What is Uniform flow (normal flow)? Uniform flow means that depth (and velocity) remain constant over a certain reach of the channel.
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1 Hydraulic Lecture # CWR 4 age () Lecture # Outlie: Uiform flow i rectagular cael (age 7-7) Review for tet Aoucemet: Wat i Uiform flow (ormal flow)? Uiform flow mea tat det (ad velocity) remai cotat over a certai reac of te cael. Wat are te tree loe i a oe cael? Cael loe, Water urface, w (loe of HGL) Eergy loe, (loe of EGL) For uiform flow, w. frictio reitace force gravity drivig force
2 Hydraulic Lecture # CWR 4 age () For a give dicarge i a cael, tere i oe ad oly oe uiform or ormal det. Wat formula (equatio) are ued for relatioi betwee dicarge ad det for uiform flow? Cezy: C R R ; W CCezy coefficiet C A AArea of flow Maig: m AR ( ) R.49 ( f) R.49 AR Maig rouge coefficiet A g f ffrictio factor form te Moody iagram (I Uit) (I Uit) (Egli uit) (Egli uit) Wy i ormal det imortat? If a cael i log eoug, you wat to deig a cro-ectio to adle uiform flow. Tyical cro ectio we eed to adle i oe cael flow: rectagular, traezoidal, circular, ad comlex.
3 Hydraulic Lecture # CWR 4 age () Two tye of roblem:. Give dicarge, etimate ormal det (deig cro-ectio).. Give ormal det, etimate dicarge (rectagular cael calculate area, ydraulic radiu, ad relace i equatio.) Examle of tye : A rectagular cael o a. loe i cotructed of fiied cocrete ad i wide. Wat i te dicarge if water i dee? fiied cocrete. (table 4-, age 6) A 4 ft A 4 R. ft W cf..49 Tye : Give, etimate y. AR, AR i a oliear fuctio of y, o ome iteratio or ue of ecial gra i required. Examle of tye : A rectagular cael o a. loe i cotructed of fiied cocrete ad i wide. Wat i te det of flow if te dicarge i 7 cf?.49 AR A y y R y.49 y 7. y ( y ) (.) y ( y). (oliear) Aume: y ; LH.6<. y4 ; LH.7<. y ; LH.. olve for y, aume ya, calculate LH ad comare to RH. (ti i difficult to olve)
4 Hydraulic Lecture # CWR 4 age (4) A alterative aroac i to ue te curve o age 6 for a rectagular cro ectio. AR O te x-axi, we ave. b O te y-axi, we ave y/b (b i te widt of te cael).49 AR, we fid tat AR AR b.49.49b Procedure: Calculate te RH ad eter te x-axi of Figure 4-7 util you it z, move orizotally ad get y/b. Let u do tat b.49. Go to te rectagular area, y/b.6; y.6* Exam Review: Ay quetio about te midterm exam? Wat ould you exect? Te tet will require our. Problem will be imilar (era ligtly more difficult) ta wat you ould exect o te PE exam. Place ome reure o you (it i good for you). o t give u. Te fial grade for cla deed o my imreio about te cla (o relatio to difficulty i tet) Proortioal to effort ow i cla Wat do you like? difficult (callegig) eay Problem - Wat i te role of te ozzle? (Igore mior loe) A ozzel ozzel A ie ie A ozzle i maller iger velocity or iger kietic eergy ead You ca ue a ozzle o te oe we you are irrigatig te law to icreae velocity ead.
5 Hydraulic Lecture # CWR 4 age () Eergy equatio from urface to ozzle: z z L mi or γ g γ g z ' z 6' (Were i ead lo occurrig?) L L f g L ' ' k.6 (aume f. from Moody diagram) ' ' 6'. mi or g ' g Mior ead loe ca be eglected if: legt of ie > *diameter of ie A A π () π (.) ' '... ' f π (.) cf Ceck f: 6. R e 7.6. f. k.6
6 Problem -: " ' Igore mior ead loe (L>) Aly Beroulli equatio: z γ g γ g ' ' L z L Hydraulic Lecture # CWR 4 age (6) L f L g L. ( ) π. 4 L.. ' ytem curve Higer dicarge, iger frictioal loe, iger ead required by um (Ue Table A- age 6 coverio table cf449gm) Pum caracteritic curve: gm 7 ft ' ' ytem Curve Pum Caracteritic Curve
7 Hydraulic Lecture # CWR 4 age (7) Problem -: eig: Cooe: a. Pie material (affect k, but alo durability of material) & ie diameter b. Pum (, ) elect a um tat i igly efficiet for te coditio Coider: a. iitial cot b. oeratioal cot Cooe teel: k. 46 ; L4m Aly Beroulli betwee lower reervoir & uer tak L 4 f g ( π 4 ) ( π 4 ) L f g. f f (.) 4.7 ay owaday, we care more about eergy cot ad eed to kee low. Te, cooe teel wit k. 46 ad f.4. Aume flow i i turbulet rage. k. Aume:.46. mm aume 4mm ad ceck f. 4mm.. 6 ; π 4 (.4) m R e Flow i wolly turbulet rage if f.4 Pum required: Buy m (.4) m ;. m 4 6
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