SERIES AND PARALLEL PIPES WITH SOLVER
Exercise: There are two reservoirs A and D, whose water bodies are located at levels +30 meters above sea level and +21 meters above sea level. Then we have the pipes AB, BC, BWC and CD whose characteristics are as indicated. We are asked to determine the circulating flow in each of the pipes.
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SOLUTION :
Step 01: Define the equations that allow the system to be
analyzed
Equations:
h1 + h2 + h4 = 9 m
h2=h3
Q1= Q2+Q3
Q1= Q4
Step 02: Assume the flows that circulate through pipe 1, 2, 3 and 4 in m3/s. (Cell range B16:B19)
Step 03: We determine the area for each of the pipes. (Range of cells F16:F19)
A=3.1416D^2/4
Step 04: We calculate the speed. (Cell range G16:G19)
V=Q/A
where: V=velocity in m/s
Q= flow
rate in m3/s
A= Area
in m2
Step 05: We calculate the Reynolds number. (Cell range
H16:H19)
Re = VD/visc
where: Re = Reynolds number
V=speed
in m/s
D=
diameter of the pipe in m
Kinematic
viscosity = 10^-6 m2/s
Step 06: We calculate the head loss in each pipe.
Darcy Weisbach hf = f L/D V^2/(2g)
where: f = Darcy's coefficient of friction
L= length
of the pipe in m
D= Pipe
diameter in m
k =
Absolute roughness of the pipe 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)
RHS=-2 log(K/(3.7*D) + 5.1286/Re^0.89)
f=1/RHS^2
- We calculate the RHS (Cell range I16:I19)
RHS=-2
log(K/(3.7*D) + 5.1286/Re^0.89)
- We calculate
the Darcy friction coefficient (cell range J16:J19)
f=1/RHS^2
- We calculate the pressure loss in each pipe. (K16:K19 cell range)
Darcy Weisbach hf = f L/D V^2/(2g)
Step 07: Define the conditions or restrictions.
h1 + h2 + h4 - 9 = 0
h2 - h3 = 0
Q1 - Q2 - Q3 = 0
Q1 - Q4 = 0
h2 - h3 = 0
Q1 - Q2 - Q3 = 0
Q1 - Q4 = 0
Step 08: Define the objective
The objective is the sum of all the conditions, which in
this case must be zero.
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RESULTS:
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