In this article we will discuss about:- 1. Layout of Distribution System 2. Design of a Distribution System 3. Analysis of Pipe Networks.
Layout of Distribution System:
Depending upon the layout of various pipes of a distribution system there are four different systems of layout of distribution system as indicated below:
1. Dead-End System or Tree System:
In this system, one main pipe line runs through the centre of the area to be served, and from both sides of the main pipe line sub-mains take off. The sub-mains divide into several branch lines from which service connections are given to the consumers.
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Thus the entire distribution area is covered by a net-work of pipe lines running like branches of a tree. There are no cross connections between different sub-mains and branches, and hence there are a number of dead ends in this system. Due to several dead ends, there is accumulation of sediment there and stagnation of water.
The dead-end system of layout is adopted in towns or cities which have developed in a haphazard manner without proper planning. The water supply mains are laid at random without any planning of future roads.
The various advantages of dead-end system of layout are as follows:
(i) In this case the discharge and pressure at any point in the distribution system can be worked out accurately and hence the design calculations are simple and easy.
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(ii) The pipe diameters are to be designed for the population likely to be served by them only. This may make the system cheap and economical.
(iii) In this system of layout comparatively less number of cutoff valves are required.
(iv) The laying of pipes is simple.
The various disadvantages of dead-end system of layout are as follows:
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(i) In the case of damage or repair in any section of the system, the water supply to the entire portion beyond that point will be completely cut-off. Thus large portion of the distribution area will be affected resulting in great inconvenience to the consumers of that area.
(ii) There are number of dead-ends in the system due to which free circulation of water is prevented and stagnation of water results. This stagnation of water may lead to degradation in its quality. Further there may be accumulation of sediment at the dead ends.
As such in order to remove this stale water as well as the deposited sediment, scour valves are provided at the dead ends. However, this measure is costly because besides the cost of scour valves, large quantity of treated water is thrown to waste and also careful attendance and operation of scour valves is required.
(iii) The system is less successful in maintaining satisfactory pressures in the remote parts.
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(iv) In this system since water supplied to any area is obtained from the main pipe line at one point only, the water available for firefighting will be limited. Further in this system it is not possible to increase the supplies by diverting from any other side.
2. Grid-Iron System or Reticulation System or Interlaced System:
In this system of layout the mains, sub-mains, and branches are interconnected with each other. The main pipe line runs through the centre of the area to be served and from both sides of the main pipe line sub-mains take off in perpendicular directions.
The branch lines interconnect all the sub-mains. Thus in this case water can be made to circulate through the entire distribution system. This system of layout is more suitable for cities laid out on a rectangular plan resembling a grid-iron.
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The various advantages of grid-iron system of layout are as follows:
(i) There is free circulation of water, without any stagnation or sediment deposit. Thus chances of pollution of water due to stagnation are not there.
(ii) Due to interconnection water is delivered at every point of distribution system with minimum loss of head.
(iii) In the case of damage or repair in any section of the system, the water supply to only very small area of the distribution system is affected.
(iv) When fire occurs, plenty of water can be made available for firefighting purpose by manipulating the cutoff valves and diverting the supplies from other sections.
The various disadvantages of grid-iron system of layout are as follows:
(i) In this system of layout a large number of cutoff valves are required.
(ii) This system of layout requires longer lengths of pipes.
(iii) The procedure for calculating the sizes of pipes and for working out pressures at various points in the distribution system is laborious, complicated and difficult.
(iv) In this system of layout the cost of laying distribution pipes is more.
3. Circular System or Ring System:
In this system of layout the main pipe line is laid to form a closed ring, either circular or rectangular, around the area to be served.
The entire distribution area is divided into small circular or rectangular blocks and the main pipe lines are laid on the periphery of these blocks. The sub-mains take off from the main pipe lines and run on the interior of the area. Thus in this case water can be supplied to any point from at least two directions. This system of layout is most suitable for cities having well planned streets and roads.
