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The main supply pipe to the distribution system should therefore be designed with a capacity of 2. The water pressure within the distribution system must be above acceptable levels when the system demand is 2.
Pipelines in water-distribution systems include transmission lines, arterial mains, and distribution mains. Transmission lines carry ow from the water-treatment plant to the service area, typically have diameters greater than mm, and are usually on the order of 3 km apart. Arterial mains are connected to transmission mains and are laid out in interlocking loops with the pipelines not more than 1 km apart and diameters in the range of mm.
Smaller form a grid over the entire service area, with diameters in the range of mm, and supply water to every user. Pipelines in distribution systems are collectively called water mains, and a pipe that carries water from a main to a building or property is called a service line. Water mains are normally installed within the rights-of-way of streets. Dead ends in water-distribution systems should be avoided whenever possible, since the lack of ow in such lines may contribute to water-quality problems.
Pipelines in water-distribution systems are typically designed with constraints relating to the minimum pipe size, maximum allowable velocity, and commercially available materials that will perform adequately under operating conditions. Minimum Size. The size of a water main determines its carrying capacity. Main sizes must be selected to provide the capacity to meet peak domestic, commercial, and industrial demands in the area to be served, and must also provide for re ow at the necessary pressure.
For re protection, insurance underwriters typically require a minimum main size of mm for residential areas and mm for high-value districts such as sports stadiums, shopping centers, and libraries if cross-connecting mains are not more than m apart.
On principal streets, and for all long lines not connected at frequent intervals, mm and larger mains are required. Service Lines.
Service lines are pipes, including accessories, that carry water from the main to the point of service, which is normally a meter setting or curb stop located at the property line. Service lines can be any size, depending on how much water is required to serve a particular customer. To properly size service lines it is essential to know the peak demands than any service tap will be called on to serve. A common method to estimate service ows is to sum the xture units associated with the number and type of xtures served by the service line and then use a curve called the Hunter curve to relate the peak owrate to total xture units.
Recent research has indicated that the peak ows estimated from xture units and the Hunter curve provide conservative estimates of peak ows AWWA, Irrigation demands that occur simultaneously with peak domestic demands must be added to the estimated peak domestic demands. Service lines are sized to provide an adequate service pressure downstream of the water meter when the service line is delivering the peak ow.
This requires that the pressure and elevation at the tap, length of service pipe, head loss at the meter, elevation at the water meter, valve losses, and desired pressure downstream of the meter be known. Using the energy equation, the minimum service line diameter is calculated using this information. It is usually better to overdesign a service line than to underdesign a service line because of 72 the cost of replacing a service line if service pressures turn out to be inadequate.
Materials used for service- line pipe and tubing are typically either copper tubing or plastic, which includes polyvinyl chloride PVC and polyethylene PE. Type K copper is the most commonly used material for copper service lines.
Older service lines used lead and galvanized iron, which are no longer recommended. The valve used to connect a small-diameter service line to a water main is called a corporation stop, which is sometimes loosely referred to as the corporation cock, corporation tap, corp stop, corporation, or simply corp or stop AWWA, c.
Tapping a water main and inserting a corporation stop directly into the pipe wall requires a tapping machine, and taps are typically installed at the 10 or 2 oclock position on the pipe. Good construction practices must be used when installing service lines to avoid costly repairs in the future. This must include burying the pipe below frost lines, maintaining proper ditch conditions, proper backll, trench compaction, and protection from underground structures that may cause damage to the ppe.
Allowable Velocities. Maximum allowable velocities in pipeline systems are imposed to control friction losses and hydraulic transients. Maximum allowable velocities of 0. The importance of controlling the maximum velocities in water distribution systems is supported by the fact that a change in velocity of 0. Pipeline materials should generally be selected based on a consideration of service con- ditions, availability, properties of the pipe, and economics.
In selecting pipe materials the following considerations should be taken into account: CIP is no longer manufactured in the United States. For new distribution mains, ductile iron pipe DIP is most widely used for pipe diam- eters up to mm 30 in. DIP is manufac- tured in diameters from 76 to mm in. For diameters from to mm in. The standard lengths of DIP are 5.
