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Three Reservoir Problem

This document summarizes the results of solving a three reservoir pipe flow problem using Microsoft Excel Solver. The solver found a solution that satisfied all constraints and optimality conditions, solving in 0.047 seconds over 2 iterations. The flowrates in each of the three pipes were solved to be 0, with velocities of 0 m/s and no slack in the constraints. Additional documentation on the three reservoir problem equations is provided in a linked blog post.

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115 views5 pages

Three Reservoir Problem

This document summarizes the results of solving a three reservoir pipe flow problem using Microsoft Excel Solver. The solver found a solution that satisfied all constraints and optimality conditions, solving in 0.047 seconds over 2 iterations. The flowrates in each of the three pipes were solved to be 0, with velocities of 0 m/s and no slack in the constraints. Additional documentation on the three reservoir problem equations is provided in a linked blog post.

Uploaded by

prateek_bhoir
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as XLSX, PDF, TXT or read online on Scribd
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Microsoft Excel 14.0 Answer Report Worksheet: [ThreeReservoirProblem.xlsx]Sheet1 Report Created: 08/05/2011 12:48:15 PM Result: Solver found a solution.

All Constraints and optimality conditions are satisfied. Solver Engine Engine: GRG Nonlinear Solution Time: 0.047 Seconds. Iterations: 2 Subproblems: 0 Solver Options Max Time Unlimited, Iterations Unlimited, Precision 0.000001 Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Central Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative Objective Cell (Value Of) Cell Name $D$15 Velocity (m s-1) Pipe 3

Original Value Final Value -0.2571378 0

Variable Cells Cell Name $B$18 Flowrates Pipe 1 $C$18 Flowrates Pipe 2 $D$18 Flowrates Pipe 3

Original Value Final Value 3.04E-03 0.00E+00 -1.90E-03 0.00E+00 -1.14E-03 0.00E+00

Integer Contin Contin Contin

Constraints Cell Name $B$22 Restriction Q1+Q2+Q3= Pipe 1 $D$15 Velocity (m s-1) Pipe 3

Cell Value Formula 0.00E+00 $B$22=0 0 $D$15=0

Status Binding Binding

Slack 0 0

NonNegative

Microsoft Excel 14.0 Sensitivity Report Worksheet: [ThreeReservoirProblem.xlsx]Sheet1 Report Created: 08/05/2011 12:48:16 PM

Variable Cells Cell Name $B$18 Flowrates Pipe 1 $C$18 Flowrates Pipe 2 $D$18 Flowrates Pipe 3 Constraints Cell Name $B$22 Restriction Q1+Q2+Q3= Pipe 1 $D$15 Velocity (m s-1) Pipe 3 Final Lagrange Value Multiplier 0 0 0 0 Final Reduced Value Gradient 0 0 0 0 0 0

The Three Reservoir Problem


http://excelcalculations.blogspot.com Click here to discover how the equations were derived and for complete documentation

Liquid Properties
Viscosity (Pa s) Density (kg m )
-3

0.001 1000

Pipe 1
Reservoir Height (m) Roughness (m) Diameter (m) Length (m) Flowrates (m3 s-1) Area Velocity (m s-1) Reynolds Number Friction Factor Junction Head at Junction (m) External Demand (m s )
3 -1

Pipe 2
80 0.0005 0.05 600

Pipe 3
60 0.0005 0.075 700

120 0.0005 0.1 500

0.016465 -0.00092 -0.0055411 0.007854 0.001963 0.0044179 2.096441 0.470759 209644.1 23537.96 0.03084 0.040263 1.2542421 94068.159 0.0340184

Set initial guess values

85.45743 0.01

Set initial guess value Sum of flowrates in pipes (constraint)


-8.51E-07 2.68E-11

Errors in Bernoulli equation in each pipeline Errors -6.44E-07 5.06E-06

Total error (to be minimized)

Legend Parameters you specify Calculated values To be varied by Solver Constraint in Solver To be minimized by Solver

Solver Instructions
Minimize the Total Error by varying the Flowrates and the Head at Junction while maintaining the External Demand at 0.01 m3 s-1

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