# Pressure Head: Pressure head is the height of a column of water that would exert a unit pressure equal to the pressure of the water.

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2 Pressure flow design requires that the flow in the conduit be at a pressure greater than atmospheric. Under this condition, there is no exposed flow surface within the conduit. In pressure flow, flow energy is again derived from the flow velocity, depth, and elevation. The significant difference here is that the pressure head will be above the top of the conduit, and will not equal the depth of flow in the conduit. In this case, the pressure head rises to a level represented by the hydraulic grade line. The question of whether open channel or pressure flow should control design has been debated. For a given flow rate, a design based on open channel flow requires a larger storm sewer than those sized based on pressure flow. While it may be more expensive to construct storm drainage systems designed for 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. This factor of safety is often desirable since the methods of runoff estimation are not exact, and once placed, storm drains are difficult and expensive to replace. Under ordinary conditions, it is recommended that storm drains be sized based on a gravity flow criteria at flow full or near full. Designing for full flow is a conservative assumption since the peak flow capacity actually occurs at 93% of the full flow depth. When allowed by the Jurisdiction, pressure flow may be used. When pressure flow is allowed, special emphasis should be placed on the proper design of the joints so that they are able to withstand the pressure flow on a regular basis. 3. Hydraulic Capacity: A storm sewer s size, shape, slope, and friction resistance control its hydraulic capacity. These properties are all accounted for with the Manning Equation given as: V = Q A = n r 3s 1 Equation D-.01 V = Average velocity, ft/s Q = Discharge, cfs A = Cross-sectional area of flow, ft n = Manning s roughness coefficient r = hydraulic radius, ft = A/p (note: for circular pipes flowing full, r=d/4) p = wetted perimeter, ft s = slope of hydraulic grade line (pipe/channel slope), ft/ft Revised: 013 Edition

3 Table D-.01: Manning Coefficients for Common Storm Sewer Materials Type of Pipe Manning s n Concrete pipe PVC pipe (smooth wall) HDPE or Polypropylene (corrugated exterior, smooth interior - dual or triple wall) 0.01 HDPE or Polypropylene (corrugated exterior and interior - single wall) 0.00 CMP (-/3" x 1/" corrugations) 0.04 CMP (3" x 1" corrugations) 0.07 CMP (5 x1 corrugations) 0.05 Structural Plate 0.03 Note: for additional manning coefficients, see the pipe manufacturer s information. D. Conservation of Energy 1. Bernoulli Equation: The law of conservation of energy, as expressed by the Bernoulli Equation, is the basic principle most often used in hydraulics. This equation may be applied to any conduit with a constant discharge. Friction flow formulas such as the Manning s Equation have been developed to express the rate of energy dissipation as it applies to the Bernoulli Equation. The theorem states that the energy head at any cross-section must equal that in any other downstream section plus the intervening losses. Bernoulli s equation, where the total energy at Section 1 is equal to the energy at Section plus the intervening head loss, is summarized in two versions below: 3 Revised: 018 Edition

4 For open (non-pressure) conduit flow: V 1 g + Y 1 + Z 1 = V g + Y + Z + h f Equation D-.0 For pressure conduit flow V 1 g + P 1 γ + Z 1 = V g + P γ + Z + h f Equation D-.03 EGL HGL = Energy grade line = Hydraulic grade line Y = Water depth, ft V g = Energy head, ft V S f S w =Average velocity, fps = Slope of EGL = Slope of HGL g = acceleration of gravity (3. fps) P γ = Pressure head, ft P = Pressure at given location (lb/ft ) = Specific weight of water (6. lb/ft 3 ) Z S 0 h f = Elevation relative to some datum = Slope of bottom, ft/ft = Head loss, ft Figure D-.01: Terms Used in the Energy Equation V1 / g EGL 1 Sf HGL 1 Sw hf V / g Y1 P 1 Flow Conduit Bottom 1 So Y P Z1 Datum Z Section 1 Section Source: FHWA, HEC- 4 Revised: 013 Edition

