Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 19 page Class Notes was uploaded by Jolie Shields on Saturday September 19, 2015. The Class Notes belongs to CE 321 at Michigan State University taught by Roger Wallace in Fall. Since its upload, it has received 52 views. For similar materials see /class/207369/ce-321-michigan-state-university in Civil Engineering at Michigan State University.
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Date Created: 09/19/15
Lecture 18 Energy Equation 3 Kinetic Energy Correction Factors The average flow velocity Vavg was defined such that the quantity pVang gives us the actual mass flow rate Therefore there is no such thing as a correction factor for mass flow rate However the kinetic energy of a fluid obtained from VJ2 is NOT the same as the kinetic energy of the fluid stream since the square of a sum is not equal to the sum of the squares of its components see the next two slides since velocity is a vector and has 3 components in general This is the basis for the Kinetic energy correction factor Kinetic Energy Correction Factors Are needed to take into account the nonuniform flow across the crosssection Important for laminar flows Most flows are turbulent correction factor unity approximately Kinetic Energy Correction Factor A llTr lg Determination of quota kinetic energy 39 quot correction factor using the actual velocity V 31 m Hm distribution Vr and 39IIFJQ quotrv l 39 l was I quot L the average VGIOCItyVavg at a crosssection KER Jliuz rii L 1 quot l4i 3ftr1lquot391l will 1 l 3393 J Actual f A1 4339 J A HEW iii INA Based on average velocity Hrs 1 Hm LI w H A A sakfng mfg Energy Equation with Kinetic Energy Correction Factor Pl ct39JTl 1 Lf l 1 4 lJlJ P pump 1 I at 2 nturbinem L sh 39 quot H t The suffix u for the pump head denotes useful head delivered TO the fluid by the pump The suffix e for the turbine head denotes the extracted head removed FROM the fluid by the turbine Mechanical Energy The mechanical ew c a cums fmm At 7 mech mec h P P1 p w P 2 p 2 Vi V 7 37quot7 7 In the absence of of losses the mechanical energy change represents the mechanical work supplied to the fluid gt0 or extracted from the fluid lt0 The maximum ideal power generated by a turbine for example us I mach 39 1139 mt Mechanical Efficiency of a Device Pump or Turbine Mechanical energy output Emucmquot Elmmw 7 cl 7 39quotL Mechanical energy 111le1 E E IHCDIL in meelL in Pump or Turbine Efficiency h lechnnicnl energv increaw of the uid AEmmnmd W mm W 7 7 p 1 npump 7 i 39 Mulmmml snug lllpllf ii hm5m H pmnp Mechanical energy uulpul mum Wmmme Wlurhme Mcclmmcal energy nlcureasc 01 lhe uul HEW mudi H 1mm 1 Motor and Generator A pump is generally packaged together with its motor and a turbine with its generator The mechanical efficiency should not be confused with the motor efficiency and the generator efficiency next slide Motor and Generator Efficiencies in mechanical ef ciency Iioulxl nnl be con ned will lhc Ill 39hr rf cimr and lllc gmmmlnr ci ciuuc which are de ned us i Medium mwr uuipul 7 ii imi m Inmr umquot v Eiscinr pmh39l mle u M m and El pouer mupui 39 m m ummim awnquot gt NR ml pimer inpul u M H 17mm 075 quotgamma 097 w um uni mmmm rimmugemm o 75 x 0 07 073 Overall Efficiency We are ienerall interested in the combined or the overall efficienc of the pumpmotor and the turbinegenerator combinations This leads to some more definitions of efficiency npump motor 77 pump motor nturbme generator 77 turbine 77 generator I P V 7 57 meup p 7 53912 39mrbinc quotmecths 1 P1 1 Pl V P 2 V 39 39 m T T gzl Wpump 1 7 T 22 Wlm39hine Emech loss 1 2 HWWJM Wm Wm WWW hww 7 P M is me use911 head delivered mg m the uid by fhz plqnp Because urnreversible losses in the pump hm quot is 1m llmn WWWmg by he mm 71W 7 WWW 7 7 WWW 39 hmmW 7 7 5 WE Vuutunemg in he flum the uid by my turbine BcguuscoriImvc bl In L lurbinc hmhmc I is grcalcr hull erbmrhg by lhc lucmr nmbm 9mm m piping Emerh mas piping 11L llmll rcwrslble V 5 In I and 2 LINE In all componenlsol llm piping syslcm other him the pump or lurbilm Problem 1 1 s oluuon The pressures across the pump are measured The mechanical el cienc ofthe um is to be determined Assumptions 1 Flow is steady and incompressible 2 2122 elevation difference is negligible 3 V1V2 since diameters are the same KE correction fac ors are equal to 1 for both inlet and outlet turbulent flow Frupelties We take the density of water to be 1 kyL 1000 kgm3 an speci c heat to be 418 k g Analysis a The mass flow rate or water through the pump is m 0 1 kgL50 Us so kgs The motor draws 15 f power and is 90 percent efficient Thus mechanical shaft power it delivers to the bu s 5 52 The turbine Shawn in Fig P5 52 deve eps 100 hp when the ewrate of water is 20 figS If all leases are negligible determine a the elevation It b the pressure difference across the turbine and e the ewrate expected if the turbine were removed 51h wnern Volume A and W77 e3 Ma a 957 A gal v f a 1 J J 39 I r a 2 1 13 fad576 For a 39Ah fnaJ hr J and 79 5 5 58 we 767 55 fin6 09 5F a s I 64 761 Ar Wie f r 7Q 62 g r Siam Q 4lwe luge 7 93 143 209 it 295 4 271 7r 392quot Wequot 14 Brit 7 221 39zl zzl39l h5 2539 q439lff 27 23221L