Further this system of layout possesses the same advantages and disadvantages as those of grid-iron system of layout. However, in the case of circular system of layout the length of the main pipe line is much larger and also large quantity of water can be made available for firefighting.
This system of layout is just the reverse of the circular or ring system of layout, with water flowing towards the outer periphery instead of from it. In this system the entire distribution area is divided into a number of small distribution zones and in the centre of each zone a distribution reservoir is provided.
Water obtained from the main pipe line is pumped into the distribution reservoir from where it is supplied through radially laid distribution pipes running towards the periphery of the distribution zone. This system of layout ensures high pressure in distribution and it gives quick and efficient water distribution. The calculations for design of pipe sizes are also simple. The radial system of layout is most suitable for cities having roads laid out radially.
It may, however, be stated that generally only any one of these four systems of layout may not be suitable for the entire city or town. In actual practice for any city or town depending upon the various factors such as relative levels of different zones of the city or town, layout of its roads and streets, etc., a combination of two or more of these four systems of layout may be more suitable and the same may therefore be adopted.
Design of a Distribution System:
The various steps involved in the design of a distribution system are as indicated below:
1. Survey and Preparation of Contoured Plans and Maps:
The strip of land lying between the treatment plant (water works) and the distribution area is surveyed to obtain levels for fixing the alignment of the main pipe line which will bring treated water to the distribution area. The distribution area (city or town) is also completely surveyed and contoured plan of the area is prepared to locate the positions of the distribution zones, distribution or service reservoirs, pumping stations, etc.
Further detailed maps of the distribution area are prepared to show the positions of roads, streets, lanes, commercial locality, industrial area, parks and gardens, etc. The cross- sections of the roads, streets, lanes, etc., are also prepared showing the positions of the existing underground service lines such as electric lines, telephone lines, gas lines, sewer lines, existing water supply lines, if any, etc.
The entire distribution area (city or town) is divided into various distribution zones and the same are marked on the detailed map of the distribution area. The density of population (i.e., average number of persons per hectare area) for each zone is also marked. The system of layout to be adopted is decided and tentative alignment of all mains, sub-mains and branches as well as positions of distribution or service reservoirs, valves, hydrants and other appurtenances are marked.
The discharge desired to be carried by each pipe line is computed on the basis of density of population, type of distribution zone (i.e., residential, commercial, etc.) and fire demand. The size of the distribution pipes are so fixed that the minimum residual pressure is maintained at all points.
The pipes are designed for a discharge ranging from 2.25 to 3 times the average rate of supply. For population over 50,000 the distribution mains are designed for a discharge of 2.25 times the average rate of supply, while for population below 50,000 the distribution mains are designed for a discharge of 3 times the average rate of supply.
4. Calculation of Pipe Diameters:
For the known design discharge the pipe diameters are assumed in such a way that the velocity of flow varies from 0.6 to 3 m/s. Smaller velocity is assumed for pipes of smaller diameter and larger velocity for pipes of larger diameter.
The loss of head in the pipes is then calculated using Hazen-Williams formula or Darcy-Weisbach formula or Manning’s formula. Out of these formulae Hazen-Williams formula is more commonly used. The use of Hazen-Williams formula, however, involves trial error solution, and in order to avoid this a nomogram of Hazen-Williams formula has been developed.
There are in all four variables:
(i) Discharge Q in m3/s or litres/s second;
(ii) Diameter of pipe in mm,
(iii) Loss of head in metres per 1000 m length of pipe, and
(iv) Velocity of flow in m/s.
If out of the four quantities, any two are known, the other two can be found from the nomogram. For this a straight edge is placed on the values of the two known quantities, and the values of the two unknown quantities are then directly read out. The nomogram is valid for a value of roughness coefficient CH equal to 100. For any other value of CH the head loss obtained from the nomogram is multiplied by the factor CH /100.
5. Computation of Available Residual Pressure Heads:
Starting from the distribution or service reservoir, or the pumping station where the total pressure head is known, the pressure head available at the end of any pipe line may be determined by allowing for the frictional loss of head and any rise or fall due to slope of the pipe line and the ground levels. If the available residual pressure head is less than the required minimum residual pressure head then the assumed pipe size should be revised.
