Supplementary Material, Appendix 0 – A0.49

APPENDIX 0 – Pre-requisite: Steady State Hydraulics

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Surge Analysis and the Wave Plan Method

Supplementary Material: Example Problems and Solutions

Appendix 0 – Problem 49

A0.49 Consider the classical three-reservoir problem as shown in the following.

Length, diameter, and Hazen-William roughness coefficient of the pipeline are:

  •  From A to J are 200m, 500 mm, and 100
  • From J to B are 2000m, 500 mm, and 100
  • From J to C are 400m, 200 mm, and 140

Hydraulic grades at reservoirs A, B, and C are 200m, 180m, and 185m, respectively. Compute steady state flowrates in all three pipelines neglecting minor losses.

Solution:

Assuming that the flow takes place from reservoir A to junction node J, and from there to reservoirs B and C, there are three unknown flowrates: QAJ, QJB, and QJC. We need to setup 3 non-redundant equations to solve for these three unknown flowrates.

Eq. 1.   Energy equation between reservoirs A and B:

EA – ΔHAJ – ΔHJB = EB

Eq.2.   Energy equation between reservoirs A and C:

EB – ΔHAJ – ΔHJC = EC

Eq. 3.   Continuity equation at junction J:

QAJ = QJB + QJC

Substituting the appropriate Hazen-William expressions for ΔH terms:

EA – (10.67 LAJ QAJ1.852)/(CAJ1.852 DAJ4.87) – (10.67 LJB QJB1.852)/(CJB1.852 DJB4.87) = EB

EA – (10.67 LAJ QAJ1.852)/(CAJ1.852 DAJ4.87) – (10.67 LJC QJC1.852)/(CJC1.852 DJC4.87) = EC

QAJ = QJB + QJC

The only unknowns in the above 3 equations are QAJ, QJB, and QJC.

Solve these equations iteratively to obtain:  QAJ = 0.433, QJB = 0.346, and QJC =0.087 m3/s.


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