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ENERGY LOSSES IN PIPELINES

ENERGY LOSSES IN PIPELINES. IDEAL FLOW BERNOULLI EQUATION ENERGY LOSSES DUE TO FRICTION ENERGY LOSSES DUE TO SHOCKS FLOW RATES IN PIPELINES. BERNOULLI EQUATION.

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ENERGY LOSSES IN PIPELINES

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  1. ENERGY LOSSES IN PIPELINES IDEAL FLOW BERNOULLI EQUATION ENERGY LOSSES DUE TO FRICTION ENERGY LOSSES DUE TO SHOCKS FLOW RATES IN PIPELINES KK's FLM 221: Week12: Energy losses

  2. BERNOULLI EQUATION • Bernoulli’s equation: Total fluid energy per unit mass remains constant in the system for ideal flow: (12.1) Meaning of terms: P/ρ – Flow energy (J/kg) of the fluid due to its pressure. v2/2 – Kinetic energy (J/kg) of the fluid due to its motion; v is the AVERAGE velocity of the fluid in the system. QUESTION: (What is the maximum particle velocity in lamina and turbulent flow?) gz – Potential energy (J/kg) of the fluid due to its position in the gravity field ET – Total energy of fluid (J) of mass m (kg) EXERCISE: (Rewrite the above equation for i) unit volume (J/m3 = N/m2) and ii) for unit weight (J/N = m)) (12.2) P2; v2; z2 FIGURE 12.1: BERNOULLI’S EQUATION P1; v1; z1 KK's FLM 221: Week12: Energy losses

  3. ENERGY LOSSES DUE TO FRICTION Equation 12.1 (or 12.2) does not hold when there is appreciable friction from viscosity effects. Viscosity causes energy losses which increase if: • Dynamic viscosity ‘µ’ increases • Length of pipeline ‘l’ increases • averagevelocity ‘v’ in pipeline increases • Diameter of pipe ‘d’ decreases The viscosity ‘µ’ affects the loss per unit mass through a friction factor ‘f ‘ which also depends on the roughness of the pipe. The Darcy equation for energy loss per unit weight (m) is given as: (12.3) EXERCISE: (For a given flow rate Q in a pipe of diameter d, what will be the energy loss? Hence what can you say to the friction energy loss if you halved the diameter of the pipe but kept the flow rate at its original value?) KK's FLM 221: Week12: Energy losses

  4. ENERGY LOSSES DUE TO FRICTION - Examples 15 m X 20 mm straight Hose pipe; f = 0.005 1)For the above gardening hose system, we try to find the discharge rate ate the instant shown. 2) What pump power is required for this job? Change diam. to 75 mm. What new pump power will be required? 3 m 27m3/hr flow rate required 1 km X 50 mm pipeline; f = 0.0025 20 m elevation difference Water pump KK's FLM 221: Week12: Energy losses

  5. ENERGY LOSSES DUE TO SHOCKS Fluid loses energy whenever there is an interruption in its flow pattern. This interruption occurs if: • Velocity changes e.g. on entry into pipe, or exit, or change of section • Fluid negotiates a bend • Fluid meets a valve, filter, strainer, dryer, coupling, etcetera The loss is complex but proportional to the kinetic energy. The proportionality constant is called the “LOSS COEFFICIENT” ‘K’. The tables shown give the various coefficients for different fittings. EQUIVALENT PIPE LENGTH: ‘le’ The additional pipe length that would give an equivalent frictional loss as the shock loss caused by the fitting: It is given by: (12.4) KK's FLM 221: Week12: Energy losses

  6. FLOW RATES IN PIPES • We determine the flow rates by applying the Bernoulli equation with losses accounted for as in the equation: (12.5) 2 1 KK's FLM 221: Week12: Energy losses

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