Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 17 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 50 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 14 Conservation of Mass and Linear Momentum Additional Problems Problem 1 Water flows in and out of the device as shown in the figure below Calculate the rate of change of the mass of water dmdt in the device Q 03 ft3sec VI 30 ftsec 3 1522 03 slugsec Control volume Problem 1 Solution D33 8 QB Dty Z pOUtAoutvoutbout ZIOWAmvmbm 0 B 2 mb b1f0r massBm Dm dm 3952 4 Av Av0 Dt Zpout out out 2pm m m dm 0Ep1A1V1m203 J3 dm 52 E l zlxwx gtlt3003194gtlt03 dm slugs Linear Momentum Equation 210Asz ulpAlVl Z Fx Time rate of change of V2914sz leAlVl Z Fy the linear momentum of the system sum of V Mivj external forces acting m1 9711141 on the system m2 pu2A2 m a 2F 2 m2u2m1u1ZFx 1 V TV m2V2 m1v1 ZFy Pressure Forces in the Momentum Equation FR F R W P mm P1 Parm P gage With atmospheric With atmospheric pressure considered pressure cancelled out Problem 2 A 3 in diameter horizontal water jet having a veloc ity of 140 fts strikes a curved plate which de ects the water 1800 at the same speed Ignoring the frictional effects deter mine the force required to hold the plate against the water stream Water J t 39 140 fts 4 140 ftS gt 1w Solution density of water 624 lbmft3 m pVA 0V7rD2 4 194 slugsft3140 fts7r312 ft2 4 1333 slugss Z ZmV me out in 1 1b F 2 1333 slu 88 140 ftS 37324 1b Rx g slugftszj Discussion Note that a negative value for FRX indicates the assumed direction is wrong as expected and should be reversed Also there is no need for an analysis in the vertical direction since the fluid streams are horizontal 140 fts Problem 3 A 3indiarneter horizontal jet of water with veloc ity 140 fts strikes a bent plate which de ects the water by 1350 from its original direction How much force is required to hold the plate against the water stream and What is its direction Disregard frictional and gravitational effects 135 F 1 Solution 3Tr Waterjet m pVA 0VL7ID2 41 94 slugsft3140 fts7r3 14 ft2 4 1333 slugss Fm COS 45 m V1 COS 45 FR sin 450 mV Sin 45 2 FRx 21333 slugss140 fts1 cos45 2 63716 1b slugfts FRZ 1333 slugss140 ftssin45 13196 1b s lugft s F FR JFI X 17 J 63712 13192 6506b taan39lF Mztan39l 1319 117 1683 2168 Rx 6371 Problem 4 Choice of CV Fire ghters are holding a nozzle at the end of n hcse while tiying to extinguish a re If the nozzle exit diameter is 6 cm and the water ow rate is 5 mVmin determine u the average water exit velocity and b the horizontal resistance force required of the re ghters to hold the nozzle How to choose the control volume The choice of the control volume CV is very important Sometimes we can choose the CV to simplify our calculations For this problem let us choose the CV such that water enters the CV vertically and exits horizontally this way the pressure force and the momentum flux at the inlet are in the vertical direction with no contribution to the force balance in the horizontal direction Solution FRZ F X f 3 2 Q SUImm 1768rnmin295mS A 7zD2 4 7z006 m24 m pQ 1000 kgm35 m3min 5000 kgmin 833 kgs FRx mVe 0 141V 833 ks 295 ms 2457 N 2 2460 N 1 1kgm52 Discussion The force of 2460 N is equivalent to the weight of about 250 kg That is holding the nozzle requires the strength of holding a weight of 250 kg which cannot be done by a single person This demonstrates why several firemen are used to hold a hose with a high flow rate A converging elbow see Fi turns water through an angle of 135 in a vertical plane The ow cross section diameter is mm a Ihe elbow inlet section 1 and 200 mm at the elbow outlet section 2 The elbow ow passage volume is 02 mquot be The water volume owr is 04 mls and the elbow inlet and outlet pressures are 150 kPa and 90 kl a The elbow mass is 12 kg Calculate the horizontal x direction and vertical 1 direciion Problem 519 anchonng forces required to hold the elbow in place D2 200 mm Problem 519 solution ullaulAl Vlm lrbIl L EA F p Alla iquot Frdm canrermfam of mu M m4 f W04 0 llIIIIIIIIlllllllllllllllll z 1 s 400 mm 0 JM T i F W I I I 1 Wr Thu F A p Alx I Nix 1 1 1 Mfr gmlS FA pl1x 05 7529 yawn19351111an x A Al 39 39 7 7rp quotI i 2 mm 1 7 39D 71 h 04 m3 l MW T 0545100 I N 39 5 21 mm quotf 1 1 2 zaomn 5 won 1 3 50 UPWM aw Mm 0059 64 was 11 m z 700 N ppjcn ln a 1 may a z miceion Lemme 14 Age mama um eggion Edds In 41501 1 fig11 41914 iii Vi HQ wlu39cA wllm canAlma w4A E1 gIe 1 I 1 n p a pawn5 y539WW ZrAm 17 gt45 1 3 A 5z In w a Fig 4 51 7 a i 1 F 97 3 fgi a N A 3 s aquot 62 W f a vgzoommq539 2 Mama I y 0 ffmam In W KamaI132 6z y glg i N M SI IJ 2 3520 17 n Problem A constant velocity horizontal water jet from a sta tionary nozzle impinges normally on a vertical at plate that is held in a nearly frictionless track As the water jet hits the plate it begins to move due to the water force Will the accel eration of the plate remain constant or change Explain gt Nozzle gt KWater jet 0 G