DIP is usually coated outside and inside with an bituminous coating to minimize corrosion. An internal cement-mortar lining 1.
DIP used in water systems in the United States are provided with a cement-mortar lining unless otherwise specied by the downloadr. A variety of joints are available for use with DIP, which includes push-on the most common , mechanical, anged, ball-and-socket, and numerous joint designs.
A stack of DIP is shown in Figure 2. A rubber gasket, to ensure a tight t, is contained in the bell side of the pipe. As a consequence, steel pipe is primarily used for transmission lines in water distri- bution systems.
Steel pipe available in diameters from to mm in. The standard length of steel pipe is The interior of steel pipe is usually pro- tected with either cement mortar or epoxy, and the exterior is protected by a variety of plastic coatings, bituminous materials, and polyethylene tapes depending on the degree of protection required. PVC pipe is by far the most widely used type of plastic pipe material for small-diameter water mains.
PVC pipe is commonly available in diameters from to mm. Extruded PE and PB pipe are primarily used for water service pipe in small sizes, however, the use of PB has decreased remarkably because of structural diculties caused by premature pipe failures. In the hydraulic design of PVC pipes, a roughness height of 0. Asbestos-cement A-C pipe has been widely installed in water distribution systems, especially in areas where metallic pipe is subject to corrosion, such as in coastal areas.
It has also been installed in remote areas where its light weight makes it much easier to install than CIP. Common diameters are in the range of to mm. The U. Environmental Protection Agency banned most uses of asbestos in and, due to the manufacturing ban, new A-C pipe is no longer being installed in the United States.
Fiberglass pipe is available for potable water used is sizes from 25 to mm. Ad- vantages of berglass pipe include corrosion resistance, light weight, low installation cost, ease of repair, and hydraulic smoothness. Disadvantages include susceptibility to mechanical damage, low modulus of elasticity, and lack of standard joining system. The use of concrete pressure pipe has grown rapidly since The pipe provides a combination of the high tensile strength of steel and the high compressive strength and corrosion resistance of concrete.
The pipe is available in diameters ranging from to mm and in standard lengths from 3. Concrete pipe is available with various types of liners and reinforcement, and the four types in common use in the United States and Canada are: Pipelines in water-distribution systems should be buried to a depth below the frost line in northern climates and at a depth sucient to cushion the pipe against trac loads in warmer climates Clark, Generally, a cover of 1.
In areas where frost penetration is a signicant factor, mains can have as much as 2. Trenches for water mains should be as narrow as possible and still be wide enough to allow for proper joining and compaction around the pipe. The suggested trench width is the nominal pipe diameter plus 0. Trench bottoms should be undercut 15 to 25 cm, and sand, clean ll, or crushed stone installed to provide a cushion against the bottom of the excavation, which is usually rock Clark, Standards for pipe construction, installation, and performance are published by the American Water Works Association in its C-series standards, which are continuously being updated.
When portions of the distribution system are separated by long distances or signicant changes in elevation, booster pumps are sometimes used to maintain acceptable service pressures. In some cases, re-service pumps are used to provide additional capacity for emergency re protection. Pumps operate at the intersection of the pump performance curve and the system curve.
Since the system curve is signicantly aected by variations in water demand, there is a signicant variation in pump operating conditions. In most cases, the range of operating conditions is too wide to be met by a single pump, and multiple-pump installations or variable speed pumps are required Velon and Johnson, Shuto valves or gate valves are typically provided at m intervals so that areas within the system can be isolated for repair or maintenance; air-relief valves or air-and-vacuum relief valves are required at high points to release trapped air; blowo valves or drain valves may be required at low points; and backow prevention devices are required by applicable regulations to prevent contamination from backows of nonpotable water into the distribution system from system outlets.
To maintain the performance of water-distribution systems it is recommended that each valve should be operated through a full cycle and then returned to its normal position on a regular schedule.
