CLOSED NETWORK OF TWO CIRCUITS SOLVED WITH EXCEL SOLVER

 

CLOSED NETWORK OF TWO CIRCUITS SOLVED WITH EXCEL SOLVER 

Exercise : In the closed network shown in the figure, we are asked to calculate the flow rate in each of the pipes, if the flow rate coming out of the dam is Q12 = 90 l/sec. In each intake (3, 4, 5) the flow must be 30 l/sec, the pipes are made of new steel, without seams.

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SOLUTION :

Step 01:Define the equations that allow the system to be analyzed

Q1-2=QT= 90 lt/s (fact)

Equations:

hd+he=hb

ha + hb = hc

90=Qa+Qc

Qa=Qb+Qd+30

Qc+Qb+Qe=30

Qd=30+Qe

Step 02: Assume the flows that circulate through pipe a, b, c, d and e in l/s, complying with the continuity equation. That is, the flows entering the node are equal to the flows leaving the node.

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

A=3.1416D^2/4

Step 04 : We calculate the speed.

V=Q/A
donde : V=speed in m/s
             Q= caudal en m3/s 
              A= Area en m2

Step 05: We calculate the Reynolds number.

Re = VD/visc

donde : Re = Reynolds number
             V=speed in m/s
             D= pipe diameter in m

            visc = Kinematic viscosity

Step 06: We calculate the head loss in each pipe.

donde : f = Darcy friction coefficient

             L= pipe length in m

             D= Pipe diameter in m

             k = Absolute pipe roughness in m

Darcy's coefficient of friction f: we are going to calculate it with Barr's formula

1/raiz(f) = -2 log(K/(3.7*D) + 5.1286/Re^0.89)

    - We calculate the RHS

        RHS=-2 log(K/(3.7*D) + 5.1286/Re^0.89)

     - We calculate the Darcy coefficient of friction  ha+hb-hc=0

hd+he-hb=0
90-Qa-Qc=0
Qa-Qb-Qd-30=0
Qc+Qb+Qe-30
Qd-30-Qe=0

RESULTS:

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