bridge Waterways Analysis Model (WSPRO), FHWA Culvert Analysis, and HDS 5 Hydraulic Design of Highway Culverts from www.fhwa.dot.gov/bridge/hydsoft.htm. These are applicable when flow in the upstream channel is subcritical.
(3) Open channels/bridges.
(a) Proper evaluation of the velocity, depth and width of flow requires analyses of the structures and conditions that impact the flow. Boundary flow conditions upstream and downstream from the open channel system must be established. The standard-step backwater method, using the energy equation, can be used to determine the depth, velocity and width of flow. Major stream obstructions, changes in slope, changes in cross-section and other flow controls can cause significant energy loss. In these cases, the energy equation does not apply and the momentum equation must be used to determine the depth, velocity and width of flow.
(b) Hydraulic calculations for open channels may also be made by the U.S. Army Corps of Engineer’s ‘HEC-2 Water Surface Profiles’ or ‘HEC-RAS River Analysis System’ computer programs. The HEC-2 program computes water surface profiles for one-dimensional steady, gradually varied flow in rivers of any cross-section. HEC-RAS is an integrated system of software, designed for interactive use in a multi-tasking, multi-user network environment. The system has separate hydraulic analysis components, data storage and management capabilities, graphics and reporting facilities. The HEC-RAS system is intended for calculating water surface profiles for steady gradually varied flow. The system can handle a full network of channels, a dendritic system or a single river reach. Like HEC-2, HEC-RAS is capable of modeling subcritical, supercritical and mixed flow regime water surface profiles. (From www.hec.usace.army.mil).
(Ord. 3319, passed 2-22-2005)