Introduction
In the process industry, networks of somewhat different kind are encountered in relation to the closed loop utility circulation systems viz. cooling water, refrigeration brine and thermic fluid systems.

The distribution of fluid flow in different loops of the network is dictated by process requirements as in case of utilities (water, brine, thermic fluid) or by statutory regulations as in the case of the firewater distribution system for Fire protection.

Piping networks are encountered in fire protection systems wherein ring mains have to be installed to deliver water different locations.

With a view to define the scope of this presentation, schematic diagrams for the networks referred to earlier are shown
Network Analysis
The sizes of individual pipelines or branches, which constitute the network, are governed by one or more of the following considerations:

a) Fluid now required
b) Fluid pressure required at a specific location (such as equipment inlet or farthest hydrant) 
c) Economic pipe velocity/diameter d)Maximum and minimum operating conditions 
The fact that fluid flow and pressure drop suffered by fluid are interrelated is understood. Hence, change in flow condition of one branch affects the flow and pressure in other branches of the network. It is a common experience that flow in the farther branch may reduce when the flow t hrough then nearer branch increases. 
The analysis of a network under different conditions of total flow through the network therefore is useful in understanding flow behaviour through different branches. Such analysis proves very useful in operations as well as sizing. 
Principles of Network Analysis
In a network where two pipeline branches are available for the flow of fluid from point A to B, the head difference (pressure drop) between these two points is the same irrespective of the route. The pressure drop, in turn varies with the flow.

Therefore in conformity with the pressure drop behaviour (same pressure drop irrespective of the route), the flow through the branch offering lesser resistance is more. When considered from the point of view of pressure drop due to fluid friction, the flow through the two branches would adjust such that frictional pressure drop (friction head loss) would be the same in both the branches.

Darcy of fanning equation gives the relationship between friction head loss (h) and flow (Q) as well as branch parameters (equivalent length Le and pipe diameter d) (Equivalent length Le takes into account pressure drop through the straight pipe as well as fittings in the branches).

As could be seen, the relationship between h and Q is nonlinear (apparently parabolic) 
Another reason for the nonlinear relationship is that the fanning friction factor (ff) decreases with an increase in Q in a manner such that ff is approximately proportional to Q ^{0.25}.

The analysis of the network therefore needs iterative calculations (trialerror method). The iterative calculation proced ure used is commonly known as the Hardy Cross method.

The method is based on making a trial guess for the value of flow in each branch of the network. The trial guesses are improved by employing corrections until the pressure drop criteria are satisfied.

This approach is also referred to as head balancing. 
Head Balancing
Quantity Balancing
Quantity balancing is another method of analysing piping network. This method is more convenient for analysing interconnected reservoirs each at different elevations.

In the head balancing method (discussed earlier), the flow in each branch was assumed. In the quantity balancing method, head of a junction is assumed to determine flow (quantity) in each branch.

(f) Evaluate dH ( Using eqn C ) 
(g) Use new value of Hj = Hj + dH 
(h) Repeat steps a to g till dH becomes very small, nearly zero. 
Note 1: The assumed head Hj is not elevation of the function taking into consideration head loss due to friction.

Figure 6.3 also gives a numerically solved example using the method of quantity balancing. 
In computation, Le rather than length of only straight pipe (L) in the branch is required to be used due to fact that fluid suffers pressure loss due to flow through straight pipe length as well as flow through fittings such bend, tee, value, etc.

There are two ways of computing pressure drop through fittings as represented by following equations:
Where DP Pressure drop across fittings in m/c. The numerical value of K in the former equation is decided by the type of fitting. A table showing some typical K value is given.

In the latter equation Le is the equivalent length of a straight pipe accounting for pressure loss, which is the same as that of the fitting.

On comparing the two equations, It could be seen that
A typical chart used for estimating Le values is given. 
As such in each branch K in the equation h_{f }= KQ^{n }depends on Le and Le in turn includes length of straight pipe as well as equivalent length of all fittings in the branch. (It may be noted that K in the equation h _{f }= KQ^{n }and K for fittings pressure drop are different. The nomenclature of K value for fittings is widely used and hence the same has been retained here).

Use of software tool for network analysis: 
Due to the nature of iterative calculations involved, network analysis is substantially aided by software tools. 
Some software tools are available under the proprietary names of Engineers Aide, Pipenet. (It is understood that use of pipenet for analysis of firewater distribution network is acceptable to TAC.)

Some of the important features and/or advantages of the software tools are seen as below:
 Preparation of network schematic diagram
 High speed of iternative calculations till desired convergence is achieved
 Quick assessment of effect of changes and modifications on flows through branches of network
 Facility of pipeline sizing for given flow
 Library of fluid properties
 Regression of data for H Q curve for the pump Library of K values (for pressure crop across fittings)
 Facility for computing friction factor (ff) for any Reynolds Number (Re) and using the same in the network analysis
 Network analysis under transient conditions and for pressure surges
 Analysis for flow through sprinklers
LR Bend  0.6  Non – Return Valve (open)  2.5 
U Bend  2.2  Gate Valve (open) Globe Valve (open)  0.19 10.00 
Some typical K value for friction head loss through fitting
Size  Swing Check Valve Full Open  Gate Valve Half Open  Globe Valve Full Open  L R Bend 
50 NB  4.0. m  9.1 m  15.1. m  1.0 m 
80 NB  6.1 m  15.2 m  24.4 m  1.8 m 
Some typical equivalent length (Le) for fittings
The flow in two different branches would get equally divided if resistance of both branches is the same. 
The resistance of a branch can be increased by introducing the restriction orifice. 
If flow through 124 and 134 are to be equal, K 134 = 7160, i.e. K 134 is to be increased by 5698 (7160  1462), equivalent to 3.561 mWC

Pressure drop across orifice plate is given by 
Hi,
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