The time interval between operations should be determined by the manufacturers recommendations, size of the valve, severity of the operating conditions, and the importance of the installation AWWA, d. Unlike the service line and water tap, whic when incorrectly sized will generally require expensive excavation and retapping, water meters can usually be changed less expensively.
Selection of the type and size of a meter should be based primarily on the range of ow, and the pressure loss through the meter should also be a consideration.
For many single-family residences, a mm service line with a mm meter is typical, while in areas where irrigation is prevalent, mm or mm meter may be more prevalent. Undersizing the meter can cause pressure-related problems, and oversizing the meter can result in reduced revenue and inaccurate meter recordings since the ows do not register.
Some customers such as hospitals, schools, and factories with processes requiring uninterrupted water service should have bypasses installed around the meter so that meter test and repair activities can be performed at scheduled intervals without inconvenience to either the customer or the utility. The bypass should be locked and valved appropriately.
Fire hydrants 76 are direct connections to the water mains and, in addition to providing an outlet for re protection, re hydrants are used for ushing water mains, ushing sewers, lling tank trucks for street washing, tree spraying, and providing a temporary water source for construction jobs.
A typical re hydrant is shown in Figure 2. The vertical pipe connecting the water main to the re hydrant is commonly called the riser.
The Figure 2. Fire Hydrant and Connection to Water Main water utility is usually responsible for keeping hydrants in working order, although re departments sometime assume this responsibility. Standard practice is to install hydrants only on mains mm or larger, however, larger mains are often necessary to ensure that the residual pressure during re ow remains greater than kPa. Guidelines for the placement of hydrants are as follows AWWA, c: Not too close to buildings since re ghters will not position their re pumper trucks where a building wall could fall on them.
Preferably located near street intersections, where the hose can be strung to ght a re in any of several directions. Far enough from a roadway to minimize the danger of them being struck by vehicles. Close enough to the pavement to ensure a secure connection with the pumper and hydrant without the risk of the truck getting stuck in mud or snow.
In areas of heavy snow, hydrants must be located where they are least liable to be covered by plowed snow or struck by snow-removal equipment. Hydrants should be high enough o the ground that valve caps can be removed with a standard wrench, without the wrench hitting the ground. Fire hydrants should be inspected and operated through a full cycle on a regular schedule, and the hydrant should be ushed to prevent sediment buildup in the hydrant or connecting piping.
To accommodate uctuations in demand, a storage reservoir is typically located at the head of the system to store the excess water during periods of low demand and provide water from storage during periods of DRAFT as of August 25, 77 high demand. In addition to the operational storage required to accommodate diurnal hour cycle variations in water demand, storage facilities are also used to provide storage to ght res, to provide storage for emergency conditions, and to equalize pressures in water-distribution systems.
Storage facilities are classied as either ground storage, elevated storage, or standpipes. The function and relative advantages of these types of systems are as follows: Elevated-Storage Tanks.
Elevated storage tanks are constructed above ground such that the height of the water in the elevated storage tank is sucient to deliver water to the distribution system at the required pressure. The storage tank is generally supported by a steel or concrete tower, the tank is directly connected to the distribution system through a pipe called a riser, the water level in the storage tank is equal to the elevation of the hydraulic grade line in the distribution system at the outlet of the storage tank , and the elevated storage tank is said to oat on the system.
Elevated storage is useful in the case of res and emergency conditions since pumping of water from elevated tanks is not necessary, although the water must generally be pumped into elevated storage tanks.
Occasionally, system pressure could become so high that the tank would overow, and therefore altitude valves must be installed on the tank ll line to keep the tank from overowing.
Elevated tanks are usually made of steel. Ground-Storage Reservoirs. Ground-storage reservoirs are constructed at or below ground level and usually discharge water to the distribution system through pumps. These systems, which are sometimes referred to simply as distribution-system reservoirs or ground-level tanks, are usually used where very large quantities of water must be stored or when an elevated tank is objectionable to the public. When a ground-level or buried reservoir is located at a low elevation on the distribution system, water is admitted through a remotely operated valve, and a pump station is provided to transfer water into the distribution system.
