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where!! ! hL!is!the!head!losses!due!to!friction![L]! ! f!is!an!empirical!friction!factor![Y]! ! L!is!the!length!of!the!tubing![L]! ! D!is!the!diameter!of!the!tubing![L]! ! V!is!the!average!fluid!velocity![L/t]!=!Q/A! ! Q!is!the!volumetric!flow!rate![L3/t]! ! A!is!the!crossYsectional!area!of!tubing![L2]!=!πD2/4! ! g!is!the!acceleration!due!to!gravity![L/t2]! ! Frictional!head!losses!are!proportional!to!fluid!velocity!and!tubing!length!and!inversely! proportional!to!tubing!diameter.!!The!friction!factor,!f,!is!a!function!of!the!Reynolds! number!and!can!be!calculated!using!the!Blasius!equation:!! ! ! ! ! ! f = 0.316 Re-0.25! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2)! ! where!Re!is!the!Reynolds!number! ! ! ! ! Re = ! DV υ !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (3)! and!ν!is!the!kinematic!viscosity!of!the!fluid![L2/t!].!! ! The!head!lift!and!length!of!tubing!required!at!each!of!the!six!Dead!Run!stations!is!shown! in!Table!3.!!We!calculated!the!frictional!head!losses!for!at!0˚C!and!30!˚C,!and!at!fullyY charged!and!lowYvoltage!conditions!for!both!pumps!(Appendix!A).!!! _______________________________________________! ! Table!3.!!Head!lift!and!tubing!length!at!each!station.! _______________________________________________! * Station!!!!!!!!Head*lift**********Tubing*length* * *******required* ********required* * * * (ft)!! ! ! (ft)! DRKR!! ! 9.0!! ! ! 21! DR1! ! 9.8!! ! ! 18! DR2!! ! 8.0!! ! ! 45! DR3!! !! 7.3!! ! ! 19! DR4! ! 7.4!! ! ! 36! DR5! ! 9.2!! ! ! 26! ________________________________________________! 7! !
