Wastewater collection system modeling and design free download

If the depth of flow is known, cross-section properties may be cal- culated using the relationships in Table 2. If the area is known, the depth of flow is determined by solving for y with the appropriate relationship in the second column.

Triangular with unequal 0. Hydraulic Elements D D flowing partially full2 8 4 2 8 sin. Rectangular or square sections are sometimes encountered in sanitary sewers; how- ever, the relative economy and better strength characteristics of circular pipe make noncircular sections less desirable for sewers, in most cases. For irregular or com- pound cross sections, procedures described by Haestad Methods and Durrans may be used to determine cross-section properties. Triangular Circular Figure 2.

Closed-Top Cross Sections A special category of cross sections has gradually closing tops. The most commonly used section in sanitary sewers, which rarely flow full, is circular pipe. Thus, the anal- ysis of partially full circular pipes is frequently required. The equations in the last row of Table 2. If the depth of flow, y, is known, is given by. Because these calculations are tedious, the hydraulic element chart Figure 2.

Use of the hydraulic element chart is demonstrated in Example 2. Discharge, Q Ratio of depth to diameter. Manning's n 0. Assume that a 10 in. What are the depth of flow, hydraulic radius, and velocity? Solution An analytical solution may be developed by substituting the partially full expressions for A and Rh into Equation 2.

The depth of flow is found by solving Equation 2. The hydraulic radius is found with the formula from Table 2. The flow velocity is found by combining Equations 2. The full-pipe values for Rhf, Vf, and Qf, needed for a graphical solution, are.

From Figure 2. Graphs may be developed to show the relations among y, D, and Q. For example, a graph for depth of flow versus flow for various slopes for a in. Noncircular Cross Sections Although not commonly used in sewer mains, noncircular cross sections are occasion- ally used in trunk sewer construction, especially older brick sewers. Inverted egg and elliptical pipes are quite common in parts of Europe. Inverted egg pipes are also found in some cities in the United States.

With narrowing walls near the bottom of the pipe, a greater depth of flow can be maintained for smaller flow rates, resulting in a larger hydraulic radius and higher velocity, and thus better self- cleansing than a comparable circular pipe section. The hydraulic properties of par- tially filled egg-shape sewers are described by Gill and Hager Formu- las for calculating flow and velocity in elliptical sections are presented in Haestad Methods For a more detailed discussion of the exact dimensions of noncircular conduits and methods for determining flows in those pipes, see Hager This means that commercial pipe material roughness differences have negligible effect on Mannings n.

Viscosity Water temperature, and thus viscosity, affects n. However, the effect is negligible for the range of water temperatures normally found in sewers. Diameter Calculated values of n vary significantly with diameter. Experimental and field data indicate that n does increase with increasing diameter Tullis, ; Schmidt, Velocity For hydraulically smooth flow at all diameters, the calculated Man- nings n decreases as the velocity increases.

At least theoretically, n should be independent of velocity in rough pipes; that is, the flat zone of the Moody dia- gram. Experimental data indicate that n decreases with increasing velocity Tullis, Environmental concerns include fluctuating groundwater elevations, nearby construction practices, and the shifting of soils due to sediment, slippage, and earthquakes. The apparent n-value can increase significantly due to the higher turbulence that accompanies bad align- ment, cracks, protrusions, etc.

Deposition deposits of sediment, debris, grease, and other materials can increase the value of n. The subsections that follow present methods for computing Mannings n and provide recommended values.

Calculating n with the Darcy-Weisbach Equation It is generally accepted that the Darcy-Weisbach equation see Chapter 4 is theoreti- cally the most accurate equation describing head loss for a wide range of conditions. It is informative to observe the variation in Mannings n as determined by the Darcy- Weisbach equation.

In addition, several explicit expressions have been developed for f; the Swamee-Jain equation is fre- quently used:. The result for f is then substituted into Equation 2. Solution Equation 2. It is interesting to note that the Mannings n computed in Example 2. Figures 2.

However, for smooth pipes, n decreases from 0. Rougher 0. For smoother pipes, the relation is affected by viscous forces in the pipe, and n is actually more a function of the Reynolds number than the rough- ness height. These graphs suggest that n is more appropriate for rough pipes than for smooth pipes. It should be noted that for values of ranging from approximately 0.