Completely buried reservoirs are often used where an above-ground structure is objectionable, such as in a residential neighborhood.
In some cases, the land over a buried reservoir can be used for recreational facilities such as a ball eld or tennis court. Ground-storage reservoirs are typically constructed of steel or concrete.
A tank that rests on the ground with a height that is greater than its diameter is generally referred to as a standpipe. In most installations, only water in the upper portion of the tank will furnish usable system pressure, so most larger standpipes are equipped with an adjacent pumping system that can be used in an emergency to pump water to the system from the lower portion of the tank.
Standpipes combine the advantages of elevated storage with the ability to store large quantities of water, and standpipes are usually constructed of steel. Standpipes taller than 15 m are usually uneconomical, since for taller standpipes it tends to be more economical to build an elevated tank than to accommodate the dead storage that must be pumped into the system.
Storage facilities in a distribution system are required to have sucient volume to meet the following criteria Velon and Johnson, Sizing the storage volume for re protection is based on the product of the critical re ow and duration for the service area. In extremely large systems where re demands be only a small fraction of the maximum daily demand re storage may not be necessary Walski, Emergency storage is generally necessary to provide water during power outages, breaks in water mains, problems at treatment plants, unexpected shutdowns of water-supply facilities, and other sporadic events.
Emergency volumes for most municipal water-supply systems vary from one to two days of supply capacity at the average daily demand. The recommended standards for water works developed by the Great Lakes Upper Mississippi River Board of State Public Health and Environmental Managers suggest a minimum emergency storage capacity equal to the average daily system demand.
In cases where elevated storage tanks are used, the minimum acceptable height of water in an elevated storage tank is determined by computing the minimum acceptable piezometric head in the service area and then adding to that gure an estimate of the head losses between the critical service location and the location of the elevated service tank, under the condition of average daily demand.
The maximum height of water in the elevated tank is then determined by adding the minimum acceptable piezometric head to the head loss between the tank location and the critical service location under the condition of maximum hourly demand. The dierence between the calcu- lated minimum and maximum heights of water in the elevated storage tank is then specied as the normal operating range within the tank.
The normal operating range for water in elevated tanks is usually limited to 4. In most cases, the operating range is located in the upper half of the storage tank, with storage in the lower half of the tank reserved for reghting and emergency storage. Any water stored in elevated tanks less than 14 m 46 ft above ground is referred to as ineective storage Walski et al.
Operational storage in elevated tanks is normally at elevations of more than 25 m 81 ft above the ground, since under these conditions the pressure in connected distribution pipes will exceed the usual minimum acceptable pressure during normal operations of kPa 35 psi.
A typical elevated storage tank is illustrated in Figure 2. These types of storage facilities generally have only a single pipe connection to the distribution system, and this single pipe handles both inows and outows from the storage tank. This piping arrangement is in contrast to ground storage reservoirs, which have separate inow and outow piping. The inow piping delivers the outow from the water-treatment facility to the reservoir, while the outow piping delivers the water from the reservoir to the pumps that input water into the distribution system.
Elevated tanks are generally made of steel Walski, , and the largest elevated storage tank in the United States as of has a volume of 15, m 3 ASCE, Elevated storage tanks are best placed on the downstream side of the largest demand from the source, with the advantages that: If there are multiple stor- age tanks in the distribution system, the tanks should be placed roughly the same distance from the source or sources, and all tanks should have approximately the same overow elevation other- wise, it may be impossible to ll the highest tank without overowing or shutting o the lower tanks.
Elevated Storage Tank Example 2. Estimate the required volume of service storage. The required storage is the sum of three components: Taking the maximum daily demand factor as 1. This large volume will require a ground storage tank recall that the largest elevated-tank volume in the United States is 15, m 3 , and it is interesting to note that most of the storage in the service reservoir is reserved for emergencies.