Analysis of Pipe Networks of Distribution System:
A group of interconnected pipes forming several loops or circuits as shown in Fig. 10.17 is called a network of pipes.
The conditions to be satisfied in any network of pipes are as follows:
(1) According to the principle of continuity the flow into each junction must be equal to the flow out of the junction. For example at junction A, the inflow must be equal to the flow through AB and AC.
(2) In each loop, the loss of head due to flow in clockwise direction must be equal to the loss of head due to flow in anticlockwise direction. For example in the loop ABDC the sum of the head losses due to flow in AB and BD (clockwise flow) must be equal to the sum of the head losses due to flow in AC and CB (anticlockwise flow).
(3) In each pipe of network there is a relation between the head loss in the pipe and the quantity of water flowing through it. In other words Hazen- Williams’s formula or Darcy-Weisbach formula must be satisfied for flow in each pipe of the network.
The loss of head hƒ through any pipe discharging at the rate of Q can be expressed as-
hƒ = rQn
Where
r is a proportionality factor; and
n is an exponent.
According to Hazen-Williams formula the loss of head hƒ, due to friction in a pipe of length L, diameter D, and roughness coefficient CH, when carrying a discharge Q is given as –
Minor losses may be neglected if the pipe lengths are large. However, if the minor losses are large, they may be taken into account by considering them in terms of the head loss due to friction in equivalent pipe lengths.
Frequently it becomes necessary to analyze pipe networks of a given distribution system in order to determine the pressures and flows available in any section of the system and to suggest ways to improve upon the same, if found inadequate.
The various methods used for the analysis of pipe networks of a distribution system are as indicated below:
In this method a complex network of pipes is replaced by an equivalent pipe system giving the same discharge with same loss of head as in the complex network, of pipes. For the purpose of analysis the entire network of pipes is considered to be split up into two portions viz.- (i) pipes in series, and (ii) pipes in parallel. In the pipe network shown in Fig. 10.17 pipes AB and BD, and pipes AC and CD are in series, while pipes ABD and ACD are in parallel.
For the pipes in series the discharge through each pipe is the same and the total loss of head is equal to the sum of the loss of head in each pipe. On the other hand for the pipes in parallel the discharge through each pipe is different and it is so distributed that the loss of head through each pipe is the same.
The length and diameter of an equivalent pipe required to replace a system of pipes in series or in parallel may be determined as indicated below:
(a) Pipes in Series:
According to Hazen-Williams formula the loss of head due to friction in a pipe of length L, diameter D, and roughness coefficient CH when carrying discharge Q is given as –
From Eq. 10.3 or 10.4 the length LE of equivalent pipe can be determined if its diameter DE is given or specified, and its diameter DE can be determined if its length LE is given or specified. The length LE of equivalent pipe may be taken equal to the sum of the lengths of all the pipes in series, i.e., LE = L1 + L2 +….. + Ln, and its diameter DE may be determined.
However, the diameter DE determined for any given or specified length LE will usually be a non-standard diameter. On the other hand if for a given or specified standard diameter DE, the length LE of equivalent pipe is determined, it will usually be different from the sum of the lengths of all the pipes in series.
(b) Pipes in Parallel:
For pipes ABD and ACD which are in parallel as shown in Figure 10.17, we have –
Again if pipes ABD and ADC can be replaced by an equivalent pipe of length LE, diameter DE, roughness coefficient CH, and carrying the total discharge Q, then the loss of head due to friction in the equivalent pipe is given, by –
If instead of Hazen-Williams formula, Darcy-Weisbach formula is used then the following equation relating length LE and diameter DE of equivalent pipe is obtained.
From Eq. 10.6 or 10.7 the length LE of equivalent pipe can be determined if its diameter DE is given or specified, and its diameter DE can be determined if the length LE is given or specified. The length LE of the equivalent pipe may be taken equal to AD shown in Fig. 10.17 and its diameter DE may be determined, which, however, may be a non-standard diameter.
