Question

Two large tanks are open to the atmosphere at the top. Water s pumped from the lower tank to the upper tank through a single PVC (smooth) pipe. The relationship between Velocity in the pipe (ft/s) and the pump head (ft) is given. There are no significant minor losses. What is the flow rate, Q (cfs), in the pipe?

Pump Coefficients 1.30 sec /ft Pipe Length Inside Pipe Diameter 300 ft 0.250 feet a = 3.24 sec b 107.00 ft C = hs a V2b V+c elev 90 ft elev 40 ft Pump

Answer 1

Sobo Givenつ Reservoirs conneetion with PVC (smooth) pipe and pump is also Connected. a he (pump head) aV bV+c wheve, vis velocity o oater in pipe ts 35ec/4) b 3.24(sec) a = C l07.00ft) Negligible minor losse

To determine flow rate in pipe (fts) Colculation: minor losses are negligible, but there twil1 be some major losses . pump headhs need to overcome that to So, hs static head major losse (due to pipe friction) hs(90-40h according toDarey Weisbach eqwation, wheve, fis friction factor for pipe material Lis length o pipe, b1ow velocity in pipe, d is inside dia. oh pipe, and is acceleration due to grovity (98 mls 32.15 ft/st Vis

= 50 + X300 X V2 ax 32.15X d25 50+ 1866 f V also, hs13V 3-24V+ 10a) thus, 1.3v 3.2uV+ 10t50+18-66fV - 18.66f+1.3) V-324V-57 - O for PVC (smooth) pipe, Coebbicient (E) 00025 mm de 025ft-0-25X0305X100) 76.25 mm Roughness 2

1d19 lm2 1000 mm O 305 m as, Relative Rough ness O0025 d 3.3 X105 bor v'using hit need to solve Now, we and trial method, to be laminar, 30, taking blow Re (Reynold's nomber) and, reading rom moody's chart, 4nitial gvess ob 0 02 2 3au V-57-0 18-66X0-02) V2 SO, V 12.44 ft/s 131l520305 m s V 2 5.32 m)s Jw l000 kg/m2 76.25m d 0as ft Nw-7-6X10NS

Re- l000 X 5.32 X (625 1000 7-65 X10 5.3X 10 for, 3. 3 X1D S Re 5 3X10 From moody's chort, 0.013 again. bor f0.013 SO, -57 18 66 X0 013) v 3.a4V 4tis 2) o 23-4 fts V V2 13 and, Re 91X10 again brom moody's f 0012 stop O 2וט 0.013 aas 2 0.012 223.4 f41s -7.137 m)s SO

and, Q AV 2 x (0as)x23.4 115 ft/s) 2 Ans