In order to ensure a head loss of 7.95 m in this equivalent pipe also, the length of this pipe should be, of300 mm and a discharge of 116 l/s, the rate of loss of head per 1000 m is found from nomogram as 15 m. Now, for this equivalent pipe having a dia. Therefore, the circuits ABC and ADC can be replaced by an equivalent pipe carrying a total discharge of 60 + 56 = 116 l/s. 4.25 m per 1000 m) will occur only if the discharge is 56 l/s (from Hazen-WilliamвЂ™s monogram).

The rate of loss of head per 1000 m will be, Hence, if a loss of head of 7.95 m is to occur via route ADC also (i.e., 300 mm dia pipe of 1865 m length) Moreover, the loss of head via both the routes should be the same, provided that the flows are properly divided. Similarly, length of 300 mm dia pipe required for replacing route ADC, Length of 300 dia pipe required for replacing route ABC, pipe offers a head loss of 4.5 m per 1000 m length. pipes each, then the length of each pipe required can be obtained from the fact that a 300 mm dia. Now, if the routes ABC and ADC are replaced by 300 mm. Using Hazen-WilliamвЂ™s nomogram, the head losses into the two circuits will be, 20.9.ДЄs a flow of 60 1/s be assumed to be flowing through the routes ABC and ADC. 20.9 by equivalent pipe method using Hazen-William s formula.ДЄs Loop ABCD represents a pipe circuit with the pipe sizes and lengths, as indicated in fig. Solve the following problem as illustrated in fig. The use of this method can be under stood with the help of example illustrated below: (ii) The quantity of discharge flowing through the different pipes connected in parallel will be such as to cause equal head loss through each pipe. (i) The loss of head caused by a given flow of water through the pipes connected in series, is additive. In this method, pipe circuit can be reduced into a single equivalent pipe of using the following two principles of hydraulics: This method is sometimes used as an aid in solving large networks of pipes, in which it becomes convenient to first of all, replace the different small loops by single equivalent pipes having the same head loss.

These flows are marked on the given pipe network in fig.

Hence, corrected flows after second correction, are: These discharges are now again used to re-analyse both the loops for the second correction in Table 20.6. Now, both the loops are analysed for Hardy Cross method procedure in Table 20.5. The analysis of the pipe loops will require computation of head loss (H2) in each pipe, which is to be computed by HazenвЂ™s WilliamвЂ™s formula as below:ДЇor all the pipes of both the loops, we first compute values of k, as given in Table 20.4 below: The two closed loops i.e., ABCDA and DCFED are then analysed by Hardy-cross method. Compute the corrected flows after two corrections.ДЇirst of all, the magnitudes as well as the directions of the possible flows in each pipe are assumed keeping in consideration the law of continuity at each junction (i.e., input equals the output at each junction). Make use of Hardy-cross method with Hazen-WilliamвЂ™s formula. The diameters and the lengths of the pipes used are given against each pipe. The correction is small and hence the assumed diameters of the pipes are O.K.Д¬alculate the head losses and the corrected flows in the various pipes of a distribution network shown in fig. Using Hardy Cross equation, and table 20.3, The pipe diameters are now chosen by common sense as shown in Fig. In case of network of pipes having many loops, the system must be divided into two or more loops, such that each pipe in the network is included in the circuit of one loop. The minor losses are usually neglected, although they can be calculated by substituting an equivalent length of pipe. The value of x is taken 1.85 (as per Hazen Williams formula) in this method known as Hardy Cross Method. As a common practice + ve sign is given to the head losses in clockwise direction and вЂ“ ve signs to those in the anti-clockwise direction. In this equation the numerator is obtained by the algebraic sum of the head losses in the various pipes of the closed loop. If the head loss in the pipe under reference is H t, it can be determined by the formula Now if Q a be the assumed flow in a pipe and Q be the actual flow in that pipe, then correction will be given by the relation The successive corrections are made in the flows in each pipe until the heads are balanced and the principle of continuity is satisfied at each junction. The head loss in each pipe is determined by pipe flow formula. In this method, the corrections are applied to the assumed flow in each successive trial. The following points highlight the top two methods used for the analysis of flow in a pipe network.

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