SERIES AND PARALLEL PIPES WITH SOLVER

 SERIES AND PARALLEL PIPES WITH SOLVER

Exercise: In the conduction system shown in the adjacent figure, there are two reservoirs joined by a system of 8 ductile iron pipes with some years of use (C=130). Calculate the flow rate that reaches the lower reservoir.

Pipeline L (m) D (m) C (HW)

    1         580         0.61             130

    2         320         0.61             130

    3         260         0.46             130

    4         260         0.31             130

    5         260         0.46             130

    6         465         0.76             130

    7         510         0.61             130

    8         510         0.46             130

Solution :

 Excel template write to iyoba14@hotmail.com

Step 01: Assume the flows that circulate through pipe 1, 2, 3, 4, 5, 6, 7 and 8 in m3/s. (Cell range B56:B63)

Step 02: We determine the area for each of the pipes. (Cell range E56:E63)

A=3.1416D^2/4

Step 03: We calculate the S^0.54. (Range of cells G56:G63)

From the Hazen and Williams equation

 Q = 0.2784 C D^2.63 S^0.54

 S^0.54=Q /( 0.2784 C D^2.63) 

Step 04: We calculate the slope. (Cell range H56:H63)

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

Step 05: We calculate the pressure loss in each pipe. (Cell range I56:I63)

h=S*L

Step 08: Define the objective 

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

Step 09: We go to the Data - solver tab and the following window opens.

Step 10: We place the objective, the cells that will change to meet the objective and the conditions or restrictions explained above in the window.

Step 11: We observe that all the given conditions or restrictions are being met and therefore the objective is zero. Our answer is that the flow that reaches the low reservoir, which is the flow that circulates in pipe 6 is 1.719 m3/s.

Step 12: We observe all the flows that circulate through each pipe in m3/s.

 Excel template write to iyoba14@hotmail.com

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