A water-supply system is to be designed in an area where the minimum allowable pressure in the distribution system 80 is kPa. A hydraulic analysis of the distribution network under average daily demand conditions indicates that the head loss between the low-pressure service location, which has a pipeline elevation of 5. Under maximum hourly demand conditions, the head loss between the low-pressure service location and the elevated storage tank is 12 m. Determine the normal operating range for the water stored in the elevated tank.
It is important to keep in mind that the best hydraulic location and most economical design are not always the deciding factors in the location of an elevated tank. In some cases, the only acceptable location will be in an industrial area or public park. In cases where public feeling is very strong, a water utility may have to construct ground-level storage, which is more aesthetically acceptable. Real-time operation of water distribution systems are typically based on remote measurements of pressures and storage-tank water levels within the distribution system.
The pressure and water-level data are typically transmitted to a central control facility via telemetry, and adjustments to the distribution system are made from the central facility by remote control of pumps and valves within the distribution system.
These electronic control systems are generally called supervisory control and data acquisition SCADA systems Chase, Operating criteria for service pressures and storage facilities are described below.
The requirement that adequate pressures be maintained in the distribution system while sup- plying the service demands requires that the system be analyzed on the basis of allowable pres- sures. Minimum acceptable pressures are necessary to prevent contamination of the water supply from cross-connections. GLUMB There are several considerations in assessing the adequacy of service pressures, including 1 the pressure required at street level for excellent ow to a 3-story building is about kPa; 2 ow is adequate for residential areas if the pressure is not reduced below kPa; 3 the pressure required for adequate ow to a story building is about kPa, which is not desirable because of the associated leakage and waste; 4 very tall buildings are usu- ally served with their own pumping equipment; and 5 it is usually desirable to maintain normal pressures of kPa since these pressures are adequate for the following purposes: To supply ordinary consumption for buildings up to 10 stories.
To provide adequate sprinkler service in buildings of 4 to 5 stories. To provide direct hydrant service for quick response. To allow larger margin for uctuations in pressure caused by clogged pipes and excessive length of service pipes. Pressures higher than kPa should be avoided if possible because of excessive leakage and water use, and the added burden of installing and maintaining pressure-reducing valves and other specialized equipment Clark, Customers do not generally like high pressure because water comes out of a quickly-opened faucet with too much force AWWA, c.
In addition, excessive pressures decrease the the life of water heaters and other plumbing xtures. The principal factors aecting water quality in distribution systems are the quality of the treated water fed to the system; the material and condition of the pipes, valves, and storage facilities that make up the system; and the amount of time that the water is kept in the system Grayman et al.
Key processes that aect water quality within the distribution system usually include the loss of disinfection residual with resulting microbial regrowth, and the formation of disinfection byproducts such as trihalomethanes. Water-quality deterioration is often proportional to the time the water is resident in the distribution system. The longer the water is in contact with the pipe walls and is held in storage facilities, the greater the 82 opportunity for water-quality changes.
Generally, a hydraulic detention time of less than 7 days in the distribution system is recommended AWWA, c. The velocity of ow in most mains is normally very low because mains are designed to handle re ow, which may be several times larger than domestic ow.
As a result, corrosion products and other solids tend to settle on the pipe bottom, and this problem is especially bad in dead-end mains or in areas of low water consumption. These deposits can can be a source of color, odor, and taste in the water when the deposits are stirred up by an increase in ow velocity or a reversal of ow in the distribution system.
To prevent these sediments from accumulating and causing water-quality problems, pipe ushing is a typical maintenance routine. Flushing involves opening a hydrant located near the problem area, and the hydrant should be kept open as long as needed to ush out the sediment, which typically requires the removal of up to three pipe volumes AWWA, c. Only through experience will an operator be able to how often or how long certain areas should be ushed. Some systems nd that dead-end mains must be ushed as often as weekly to avoid customer complaints of rusty water.
The ow required for eective ushing is in the range of 0. If ushing proves to be inadequate for cleaning mains, air purging or cleaning devices such as swabs or pigs may need to be used.
