flows in piping systemssyahruls/resources/skmm-4343/2-pipe-system.pdf · 11.4 analysis of pipe...
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Flows in Piping Systems
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From delivering potable water to transporting chemicals and other industrial liquids, engineers have designed and constructed untold kilometers of relatively large-scale piping systems.
Elements: Reaches of constant-diameter piping.
Components: Valves, tees, bends, reducers, or any other device that creates a loss to the system.
11.1 Introduction
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Frictional Losses in Pipe Elements
Frictional losses in piping are commonly evaluated using the Darcy–Weisbach or Hazen–Williams equation. The Darcy–Weisbach formulation provides a more accurate estimation.
11.2 Losses in Piping Systems
11.2 Losses in Piping Systems
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This R is the resistance coefficient, not the hydraulic radius.
11.2 Losses in Piping Systems
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11.2 Losses in Piping Systems
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11.2 Losses in Piping Systems
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11.2 Losses in Piping Systems
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11.2 Losses in Piping Systems
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11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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Parallel Piping
11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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Branch Piping
11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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11.3 Simple Pipe Systems
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11.4 Analysis of Pipe Networks
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The system equations are given as follows:1. Energy balance for each pipe:
2. Continuity balance for each interior node:
3. Approximation of pump curve:
11.4 Analysis of Pipe Networks
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Generalized Network Equations1. Continuity at the jth interior node:
2. Energy balance around an interior loop:
3. Energy balance along a unique path or pseudoloopconnecting two fixed-grade nodes:
11.4 Analysis of Pipe Networks
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Linearization of System Energy Equations
Complex pipe systems require special techniques to solve for discharges and piezometric heads. One of them is the Hardy Cross method of solution.
11.4 Analysis of Pipe Networks
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Hardy Cross Method
11.4 Analysis of Pipe Networks
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11.4 Analysis of Pipe Networks
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11.4 Analysis of Pipe Networks
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11.4 Analysis of Pipe Networks
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11.4 Analysis of Pipe Networks
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Incompressible Flow in an Inelastic PipeUnsteady, or transient flows in pipelines traditionally have been associated with hydropower piping and with long water and oil pipeline delivery systems.
For unsteady flow to occur in piping, an excitation to the system is required (e.g., sudden closure of a valve).
The velocity does not vary with position, only with time.
11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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Compressible Flow in an Elastic PipeWater hammer is accompanied by pressure and velocity perturbations that travel at high velocities.
11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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Joukowsky equation: Relates the pressure change to the pressure wave speed and the change in velocity.
11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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11.5 Unsteady Flow in Pipelines
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A methodology for dealing with losses in piping has been provided in Section 11.2 using the resistance coefficient as a generalized term that can include minor losses along with a chosen empirical friction loss.
For more complex piping networks, a systematic solution approach has been presented in Section 11.4.
Finally, analysis of unsteady flows in pipes has been introduced in Section 11.5. We have focused on flow that behaves either in an incompressible or compressible manner; the latter behavior is commonly called “water hammer.”
11.6 Summary