Thus, for a given pipe diameter and flow velocity, there is a large range of pipe roughness for very little difference in n. Some concrete pipe-forming methods leave rough surfaces with val- ues of higher than 0.

Such high values of move the hydraulic regime in the pipe significantly away from the hydraulically smooth boundary and cause a significant increase in nas much as 20 to 25 percent higher than for smooth- finish concrete.

In general, n increases with increasing diameter and decreases with increasing veloc- ity. Therefore, n is lowest for small diameters and high velocities and highest for large diameters and low velocities. Variation of n with Depth Experiments conducted to determine the effect of variation of depth of flow on Man- nings n have shown that n is greater in partially filled round sewer pipe ASCE, and WPCF, than in a full pipe.

This variation is indicated in Figure 2. An empirical relationship for n as a function of depth of flow is Schmidt, Thus it is question- able whether the variation in n as shown on many traditional charts is properly repre- sented as simply a function of flow depth.

The practice of varying n with depth of flow is not recommended, but it makes little difference in actual design. However, Mannings n does vary with water temperature, pipe diameter, and velocity of flow, as described in the following section. Many experiments on full- scale sewer-line installations, including operating sewers, report n 0. Most of these tests were on 8 to 18 in. In operating sewers, however, such fac- tors as serious misalignment, pipe interior deterioration, joint separation, cracks, protruding connections, buildup of sediment, and buildup of coating materials may result in much higher n values.

If the regulatory agency allows discretion in selecting n values, the values in Table 2. Condition 6 8 10 12 15 18 Extra care 0. The extra care values in Table 2. The extra-care values correspond to clean water flowing in a clean, well-aligned pipe. It seems reasonable to increase them by about 15 percent to allow for goodbut less than idealconditions in the pipe.

The type of pipe, the care taken during construc- tion and in making connections, and cleaning maintenance determine whether extra- care, typical, or substandard conditions actually exist in a sewer pipe over its lifetime.

The total head loss along a pipe is the sum of the frictional and minor losses. Bends and valves are rare in gravity sewer systems; thus, most of the minor losses are attributed to manholes. Traditionally, the head loss is expressed as the product of a minor loss coefficient and the absolute difference between the velocity heads upstream and downstream of the appurtenance. This approach is reasonable for many types of minor loss calculations.

For most situations, the minor loss coefficient for manholes ranges from 0. From a hydraulic point of view, the most important detail of a manhole is the bot- tom channel, which can provide for a smoother flow transition. Because flow geometries are often complex at manholes and junction structures are often complex, specialized methods have been developed for minor loss prediction, as presented by Brown, Stein, and Warner These approaches, known as the energy-loss and composite energy-loss methods, are described in the subsections that follow.

Other methods for determining head loss at manholes are described in Hager Energy losses in manholes add to losses in pipes. Depending on the flow condition, these losses are added to the EGL when moving upstream or subtracted from the EGL when moving downstream. Energy-Loss Method The inlet pipe s to a manhole or junction structure in a sewer have one of a few possi- ble configurations with respect to their invert elevations, as follows: a All inlet-pipe invert elevations may lie below the elevation of the predicted depth of water in the structure.

For structures in which all inlet-pipe invert elevations lie above the predicted free water surface elevation within the structure so that there is plunging flow from all of the inlet pipes , the outlet pipe behaves hydraulically as a culvert. In that case, the water-surface elevation within the structure can be predicted using the methods pre- sented in Norman, Houghtalen, and Johnston , and the water-surface elevations in each of the upstream pipes can be determined independently as free outfalls.

The energy-loss method Brown, Stein, and Warner, for estimation of head losses at inlets, manholes, and junctions applies only to configuration a and to the pipes in configuration c whose invert elevations lie below the predicted free water-surface elevation within the structure. When one or more inlet pipes meet these criteria, the method may be applied to each to determine the corresponding head loss. This method is applicable to manholes constructed with or without benches to provide smooth transitions in flow.

