CLOSED NETWORK OF A CIRCUIT WITH THE EXCEL SOLVER TOOL

 CLOSED NETWORK OF A CIRCUIT WITH THE EXCEL SOLVER TOOL

Example: The figure shows the project of the pipe system to fight fires in an industrial facility. At points 1,2,3 and 4 it is required to install hydrants to supply costs of 15,30,60 and 15 lt/s respectively. Determine the expense in the system tubes. (Use the Hazen-Williams formula, CH=95).

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Solution :

QT= 15+30+60+15 = 120 l/s

Step 01: Assume the flows that circulate through pipe a, b, c, and d in l/s.

Step 02: We convert the flow rate to m3/s by dividing by 1000.

Step 03: We determine the area for each of the pipes 

A=3.1416D^2/4

Step 04: We calculate the slope

S=(Q /( 0.2784 C D^2.63) )^(1/0.54)

Step 05: We calculate the pressure loss in each pipe

h=S*L

Step 06:Define the equations.

Equations:

ha+hb=hc+hd

QT=Qa+Qc+15

Qa=Qb+30

Qc=Qd+15

Qb+Qd=60

Step 07: Define the conditions or restrictions.

ha+hb-hc-hd = 0

QT-Qa-Qc-15 = 0

Qa-Qb-30 = 0

Qc-Qd-15 = 0

Qb+Qd-60 = 0

Step 08: Define the objective

The objective is the sum of all the conditions, which in this case is zero.

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