Question

College of Engineering and Computing Department of Civil and Environmental Engineering CWR3201 -Fluid Mechanics Problem 1: Water at 20°C flows at a velocity of 2.4 m/s in a 250-mm diameter horizontal cast iron pipe (e 0.25 mm). Use kinematic viscosity for water 1.004 10 m'/s and estimate a. The change in pressure over 100 m of pipeline b. The change in pressure over 100 m of pipeline if the pipeline were not horizontal but 1-m lower at the downstream section

Answer 1

ge-i velo ahy of elow 2.4 mls diameter op pipe =0 mM O 5m (3) auo Kinematic visCosity .004x lo mle The charge in paessue over loom of pipeine Decrease in polegsuye = friction logs Zn pipe, it Lenolds number lek Hhan 200 it i faninar Flow, Ie Renold' omber moše than 4000 I- 8 tormbulent elucw. Re (Renola's hunmten)= l.004x 106 597609.56 > 4000 (80 it ig turbu lent t erichion From Darcy' g we have, head loas due to CApation as, 29d here, darcy friction actor. 64 .tor tuibulent flow For laminaN elou,p Moody diagra m. determined

hge2 -> ReLative pi pe vaughnes lo-3 Por Relative Pipe Youghn ess = lo3 or o.00l and - Yenald's nomber o. 6x lo6 have rickin we Pava e Pom Moody's agram ag change in preuuye Logs af head due te triction 214 O 02 x bo x 2 9.81X025 2 3486 m . TP Pipe isNot hoštzontal but Im lo Wer at e dousns team Secion change in pregsore head ogs dae to fricton t clange n elexation vesign ie dexation a ol piee end more Han Pipe orgin and ve' sign it elevakion of pipe Ona les

Page-3 Hhan Oigin o pipe Change in pressure = 2.3486 m- m 3486m deseas Cate: Due to fgichion, alwayg pressore of flou lsges but dve to elevation change it my be pyessure in Creafes oV pressuxe decreages decseases, 'e elevation incxeas by aa head of change devatior, it elexakion an amounh o& by de xea e3 (ncreaseg Preasure change in head .

-> Note:

In case a: due to friction, pressure head always decreases so change in pressure is head loss due to fiction.

In case b:

if elevation decreases then pressure increases by an amount of change in elevation. So in this case: change in pressure= friction loss - elevation difference.

Let p is Inifial presore in TO undlexstand his, Case Peinas e - eriin (oss final So, Change in ressure (r-exiion ss - evicHisn loss h case Pcinal P- tyictisn lasS + presuje gin due to elexation Sor Ghange in Pseuie= -Peinal P (P-xichion (ass + preuure gun due to P elovalion due to pnessure an lectinn Fxichion loss