By the equivalent pipe method a complex system of pipes is replaced by a single pipe line and hence a pipe network can be considerably simplified to obtain useful information on the flow and head losses at important junctions.
Hardy-Cross method, named after its original investigator, is a method of successive approximations which involves a controlled trial and error process.
The analysis of pipe network by Hardy-Cross method may be carried out in the following two ways:
(a) Balancing heads by correcting assumed flows; and
(b) Balancing flows by correcting assumed heads.
Out of these two methods the ‘method of balancing heads’ is the original Hardy-Cross method which is more commonly used. The ‘method of balancing flows’ is a modification of the original Hardy-Cross method and it is relatively less common.
Both these methods are discussed below:
(a) Balancing Heads by Correcting Assumed Flows:
In this method the assumed flows are corrected and the procedure is repeated until the loss of head in a loop in the clockwise direction is equal to that in the anticlockwise direction.
Thus various steps involved in the computation are as indicated below:
(i) Assume suitable values flow Q in each pipe line such that the flows coming into each junction of the loop are equal to the flows leaving the junction.
(ii) With the assumed values of Q, compute the head loss hƒ in each pipe using the equation hƒ = rQn.
(iii) Consider different loops and compute the net head loss around each loop considering the head loss in clockwise flow as positive and anticlockwise flows as negative. For a correct distribution of flow the net head loss around each loop should be equal to zero, so that the loop will be balanced.
However, in most of the cases, for the assumed distribution of flow the head loss around the loop will not be equal to zero. The assumed flows are then corrected by introducing correction ΔQ for the flows, till the loop is balanced.
The value of the correction ΔQ to be applied to the assumed flows of the loop may be obtained as follows:
For any pipe if Q0 is the assumed discharge and Q is the correct discharge, then –
In the above expression for the correction ΔQ, the denominator is the sum of absolute terms and hence it has no sign. Further if the head losses due to flow in the clockwise direction are more than the head losses due to flow in the anticlockwise direction, then according to the sign convention adopted, ΔQ will be negative and hence it should be added to the flow in the anticlockwise direction and subtracted from the flow in the clockwise direction.
On the other hand if the head losses due to flow in the clockwise direction are less than the head losses due to flow in the anticlockwise direction, then Q will be positive and hence it should be added to the flow in the clockwise direction and subtracted from the flow in the anticlockwise direction.
(iv) For pipes common to two loops, a correction from both the loops will be required to be applied with due regard to the sign of flows.
(v) With the corrected flows in all the pipes, a second trial calculation is made for all the loops and the process are repeated till the corrections become negligible.
The method of balancing heads is applicable when the quantities of water entering and leaving the network are known. When the quantities of water are unknown and there are several inlets, the distribution of flow among them can be more conveniently determined by the method of balancing flows.
(b) Balancing Flows by Correcting Assumed Heads:
In this method the flows at each junction are made to balance for the assumed heads at the junctions and the corresponding head losses in the pipes.
The various steps involved in the computation are as indicated below:
(i) Assume head at all the free junctions such that the sum of the head losses in clockwise direction equals the sum of the head losses in the anticlockwise direction in all the loops.
(ii) Assign positive sign to head losses for flows towards the junction and negative sign to those away from the junction.
(iii) Compute the flows in each pipe using equation, hƒ = rQn, giving same signs as for the head losses.
(iv) Compute ƩQ i.e., algebraic sum of the flows at each free junction and if this is nearly equal to zero at all junctions the assumed head losses are correct.
(v) If ƩQ is not equal to zero at any junction, then the assumed head losses are corrected by introducing a correction Δhƒ which is given by the following expression-
The correction Δhƒ, is added to or subtracted from the assumed head losses with due regard to the signs of head losses.
(vi) For pipes common to two loops, a correction from both the loops will be required to be applied with due regard to the sign of head losses.
(vii) With the corrected head losses in all the pipes, a second trial calculation is made and the process is repeated till ƩQ at each free junction is nearly equal to zero.