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# CribSheet for CE 330 with Professor Parr at KU

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 38 views.

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Date Created: 02/06/15

Test 1 Equation Sheets Fall 09 Hydrostatics Composite Planes dp EZ V R F1 F2 p y I ycpJE ycp2F2 Z consl cpcompome E F2 7 y r39 xcpJE xcp2F2 pabsolute pgauge pazm 139 xcpycomposm E F2 Inclined Plane y F y y sin A r y Ix 1 2 Cp ch aycp x 1 I bh3 rect 12 h mm 62411 f 1 Ix gbhmnangle 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 s 2 speci c gravity 2 y water x see i ure op fg b2 ll b2 pwmr 19411 ff Horizontal Force g 322ftsec2 EC PcxAx plop equivalent Fy Pay1y Act through centers of pressure Vertical Force for body on tank bottom Vertical Force F F B PhotAbot yIdisplaced PhotAbot F2 2 yV where Acts through centroid of V PM 2 pressure at bottom of tank Bouyant F 0706 Am 2 area in contact with tank bottom F B yIdisplaced V Acts through centroid of Vd isplaced Continuity Eq d d G 1 dA dV Z z dV enem stpu dt 0pr onm me dt CfVJ d d C t td 39 39d odA dV gtZ Z dV ons an enszty ut CJu dtcj Q0 QM dt OJ Steady ow pu dT4 0 gt Zonu Zme ZIhm ZIhm 0 CS Steady ow constant density u 0 4 0 2Q ZQM CS Average velocity V QA1AJ 531 xxec Bernoulli Eq Along a streamline H 7 2 z 2g EnergyEq H1hp 2 H2 h h where 2 g z r 2g 550e horsepower H h constant 2 total head 550horsepower a t P 7Q hlosses hm V2 hf Z Kf friction loss 2g rQeff Z hm Z Km minor losses or local losses 2g Energy Grade Line EGL 2 Plot of total head H g z r 2g Hydraulic Grade Line HGL p V2 Plot of static head h z HGL EGL 2 7 g Test 2 Equation Sheet Fall 09 Continuity Equation For onedimensional ows Open Channel Flow Q lLabSA1 for vane series Q Vim11 for single vane st1 2 sm 02 2 sm 03 a b c A e d A e d E J E J IEnergy Equation CV CV For steady ow H1 Hz hlosxex A E where ZleA7 0 2 H z z E For steady ow with incompress ble bed y 2g bed fuids of constant density here w A E z z EVA 0291 sz E yVy Q 2 2g ZgA Bernoulli Equation Momentum Eq Along any stream line F M1 M2 H1 H2 7 where Where P V2 Q2 H z M YAig A 7 2g Geometry Energy Equation H1hFHZhthlosses 2 TorB Where A bygt bymy 550h0rsepowere 550horsepower T b zmy 21 hp ht 42 b m 7Q 792 PW b2y m 1 L V2 V2 7 by2 my hlasses hlaml hfrxctxan 2Klaml EJF 2Kfnctxang yA 7 1 Q2 1 cos I I I Q3 17 cos Won ofFlow S Momentum Equation Vanes Fn leVlsln Q o Freejets in and out 0 Velocity is tangent to the vane everywhere EEC ZMout KC 2M V36 0 Friction loses are neglected Q1 0 O 4 4 4 11 Va m2 Vr2a1ve ZFZMWV 2MmV H u y y0ut ym V2 V2 Q3 Power E 7Q Labs 2a 25 2M0 V2 ZMM V2 er 67 28 l Power 3 horsepower M pQ 0 194slugfl 550 2 2 2 a b c 2bccos 7ng 624lbfz3 1 Test 3 Equation Sheet Fall 09 Energy equation H1hp H2hth losses 2 SSOHP whereH ZVh 11 M 7 2g 9 losses f m p yQ t e yQ Darcy Weisbach equation for full owing circular pipes Moody Diagram r fLV2 8fL 2 V2 82K 2 ks lD ks 4Q h analh ZK gt f ng ngsQ m 2g ngoQ f V Dv Darcy Weisbach equation for non full owing circular pipes R A PW Moody Dagmm V2 fLPW V2 2K ks V 4R ks Q 4R f fL 3 Zanth 2K ZQZ gtff f 4R 2g 8gA 2g 2gA 4R 4R Av Parallel anal series arrangements for all pipes Let hm hf hm Q2 where 2 4 ZK for full owing circular pipes 7239 gD D anal 2 ZK for pipes that are not full owing circular pipes 2gA 4R Z gt M 52 n 11 1 1 parellel 2 gt parellel l Elk li l Uniform ow in open channels 149143 Q n PmSZZ SohfL Pipe networks H araly Cross method 2 2 Q 2 Q 22 Q522 QM Subract AQ from clockwise ows anal subtract from counter clockwise ows ows AQ Resistance coef cient 139 0100 0090 o 080 Complete turbulence rough pipes 0070 005 004 0060 003 0050 0m 0015 0040 001 g 0008 2f 0006 3 0030 2 0004 5 o 025 3 0002 E 0020 390001 00008 1 00006 00004 0015 00002 Smooth pipes 00001 0010 000005 0009 0008 000001 103 2 a 6 8104 2 a s 3105 2 4 e 8106 2 4 o 2107 2 4 6 8108 Re 390 OC Flow Equation Sheets Fall 09 Energy Equation HI H2 th 2 Hzbedy2 zbedE 2 2 E yyQ2 2g 2gA Critical ow general channels 2 FrlQl l gA A 2 E0 ye ye Q 2 2B6 2gAc A 2 E ye ye Q 213C ZgAc2 Critical ow rectangular channels only Q 6172 V 1 y b y Zgyz Z Z 2 Fr q3 V 1 ye q 1y5 E5 gy gy g 3 Momentum Eq M1 M2 E 7 Q2 where M yA gA Uniform ow Q Trapezoidal Channel A0 byg my PW7 b2ygxlm2l lFrz Ste Method ave p X2 X1 yz ylsosfnave ym 05y1y2 HQ 2 QZBM 149 A 1 S ave For a trapezoidal channel Am bym my BM b 2mm Pwm b Damm2 1 BorT E y 1 L blm Symmetrical Trapezoidal Channel Abymy2 BTb2my PW b2yxlm2l QZB 3 Flow Classi cation Fr Fr lt lsubcritical ow Fr 1 critical ow Fr gt 1 supercritical ow Slope Classi cation 2 B Fro Q 3 7 ll gAg y7 uniform depth y critical depth Fr0 gt ly7 lt y gt Steep Slope Fr0 ly7 y gt Critical Slope Fro lt ly7 gt y gtMilal Slope Flow from channel to culvert under inlet control 2 H1H2h gtzlE1 zZE2K 2 losses em 2g I yl VZ y2 y E1YZ 1Kent Zz39zl c V2 y Rectangular culverts 2 5 2g 2 39 Kent le E115Tyc zz zl V22 A Nonrectangular culverts 5 2g 235 Ac Ie E1 y2 1Kem2 Bcz2 zl Mild Slope to Steep Slope Step method calcs go upstream from ycfor mild slope downstream From yC for the steep slope yo2 Mild Slope 1 e Steep to Mild Channel M071 Speei e force for yo1 M072 Speei e force for yo2 yquot conjugate depth for yo1 y conjugate depth for yo2 Case 1 M071 2M02 Jump at slope break Case 2 M01 gt Mo 2 Jump goes downstream S 39 39 1 Case 2 M071 lt M072 Jump goes upstream

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