For inlet pipes to which the energy-loss method is applicable, the head loss through the structure can be computed with. The initial head loss coefficient, Ko, depends on the size of the structure relative to the outlet-pipe diameter and on the angle between the inlet and outlet pipes see Figure 2.

B Ou tlet Pipe Pip Inlet e. If the structure is not circular, an equivalent structure diameter, which is the diameter of a circular structure having the same area as the actual noncircular one, should be used. For example, if the inside dimensions plan view of a junction chamber are 3 ft 0.

The correction factor for pipe diameter, CD1, is important only when the predicted water depth in the structure is at least 3. In such cases, CD1 is given by.

When applying correction factors, the depth of water, d, in the structure should be determined as the difference between the hydraulic grade line at the upstream end of the outlet pipe and the invert elevation of the outlet pipe.

The correction factor for flow depth, CD2, is important only when the predicted depth in the structure is less than 3. The correction factor is given by. The correction factor for relative flow, CQ, is required when there are two or more inlet pipes at a structure. Note that this calculation is performed for each inlet pipe, yielding a CQ for each inlet. The correction factor depends on the angle between the outlet pipe and the selected inlet pipe and on the ratio of the flow in the inlet pipe to the outlet pipe:.

When an inflow pipe to a structure has an invert elevation higher than the elevation of the free water surface in the structure, it is said to have a free outfall, and the water plunges into the structure.

The resulting turbulence and energy dissipation within the structure affect the head loss of other inlet pipes whose invert elevations lie below the free water surface.

The coefficient CP is computed and applied in the head-loss calcu- lations only for the pipe s whose flow is not plunging.

The coefficient is given by. Benching of the invert of a structure, as illustrated in Figure 2. The correc- tion factor for benching, CB, depends on the depth of water in the structure relative to the outlet pipe diameter and is listed in Table 2. Depressed Flat Half Full. Bench Type Submerged Unsubmerged Flat or depressed floor 1.

The inlet- pipe invert elevations have been set so that their crown elevations match the crown of the outlet pipe. If the HGL elevation at the upstream end of the outlet pipe is Calculate the HGLs for a flat-benched and full-benched man- hole. Invert The correction factor for flow depth is determined using Equation 2. Thus, the correction factors are 0. Composite Energy-Loss Method The composite energy-loss method can be used in situations similar to those to which the energy-loss method applies Brown, Stein, and Warner, However, the com- posite method is better suited to analyzing losses in structures with many inflow pipes.

It is applicable only to subcritical flows in pipes. The method is used to compute a unique head loss through the junction structure for each of the incoming pipes.

The head loss through the structure for a particular inflow pipe is given by. These equations are presented in the following subsections. The energy-loss coefficient related to the relative access-hole diameter, expressed as the ratio of access- hole diameter, B, to outlet-pipe diameter, Do, is given by. Note that the value of C1 is the same for all incoming pipes. The coefficients C2 and C3 rep- resent the composite effect of all the inflow pipes, the outflow pipe, and the manhole.

Because of this interdependence, an iterative method is used to cal- culate these coefficients. The first step is to compute an initial estimate of d with the equation. The analysis of the factors affecting energy losses for lateral flows resulted in an equa- tion for C3 that is the most complex of any of the coefficients. Otherwise, C3 is expressed in the form.

The calculations for C3 consider the angle i between the inlet and outlet pipes. As this angle deviates from straight-line flow , the energy loss increases because the flow cannot smoothly transition to the outlet pipe. All inflow pipe angles are mea- sured clockwise from the outlet pipe. The calculation of C3 accounts for inlet-flow plunging by considering the inlet as a fourth, synthetic inflow pipe with the corre- sponding angle set to 0. C3 can have a value ranging from 1 for no lateral flow to potentially very high values for greater plunge heights.

Because empirical studies do not support this result, a value of 10 is set as a realistic upper limit on C3. Term C3A represents the energy loss from plunging flows and is valid for up to three inlet pipes plus the plunging flow from the inlet: 4 Q 0.

If the horizontal momentum check HMCi, given by. The pair that produces the highest value is then used for the calculations of C3C and C3D. The last coefficient to be determined in Equation 2. The upper limit for the value of C4 is 9. Because of the complex, iterative nature of the composite energy-loss method, its application is not well suited to manual calculations and thus it is not illustrated here through an example problem.