In recognition of the inuence of the water distribution system on water quality, water quality regulations in the United States requires that water to be sampled at at the entry point to the distri- bution system, at various points within the distribution system, and at consumers taps Kirmeyer et al. In complex pipe networks, the application of computer programs to implement these methodologies is standard practice Haestad Methods Inc. Computer programs allow engineers to easily calculate the hydraulic performance of complex networks and such parameters as the age of water delivered to consumers and also to trace the origin of the delivered water.
Water age is measured from the time the water enters the system and gives an indication of the overall quality of the delivered water. Steady-state analyses are usually adequate for assessing the performance of various components of the distribution system, including the pipelines, storage tanks, and pumping systems, while time-dependent simulations are useful in assessing the response of the system over short time periods days or less , evaluating the operation of pumping stations and variable-level storage tanks, performing energy consumption and cost studies, and water quality modeling Velon and Johnson, ; Haestad Methods, Inc.
Modelers frequently refer to time-dependent simulations as extended-period simulations, and several examples can be found in Larock et al. An important part of analyzing large water-distribution systems is the skeletonizing of the system, which consists of representing the full water-distribution system by a subset of the system that includes only the most important elements. For example, consider the case of a water supply to the subdivision shown in Figure 2. A slight degree of skeletonization could be achieved by omitting the household service DRAFT as of August 25, 83 a b c d Figure 2.
Skeletonizing a Water-Distribution System Source: Haestad Methods, Practical Guide: Hydraulics and Hydrology p. Copyright c by Haestad Methods, Inc. Reprinted by permission. This reduces the number of junctions from 48 to Further skeletonization can be achieved by modeling just 4 junctions, consisting of the ends of the main piping and the major intersections shown in Figure 2.
In this case, the water demands are associated with the nearest junctions to each of the service connections, and the dashed lines in Figure 2. A further level of skeletonization is shown in Figure 2.
Clearly, further levels of skeletonization could be possible in large water-distribution systems. As a general guideline, larger systems permit more degrees of skeletonization without introducing signicant error in the ow conditions of main distribution pipes. These results are used to assess the hydraulic performance and reliability of the network, and they are to be compared with the guidelines and specications required for acceptable performance.
In engineering practice, the use of computer models to apply the fundamental principles 84 covered in this chapter is usually essential. In choosing a model for a particular application, there are usually a variety of models to choose from, however, in doing work that is to be reviewed by regulatory bodies, models developed and maintained by agencies of the United States government have the greatest credibility and, perhaps more importantly, are almost universally acceptable in supporting permit applications and defending design protocols.
A secondary guideline in choosing a model is that the simplest model that will accomplish the design objectives should be given the most serious consideration. It performs extended-period simulation of hydraulic and water-quality behavior within pressurized pipe networks. Summary The hydraulics of ow in closed conduits is the basis for designing water-supply systems and other systems that involve the transport of water under pressure.
The fundamental relationships governing ow in closed conduits are the conservation laws of mass, momentum, and energy; the forms of these equations that are most useful in engineering applications are derived from rst principles. Of particular note is the momentum equation, the most useful form of which is the Darcy-Weisbach equation.
Techniques for analyzing ows in both single and multiple pipelines, using the nodal and loop methods, are presented. Flows in closed conduits are usually driven by pumps, and the fundamentals of pump performance using dimensional analysis and similitude are presented. Considerations in selecting a pump include the specic speed under design conditions, the application of anity laws in adjusting pump performance curves, the computation of operating points in pump-pipeline systems, practical limits on pump location based on the critical cavitation parameter, and the performance of pump systems containing multiple units.
Water-supply systems are designed to meet service-area demands during the design life of the system. Projection of water demand involves the estimation of per capita demands and population projections. Over short time scales, populations can be expected to follow either geometric, arith- metic, or declining growth models, while over longer time scales a logistic growth curve may be more appropriate. Components of water-supply systems must be designed to accommodate daily uctuations in water demand plus potential re ows.
