# CH7 - Fluid Dynamics Application II Chapter 7 Internal Flow...

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1 Fluid Dynamics Application II Chapter 7 - Internal Flow Energy Conservation in Pipes (Laminar & Turbulent) 1 Modified Bernoulli Equation Including Energy Loss & Pump-Turbine System E cv , CV & CS ± Heat transfer rate, Q ± Work W=W s +W f Conservation of Energy - Review Flow work W f to push fluid in or out of a CV Shaft work W s done through shaft of pump or turbine 1 st law states 2 Energy Equation: W Q A d V e d e dt d CV CS & & = + ∫∫ ρ s CS cv W Q A d V u p gz V E dt d & & r = + + + + ) 2 ( 2

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2 Basic Energy Equation: Assumptions: Conservation of Energy - Derivation s CS cv W Q A d V u p gz V E dt d & & r = + + + + ρ ) 2 ( 2 1 Steady Flow: 0 = cv E d 1. 2. Shaft work from pump or turbine: 3. Incompressible: 4. Energy loss head (friction & HT): 5 One inlet & outlet dt ft) (m, g m W h h h or W W W s t p s t p s & & & & = = = m m m & & & = = ) ( ft m, g m Q g u u h out in L & & = c c = = γ , 3 5. One inlet & outlet: 6. Non-uniform flow: out in m p z g V A d V p gz V A & r ) 2 ( ) 2 ( 2 2 + + = + + α V V n Applicatio g Engineerin = = = = : Turbulent : Laminar , 1 : 05 . 1 ; 2 2 Also called Modified Bernoulli equation ± Energy losses & pump & turbine effects included Simplified General Energy Equation 2 2 2 1 2 1 1 2 2 z g V p z g V p + + = + + t p L h h h + ) 2 ( 4
3 Energy Loss – Preview (Chapter 10) There are two types of energy loss ± Friction or major loss caused by friction Due to viscosity & relative motion between fluid & solid object surface ± Minor loss caused by separation Due to a sudden change in flow direction or in velocity magnitude ± h L = Major loss + Minor loss Q & 5 g m g u u h out in L &

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CH7 - Fluid Dynamics Application II Chapter 7 Internal Flow...

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