5 E. Hydraulic Losses Storm sewers should be designed to convey the minor storm runoff peaks without surcharging the sewer. In situations where surcharging is a concern, the hydraulic grade line may be calculated by accounting for pipe friction losses and pipe form losses. Total hydraulic losses will include friction, expansion, contraction, bend, and junction losses. The methods for estimating these losses are presented herein. 1. Pipe Friction Losses: The major head loss in a storm drainage system is due to pipe friction. Energy losses from pipe friction may be determined by rewriting the Manning s equation with terms as previously defined: S f = Q n A R 4 Equation D The friction head lost through a segment is simply the hydraulic gradient multiplied by the length of the run: H f = S f L Equation D-.05 H f S f L = Friction head loss, ft = Friction slope, ft/ft = Length of outflow pipe, ft. Exit Losses: The exit loss from a storm sewer outlet is a function of the change in velocity at the outlet of the pipe. For a sudden expansion such as at an endwall, the exit loss is: H o = 1.0 [( V o g ) (V d g )] Equation D-.06 V o V d g = Average outlet velocity, ft/s = Channel velocity downstream of outlet in direction of the pipe flow, ft/s = Acceleration due to gravity, 3. ft/s Note that when V d = 0, as in a reservoir, the exit loss is one velocity head. For part full flow where the pipe outlets in a channel with water moving in the same direction as the outlet water, the exit loss may be reduced to virtually zero. 3. Bend Losses: The bend loss coefficient (H b) for storm sewer design (for bends in the pipe run, not in a structure) can be estimated using the following formula: H b = K b V g Equation D-.07 K b = Bend loss coefficient (refer to Table D-.0) 5 Revised: 013 Edition

6 Table D-.0: Bend Loss Coefficients Bend Radius / Pipe Dia. (R/d) Degree of Bend or larger Source: Brater, King, et al. 4. Transition Losses: A transition is a location where a conduit or channel changes size. Transitions include expansions, contractions, or both. In small storm sewers, transitions should occur within manhole or intake structures. However, in larger storm sewers, or when a specific need arises, expansions may occur within pipe runs. Contractions must always occur within a structure and never within the pipeline, regardless of pipe size. Energy losses due to expansions in non-pressure flow can be expressed in terms of the kinetic energy at the two ends: H e = K e [( V g ) (V 1 g )] Equation D-.08 The head loss coefficient for a pipe expansion, K e, is dependent upon the rate of change in diameter (angle of cone) as shown in Table D-.03. Figure D-.0: Angle of Cone for Pipe Diameter Changes Source: FHWA, HEC- Table D-.03: Typical Values of K e for Gradual Enlargement of Pipes in Non-pressure Flow D / D 1 Angle of Cone Revised: 013 Edition

7 5. Junction Losses: A pipe junction is the connection of a lateral pipe to a larger trunk pipe without the use of a manhole or other structure. The minor loss equation for a pipe junction is a form of the momentum equation as follows: H j = { [(Q ov o ) (Q i V i ) (Q l V l cos θ j )] } + V i [0.5g(A o + A i )] g V o g Equation D-.09 H j = Junction loss, ft Q o, Q i, Q l = Outlet, inlet, and lateral flows respectively, ft 3 /s V o, V i, V l = Outlet, inlet, and lateral velocities, respectively, ft 3 /s A o, A i = Outlet and inlet cross-sectional area, ft θ = Angle between the inflow trunk pipe and inflow lateral pipe, degrees Figure D-.03: Interior Angle Definition for Pipe Junctions 6. Structure Losses: A complex situation exists where a manhole or intake exists at the junction between inflow and outflow pipes. The following method provides approximate results and estimates losses across a structure by multiplying the velocity head of the outflow pipe by a coefficient as represented in Equation D-.10. Table D-.04 tabulates typical coefficients (K ah) applicable for use in this method. Refer to HEC- for a detailed explanation of analyzing structure losses. H ah = K ah ( V 0i g ) Equation D-.10 This approximate method estimates the necessary elevation drop across a structure required to offset energy losses through the structure. This drop is then used to establish the appropriate pipe invert elevations. 7 Revised: 013 Edition

8 Table D-.04: Head Loss Coefficients through Structures Pipe Angled Through K S Straight Run Structure Drop: Where pipe size increases in a structure, the invert of the smaller sewer must be raised to maintain the same energy gradient. An approximate method of doing this is to place the 0.8 depth point of both sewers at the same elevation. When there is a change in alignment between storm sewers of 45 degrees or greater, the suggested minimum manhole drop is 0.10 foot. F. References Brater, King, et al. Handbook of Hydraulics. Seventh Ed U.S. Department of Transportation. Urban Drainage Design Manual. Hydraulic Engineering Circular No.. Third Ed Revised: 013 Edition

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