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Closed Conduit Flow

Closed Conduit Flow. General Energy Consideration. General Energy Consideration. The energy develop in the flow at any point is the sum of the position, pressure and velocity heads Bernoulli equation: h f = energy or head loss due to resistance.

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Closed Conduit Flow

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  1. Closed Conduit Flow

  2. General Energy Consideration

  3. General Energy Consideration • The energy develop in the flow at any point is the sum of the position, pressure and velocity heads • Bernoulli equation: hf = energy or head loss due to resistance

  4. Resistance Applications and Friction Losses in Pipe • Chezy Equation • Darcy – Weisbach equation f = Darcy friction factor • Compute energy losses due to resistance in most case of closed conduit flow

  5. Resistance Applications and Friction Losses in Pipe Laminar Flow in Pipes • Poiseuille equation • Can be rewritten as where is the Reynolds number of the flow

  6. Resistance Applications and Friction Losses in Pipe Turbulent Flow in Pipes • Turbulent Flow in Smooth Pipes • Friction factor, f • Turbulent flow in rough pipes • Transition Region

  7. Resistance Applications and Friction Losses in Pipe

  8. Empirical Resistance Equations • Blasius Equation generalizing where a and b are coefficient to be determined empirically. It was shown that the exponent b could be determined from where n is the exponent in the power velocity law. If Rn = 105 and n = 7, then b = -0.25

  9. Empirical Resistance Equations • Manning Equation

  10. Empirical Resistance Equations • Hazen – William Equation Where : R is the hydraulic radius of the pipe Sf is the slope of the energy grade line = friction slope CHW is the resistance coefficient related to pipe material

  11. Minor Losses in Pipes • Minor losses are normally expressed in units of velocity head, that is: • In term of the difference between the velocity head

  12. Minor Losses in Pipes

  13. Water Distribution System • Reservoir Problem

  14. Water Distribution System • Pipes in Parallel

  15. Water Distribution System • Pipe Networks

  16. Water Distribution System • Pipe Networks Assuming that the higher order terms are are much smaller than are the other terms and can be ignored,

  17. Example

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