However, it is readily adaptable to computer solutions. Sewers that collect surface-water inflow may experience periods of significantly higher sediment load. Suspended matter may be cohesive or exist as discrete particles with a range of sizes.

Butler, May, and Ackers state that typical average particle size d50 values in combined sewers in the United Kingdom are 10, 40, and 50 m for wastewater with low, medium, and high sediment loads.

The specific gravity ranges from 1. Sanitary sewers must be designed so that sediment does not accumulate during peri- ods of low flow without providing some period with enough flow to clean out the pipes.

To assure that sewers will carry suspended sediment, two approaches have been used: the minimum or self-cleansing velocity described in Section 2. Tractive Tension The forces acting on a fluid element are shown in Figure 2. In steady flow, the grav- itational force of the fluid must equal the friction force along the pipe wall.

The com- ponent of the gravitational force parallel to the axis of the pipe per unit boundary area is known as the tractive tension, tractive force, or boundary shear stress. This tension is given by. W Mara, Sleight, and Taylor, based on Barnes et al. When is small, it is approximately equal to the slope, S, and the tractive tension is given by. The equations for tractive tension can be rearranged to give the minimum slope for any tractive tension and flow rate.

In Brazil, the recommended minimum design flow is 1. Solution: The minimum slope is given by Equation 2. Applying the Manning equation to find a depth of flow at this minimum flow rate yields the results in the following table. Pipe Diameter, in. Thus a 15 in. The size selected depends on the peak flow.

The pipe slope ranged from 0. For each set of operating conditions, the tractive tension was calculated using Equation 2. The results are displayed in Figure 2. These results were linearized to yield. Note that the assumption of 1 Pa 0. For a given particle size and tractive tension calculated with Equation 2.

The slopes were calculated using Equations 2. The slope required for a velocity. Calcula- tions assume the pipe is flowing full. An important observation from tractive tension considerations is that the full-pipe velocity must increase with increasing pipe size to give the same tractive force, and hence cleansing power, as smaller diameter pipes.

Many researchers have noted that larger-diameter sewers need higher velocities to reduce sediment buildup Schmidt, ; Yao, ; May, When designing pipes in areas with minimal slope, engi- neers may increase the pipe size to convey larger maximum flows, but this has the side effect of making it more difficult to move sediment at low flow.

This phenomenon may be demonstrated by the following example. For a in. A in. The velocity in a pipe is given by the Manning equation:. Solution The required tractive tension is given by Equation 2. Equations 2. In this solution, the value of y is assumed, Rh is found with the equa- tion in Table 2. The results of a trial-and-error solution are listed in the following table. The analysis presented in Example 2. The minimum slopes are shown for flows greater than 0.

The lower limit of flow was suggested by Mara, Sleigh, and Taylor as the lower limit for tractive force analysis. For the 8-in. How- ever, based on tractive force analysis, Figure 2. For the in. Camp Formula The American Society Civil Engineers recommends the Camp formula for cal- culating the minimum velocity required to move sediment in a sewer pipe. The equa- tion was first proposed by Camp Applying the Manning equation to Equation 2.

Graphs for analyzing self-cleansing in partially full pipes were prepared by Geyer et al. Yaos Method Yao developed methods for determining minimum velocity based on shear stress much like Camp. For sewers less than one-half full, the minimum velocity becomes. This velocity can be used to check designs to ensure that scouring will occur. The solution is shown in the following graph. It states that the minimum velocity at half full can be given by.

Additional Considerations If a pipe is designed to self cleanse at Qmin using tractive force principles, in concept the deposition of particles will not occur for a long enough period of time to allow the deposited material to become highly scour resistant. If the material were to become scour resistant, very large tractive forces might be required for cleansing. Sometimes grease buildup, gravel deposition, etc.

The methods presented in this section may be used to assure that a gravity sewer pipe will move a discrete noncohesive particle of a defined size and density. This analysis does not consider the scouring of deposited material. In order for erosion of deposited material to occur, the hydrodynamic lift and drag forces acting on the solid material must overcome the restoring forces of submerged weight, particle interlocking, and cohesion.

