Longitudinal Dispersion
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1 Updated: 3 Otber 017 Print verin Leture #10 (River & Stream, nt) Chapra, L14 (nt.) David A. Rekhw CEE 577 #10 1 Lngitudinal Diperin Frm Fiher et al., 1979 m/ m -1 E U B HU. * Width (m) Where the Shear Velity i: Mean depth (m) U * ghs David A. Rekhw CEE 577 #10 1
2 Lateral Mixing Lateral r tranvere diperin effiient fr a tream: Mean depth L m Elat 06. HU Length required fr mplete mixing: Side diharge: Center diharge: 040. U B L U B m 010. E E lat * Width Shear velity lat David A. Rekhw CEE 577 #10 3 General Stream Gemetry Chapra nmenlature fr diharge effiient Velity Depth Width U a H B b f Where: b f 1 Beaue =UHB David A. Rekhw CEE 577 #10 4
3 Sample Prblem Thmann & Mueller, prblem.1 The Blak River, NY between MP 74. and MP 64.7 i t be haraterized a a ntant flw - ntant area reah. Aume the fllwing r-etinal area (A ) were meaured fr the given flw: (f) MP 74. A (ft ) MP 64.7 Etimate travel time thrugh thi reah fr flw f 600 and 3000 f David A. Rekhw CEE 577 #10 5 H B f A BH ( f ) 000 Area, q. ft A b[0]= b[1]= r ²= Flw (f) David A. Rekhw CEE 577 #10 6 3
4 Manning Equatin Derived frm the mmentum balane relate velity t hannel harateriti inluding lpe ft/ U Manning rughne effiient ee Table R 3 S n e Slpe f energy grade line = lpe f tream bed fr ntant H & U Hydrauli Radiu (ft) =A /wetted perimenter A /(B+H) David A. Rekhw CEE 577 #10 7 Manning Equatin adapted t a Trapezidal etin Area, perimeter and hydrauli radiu an all be expreed a a funtin f depth ubtitute thee int the Manning Equatin and alulate y frm knwn n A R n B B y y 3 S e y 5/3 1 1 /3 S 1/ e A R P B y A P B B y y 1 y B y y 1 1 y David A. Rekhw CEE 577 #10 8 B 4
5 Ditributed Sytem Leture #9 in Chapra bk ytem that have patial relutin Ideal Reatr V Jin A Jut A reatin t J in J ut B H David A. Rekhw CEE 577 #10 x 9 Plug Flw Reatr (PRF) V Jin A Jut A reatin t V UA U t x x A k V Cmbining and taking the limit a x0 U k t x Whih at teady tate i: 0 U k x And fr = at x=0: e David A. Rekhw CEE 577 #10 10 k x u 5
6 Plug Flw v CSTR Firt rder reatin e k x u kv Mixed Flw: intermediate read etin David A. Rekhw CEE 577 #10 11 Mixed Flw David A. Rekhw CEE 577 #10 1 6
7 Mixed Flw Pelet Number V Jin A Jut A reatin t V U E t x A U x x E x A k V x x x Cnider mixing in the lngitudinal diretin P e LU E rate f advetive tranprt rate f diperive tranprt P e > 10, PFR-like P e < 0.1, CSTR-like David A. Rekhw CEE 577 #10 13 Appliatin f PRF t tream Pint ure r r Ma balane: Water Flw Cnentratin Outfall: w w David A. Rekhw CEE 577 #10 14 w r w w r r w r 7
8 Aumptin David A. Rekhw CEE 577 #10 15 Chlride Prblem 1.55 f/mgd Determine the required indutrial redutin in hlride t maintain a deired hlride nentratin f 50 mg/l at the intake w =6.5 MGD w = 1500 mg/l Water intake =5 f =30 mg/l T = 5 f T = 30 mg/l David A. Rekhw CEE 577 #
9 W x x x+ x x+ x x x+ x David A. Rekhw CEE 577 #10 17 T next leture David A. Rekhw CEE 577 #
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