The design periods and capacities of various components of water-supply systems are listed in Table 2. Other key considerations in design- ing water distribution systems include required service pressures Table 2. Problems 2. Water at If the diameter of the pipe is suddenly expanded to mm, what is the new velocity in the pipe?
What are the volumetric and mass owrates in the pipe? A mm diameter pipe divides into two smaller pipes each of diameter mm. Calculate the average velocity and owrate in the pipe in terms of V o. Calculate the momentum correction coecient, , for the velocity distribution given in Equa- tion 2.
Water is owing in a horizontal mm diameter pipe at a rate of 0. Estimate the average shear stress on the pipe and the friction factor, f. Use Equation 2. Estimate the friction factor in the pipe, and state whether the pipe is hydraulically smooth or rough.
Compare the friction factors derived from the Moody diagram, the Colebrook equation, and the Jain equation. Estimate the change in pressure over m of pipeline. How would the friction factor and pressure change be aected if the pipe is not horizontal but 1 m lower at the downstream section? Show that the Colebrook equation can be written in the slightly more convenient form: If you had your choice of estimating the friction factor either from the Moody diagram or from the Colebrook equation, which one would you pick?
Explain your reasons. Water leaves a treatment plant in a mm diameter ductile iron pipeline at a pressure of kPa and at a owrate of 0. If the elevation of the pipeline at the treatment plant is m, then estimate the pressure in the pipeline 1 km downstream where the elevation is m. Assess whether the pressure in the pipeline would be sucient to serve the top oor of a story approximately 30 m high building. A mm diameter galvanized iron service pipe is connected to a water main in which the pressure is kPa.
If the length of the service pipe to a faucet is 20 m and the faucet is 2. If the length of the service pipe is 40 m and the head loss in the pipe is not to exceed 45 m, calculate the minimum pipe diameter that can be used. Use the Colebrook equation in your calculations. Repeat Problem 2. Use the velocity distribution given in Problem 2.
Estimate the energy and momentum correction factors corresponding to the seventh-root law. Show that the kinetic energy correction factor, , corresponding to the power-law velocity prole is given by Equation 2. Use this result to conrm your answer to Problem 2. Water enters and leaves a pump in pipelines of the same diameter and approximately the same elevation. If the pressure on the inlet side of the pump is 30 kPa and a pressure of kPa is desired for the water leaving the pump, what is the head that must be added by the pump, and what is the power delivered to the uid?
Water leaves a reservoir at 0. Would it be fair to say that for pipe lengths shorter than the length calculated in this problem that the word minor should not be used? The top oor of an oce building is 40 m above street level and is to be supplied with water from a municipal pipeline buried 1.
The water pressure in the municipal pipeline is kPa, the sum of the local loss coecients in the building pipes is The length of the pipeline in the building is 60 m, the water temperature is C, and the water pressure on the top oor must be at least kPa. Will a booster pump be required for the building? If so, what power must be supplied by the pump?
Water is pumped from a supply reservoir to a ductile iron water transmission line, as shown in Figure 2. The high point of the transmission line is at point A, 1 km downstream of the supply reservoir, and the low point of the transmission line is at point B, 1 km downstream of A. Problem 2. A pipeline is to be run from a water-treatment plant to a major suburban development 3 km away.
The average daily demand for water at the development is 0. Determine the required diameter of ductile iron pipe such that the ow velocity during peak demand is 2.
Round the pipe diameter upward to the nearest 25 mm i. The water pressure at the development is to be at least kPa during average demand conditions, and kPa during peak demand. If the water at the treatment plant is stored in a ground-level reservoir where the level of the water is Calculate the head loss over a length of m.
If the pipe is laid on a downward slope of 0. Derive the Hazen-Williams head-loss relation, Equation 2. Compare the Hazen-Williams formula for head loss Equation 2. Based on your result, identify the type of ow condition incorporated in the Hazen-Williams formula rough, smooth, or transition. Derive the Manning head-loss relation, Equation 2. Compare the Manning formula for head loss Equation 2. Based on your result, identify the type of ow condition incorporated in the Manning formula rough, smooth, or transition.