More detailed analyses of sediment transport in sewers are provided by Delleur and Butler, May, and Ackers Considerable research has been conducted in recent years in the movement of sedi- ment in sewers.

In sanitary sew- ers, particularly for small diameters, the flow regime is of consequence in only a few situations in sanitary sewer design.

Specific Energy In open channels, specific energy is the energy with respect to the channel bottom:. In general, two different depths of flow, called conjugate depths, may exist for a given specific energy. For a given flow rate, the depth at which minimum specific energy occurs is called the critical depth, yc.

Of special note is the fact that near critical depth, relatively small changes in energy cause significant depth changes in the depth of flow. However, when the specific energy is not near this minimum value, it takes relatively larger changes in the specific energy to cause significant changes in the depth.

A semiempirical equation French, is. An alternate approach is to determine yc by plotting y as a function of E and graphi- cally determine yc.

Froude Number The Froude number is a ratio of the inertial forces to the gravity forces in the flow, given by. By substituting the critical depth conditions from Equation 2. Subcritical and Supercritical Flow Under conditions of normal flow, when the depth of flow is deeper than yc, the Froude number is less than 1, the flow is called subcritical or tranquil , and the channel slope, S0, is mild.

The existence of subcritical or supercritical flow depends primarily on the slope of the pipe. For most pipe slopes, the flow is always either supercritical or subcritical. How- ever, for a narrow range of slopes, the type of flow depends on whether an increase in flow increases the velocity or depth more. Subcritical flow may exist at low flow rates, supercritical flow may exist when the pipe flows half full, and subcritical flow may return as the pipe nears full.

Thus, a particular pipe may be classified as steep for some flow rates and mild for others. Hydraulic Jumps When the flow regime changes from supercritical upstream to subcritical down- stream, a fairly abrupt change in water depth called a hydraulic jump occurs. Unless the upstream velocities are high, hydraulic jumps are very small; typically, they are only as high as a few inches.

In sewers, a jump occurs when a steep pipe flows into a mild pipe at a manhole. Whether the jump occurs in the upstream pipe or the down- stream pipe depends on the flow rate and pipe slopes. For a particular geometry, the jump location can shift with a change in flow rate; however, the jump is usually either always upstream or downstream for the normal range of flow rates in the sewer. The impulse-momentum principle describes hydraulic jumps. The relationship may be expressed as. These depths occur before and after a hydraulic jump and are called sequent or conjugate depths.

The energy lost in the turbulence of a hydraulic jump, which is in addition to the very small uniform flow loss, can be determined by applying the specific energy equation Equation 2. In closed conduits, sometimes the downstream conjugate depth needs to be deeper than the pipe height. So after the jump, the downstream pipe flows full with a slight pressure. This situation also repre- sents a condition in which the flow rate exceeds the pipes open channel flow capacity.

In that case, the jump occurs in the upstream manhole or upstream pipe and results in ponding in the manhole. In sewers, such jumps are most likely to occur where there is a transition to a milder slope. Another consideration is that hydraulic jumps induce turbulence, which can release dissolved gases such as hydrogen sulfide and cause odor problems.

For a more exten- sive discussion on hydraulic jumps in sewers, see Hager Flow Profiles With open channel flow through a series of pipes, the water surface often makes a transition from one depth to another as flow asymptotically approaches uniform con- ditions.

Most of these depth changes occur in the vicinity of manholes where flows combine and slopes change. The profile defined by the water surface through these sections of changing depth is referred to as the water surface profile or flow profile; the profile most commonly encountered is called gradually varied flow.

Since direct integration of these expressions is difficult, they are generally solved by finite-step numerical integration. A common approach in developing the finite-step equations is to apply the energy equation to the ends of the section being considered, as follows.

The energy equation for points 1 and 2 along a channel was given as Equation 2. One of the flow equations, such as the Manning equation, is used to determine S, which is an estimate of the average energy line slope for the section. A rearranged Manning equation is often used, where Vm and Rhm are the averages of the velocities and hydraulic radii at the ends of the section, in the form. Calculations begin at a known water depth downstream called a control point and the curve goes back upstream.

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