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Types of distribution schemes
With respect to the way the water is supplied, the following distribution schemes can be distinguished:
Direct pumping,
The choice of one of the above alternatives is closely linked to the existing topographical conditions.
Gravity scheme makes use of the existing topography. The source is, in this case, located at a higher elevation than the distribution area itself. The water distribution can take place without pumping and nevertheless under acceptable pressure.
The advantages of this scheme are
no energy costs
simple operation (fewer mechanical components, no power supply needed),
low maintenance costs
slower pressure changes,

Due to the fixed pressure range, the gravity systems are less flexible for extensions.
Moreover, they require larger pipe diameters in order to minimize pressure losses.
The main operational concern is capacity reduction that can be caused by air entrainment

In the direct pumping scheme, the system operates without storage provision for demand balancing. The entire demand is directly pumped into the network. As the pumping schedule has to follow variations in water demand, the proper selection of units is important in order to optimize the energy consumption. Reserve pumping capacity for irregular situations should also be planned.
Advantage of the direct pumping is .
With good design and operation, any pressure in the system can be reached.
These systems have rather complicated operation and maintenance and
they are dependent on a reliable power supply.
Additional precautions are therefore necessary, such as an alternative source of power supply, automatic mode of pump operation, stock of spare parts, etc.

Combined scheme assumes an operation with pumping stations and demand balancing reservoirs. Part of the distribution area may be supplied by the direct pumping and the other part by gravity. A considerable storage volume is needed in this case but the pumping capacities will be below those in the direct pumping scheme.

Layouts of Distribution Network
The distribution pipes are generally laid below the road pavements and as such their layouts generally follow the layout of the roads
There are in general, four different types of pipe networks: any one of which either singly or in combinations, can be used for a particular place.
They are
The dead end
The radial system
The grid iron system
The ring system
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.
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.
(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:
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.
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(to flush out the sediment.). 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.
The system is less successful in maintaining satisfactory pressures in the remote parts.
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.

The various advantages of grid-iron system of layout are as follows:
There is free circulation of water, without any stagnation or sediment deposit. Thus chances of pollution of water due to stagnation are not there.
Due to interconnection water is delivered at every point of distribution system with minimum loss of head.
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.
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:
In this system of layout a large number of cutoff valves are required.
This system of layout requires longer lengths of pipes.
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.
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.

4. Radial System:
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 none of these four systems of layout may 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.

Analysis of Pipe Networks of Distribution System:
A group of interconnected pipes forming several loops or circuits as shown in Fig. below 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
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 –

f is friction factor
Minor losses (valves, bend etc)may be neglected if the pipe lengths are large.

Hardy-Cross method, named after its original investigator, is a method of successive approximations which involves a controlled trial and error process.
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 Qa is the assumed discharge and Q is the correct discharge, then –
And the head loss in the pipe
Thus for the complete loop
By expanding the terms in the brackets by binomial theorem
ΣrQ^n=Σr(Q_a^n+nQ_a^(n-1) ∆Q+⋯..)
If ∆Q is small compared with Qa all terms of the series after the second one may be dropped
ΣrQ^n=ΣrQ_a^n+ΣrnQ_a^(n-1) ∆Q

For the corrected distribution the loop is balanced and hence

In the above expression ∆Q has been taken out of the summations as it is same for all the pipes in the loop.
Solving for ∆Q
We get
∆Q=-(∑▒〖rQ_a^n 〗)/(n∑▒|rQ_a^(n-1) | ) or=-(∑▒h_f )/(n∑▒|h_f/Q_a | )

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.

Problem: Calculate the head losses and the corrected flows in the various pipes of a distribution network as shown in figure below. The diameters and the lengths of the pipes used are given against each pipe. Compute corrected flows after two corrections.CH=100

∆Q=-(∑▒〖rQ_a^n 〗)/(n∑▒|rQ_a^(n-1) | ) or=-(∑▒h_f )/(n∑▒|h_f/Q_a | )

Shared pipes formula for correction of flow
Assumed Qp2-loop1+∆Q loop1 -∆Q loop2
Assumed Qp2- loop2+∆Q loop2 – ∆Q loop1

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