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NETWORK OF PIPES

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني       05/10/2012 16:35:59
Complex connections of pipes are used in city water supply as well as in industrial systems. Some of these are discussed in the para.

Pipes in Series—Electrical Analogy
Series flow problem can also be solved by use of resistance network. Consider equation For given pipe specification the equation can be simplified as

hf = 8 f L Q2/?2g D5 = R Q2
Note: The dimension for R is s2/m5. For flow in series Q is the same through all pipes. This leads to the relation

hf1 + hf2 + hf3 + ......... hfn = hf = (R1 + R2 + R3 + .... + Rn) Q2

The R values for the pipe can be calculated. As the total head is also known Q can be evaluated. The length L should include minor losses in terms of equivalent lengths.

Pipes in Parallel
Case (i) The head drop between locations 1 and 2 are specified: The total flow can be determined using

hf=8 f1 L1 Q12 /g D5?2= 8 f1 L1 Q12 /g D5?2

As hf and all other details except flow rates Q1, Q2 and Q3 are specified, these flow rates can be determined.

Total flow Q = Q1 + Q2

The process can be extended to any number of connections.
Case (ii) Total flow and pipe details specified. One of the methods uses the following steps:
1. Assume by proper judgment the flow rate in pipe 1 as Q1.
2. Determine the frictional loss.
3. Using the value find Q2 and Q3.
4. Divide the total Q in the proportion Q1 : Q2 : Q3 to obtain the actual flow rates. Case (iii) Electrical analogy
Branching Pipes
The simplest case is a three reservoir system interconnected by three pipes The conditions to be satisfied are (i) The net flow at any junction should be zero due to continuity principle. (ii) The Darcy-Weisbach equation should be satisfied for each pipe. If flows are Q1, Q2, Q3 , then the algebraic sum of Q1 + Q2 + Q3 = 0. If one of the flow rate is specified the solution is direct. If none are specified, trial solution becomes necessary.
The flow may be from the higher reservoir to the others or it may be from both high level reservoirs to the low level one. The hydraulic grade line controls the situation. If the head at the junction is above both the lower reservoirs, both of these will receive the flow. If the head at the junction is below the middle one, the total flow will be received by the lowest level
reservoir.


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