Determine the relationship between the Hazen-Williams roughness coecient and the Man- ning roughness coecient. Given a choice between using the Darcy-Weisbach, Hazen-Williams, or Manning equations to estimate the friction losses in a pipeline, which equation would you choose?
Calculate the Hazen-Williams roughness coecient and the Manning coecient that should be used to obtain the same head loss as the Darcy-Weisbach equation. Reservoirs A, B, and C are connected as shown in Figure 2. The water elevations in reservoirs A, B, and C are m, 80 m, and 60 m, respectively. The three pipes connecting the reservoirs meet at the junction J, with pipe AJ being m long, BJ m long, CJ m long, and the diameter of all pipes equal to mm.
If all pipes are made of ductile iron and the water temperature is C, nd the ow into or out of each reservoir. The water-supply network shown in Figure 2. The network is on at terrain, and the pipeline characteristics are as follows: Assume that the ows in all pipes are fully turbulent. Consider the pipe network shown in Figure 2. What value of r and n would you use for each pipe in the system?
The pipeline characteristics are as follows: A portion of a municipal water distribution network is shown in Figure 2. Use the Hardy Cross method to nd the owrate in each pipe.
If the pressure at point P is kPa and the distribution network is on at terrain, determine the water pressures at each pipe intersection. What is the constant that can be used to convert the specic speed in SI units Equation 2. Customary units Equation 2. What is the highest synchronous speed for a motor driving a pump? Derive the anity relationship for the power delivered to a uid by two homologous pumps.
This anity relation is given by Equation 2. The water level in the well is 1. The delivery pipe is m long, and minor losses can be neglected. Is this pump adequate?
A pump is to be selected to deliver water from a well to a treatment plant through a m long pipeline. The temperature of the water is C, the average elevation of the water surface in the well is 5 m below ground surface, the pump is 50 cm above ground surface, and the water surface in the receiving reservoir at the water-treatment plant is 4 m above ground surface. Calculate the specic speed of the required pump in U. Customary units , and state what type of pump will be required when the speed of the pump motor is 1, rpm.
Neglect minor losses. A pump lifts water through a mm diameter ductile iron pipe from a lower to an upper reservoir Figure 2.
If the pump manufacturer gives the required net positive suction head under these operating conditions as 1. There is an open gate valve located at C; The specic speed of the pump in U. Customary units is 3, Assuming that the ow is turbulent in the smooth, rough, or transition range and the temperature of the water is C, then a write the energy equation between the upper and lower reservoirs, accounting for entrance, exit, and minor losses between A and F; b calculate the owrate and velocity in the pipe; c if the required net positive suction head at the pump operating point is 3.
What is the performance curve of a pump system containing n of these pumps in parallel? If the pump is replaced by two identical pumps in parallel, what would be the owrate in the system?
If the pump is replaced by two identical pumps in series, what would be the owrate in the system? Derive an expression for the population, P, versus time, t, where the growth rate is: The design life of a planned water-distribution system is to end in the year , and the population in the town has been measured every 10 years since by the U. Census Bureau. The reported populations are tabulated below. Estimate the population in the town using: Year Population 25, 30, 30, 37, 38, 41, 56, 64, 2.
A city founded in had a population of 13, in ; , in ; and , in Assuming that the population growth follows a logistic curve, estimate the saturation population of the city.
Estimate the maximum daily demand and maximum hourly demand. Estimate the owrate and volume of water required to provide adequate re protection to a ve-story oce building constructed of joisted masonry. The eective oor area of the building is 5, m 2. What is the maximum re ow and corresponding duration that can be estimated for any building?
If the water supply is to be drawn from a river, then what should be the design capacity of the supply pumps and water-treatment plant? For what duration must the re ow be sustained, and what volume of water must be kept in the service reservoir to accommodate a re? What should the design capacity of the distribution pipes be? What is the minimum acceptable water pressure in a distribution system under average daily demand conditions?
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