Question

1/9 1 Piping system (14 points) Water is pumped from a reservoir to a large receiver vessel which is maintained at p4 6 bar (absolute) through the operation of the pump and a high pressure nitrogen supply that bleeds into the tank through a regulator. The water enters through an opening at the top of the vessel. A drain is provided at the low point in the system. Elevations are as shown. All valves are gate valves (k = 0.15) except for the swing check valve (k = 2) immediately downstream of the pump. The entrance loss coefficient is ke 0.8. The pipe is 6 inch SCH 80 commercial steel (roughness height € = 0.05 mm, ID d=146.3 mm) with flanged connections and a total length of L = 135 m from the reservoir to the vessel. The atmospheric pressure is Patm 101 325 Pa 1) 8 points - What head rise across the pump, H, is required to deliver a flow of Q = 0.15 m/s from the reservoir to the receiver vessel with conditions as shown? 2) 3 points - What is the relationship between the system head (the head rise required across the pump) and the flow rate? 2) 3 points - Is the TACO080622 pump in figure 2 suitable for the present configuration? What impeller size would you choose?

Answer 1

Flow rate is given by, Q=0.15 m/s Velocity of the flow in pipe is given by, d = 146.3mm=0.1463 m Q=AV VED А 0.15 = T -x0.14632 4 V = 8.923 m/s Reynolds number is given by, pvd Re= u Vd Re=- V 8.923x 0-1463 Re= 1.0035x10-6 Re=1300884.26 Relative roughness is given by, Egia - = 0.05mm

E 0.05mm d 146.3mm = = = 0.000342 The friction factor for the pipe is f=0.016 Minor loss coefficient in pipe, Check valve, k =2 2*gate valve, k=0.15 Entrance loss, k=0.8 Total loss coefficient, K = 2+(2x0-15)+0.8 K = 3.1 = + Total head loss = Major loss + minor loss h= (h; +h) fLV? V2 hi EK 2gd 2g 0.016x135x8.922 +3.1x 2x9.81x 0.1463 2x9.81 h; = (59.91+12-58) h = 72.5 m 8.922 hi By applying Bernoulli's theorem between bottom reservoir (1) and receiver vessel (4),

+ P P V2 -+Z+hp + + Z2 +h; pg 28 Pg 2g P1 = Pam = lbar;P, = 6 bar V, =0(Fluid at rest);V, = 0 Z=10 m Z 1 = 4 m (4 m from the pump);Z, - Z = 6 (6-1)x10 + 69.24 +6 1000 x 9.81 hp = 50.97 +6+72-5 hp = 129.5m hp = 2) Velocity of the flow in pipe is given by, d = 146-3mm=0.1463 m А O V = 5x0.1463 4 V = 54.5Qm/s Reynolds number is given by,

pVd Re: ju Vd Re= 54.5Qx0.1463 Re= 1.0035x10 Re=867256179 Relative roughness is given by, Egla = 0.05mm 0.05mm = 0.000342 d 146.3mm E The friction factor for the pipe by Haaland equation is, 1.11 1 1 =-1.8log10 [Co Ed 3.7 6.9 + Re ✓f 1.11 1 -1.8log 10 = 0.000342 3.7 + 6.9 867256170 Minor loss coefficient in pipe, Total loss coefficient, K = 2+(2x0.15)+0.8 K = 3.1 Total head loss = Major loss + minor loss

= h = (h; +h) fLV2 h, -+XK 2gd 28 fx135x(54-59)? (54-59)? hi +3.1x 2x9.81x0-1463 2x9.81 hy = 560Q2 +166430fQ? h, = (560+166430f)Q? By applying Bernoulli's theorem between bottom reservoir (1) and receiver vessel (4), Р. V? P, V, +2+hp + Z2 +h; Pg 2g Pg 2g P1 = Partim = lbar;P, = 6 bar V, = 0(Fluid at rest);V= 0 Z =10 m Z = 4 m (4 m from the pump);Z2 - 2 = 6 (6-1)×10 hp +6+(560 +166430f)Q? 1000X9.81 ho = 56.97+(560+166430f) 1 + = + If=0.016 ho = 56.97 +3222-922 3)

OSKW) Q=0.15 m3/s =2377 GPM Taco NPSHR 750 LELOR MODEL 080622 TC/TS Series TOU HREQUIRED NPS 1760 RPM March 25, 2019 25 Ourve no. 2540 Win bio, 17.72" Size X 6 X 22 KPS 08 FEET 625 °*8888 21.6 (548mm) 175 1750 500 HEAD IN FEET 150 1500 20.10510mm) (480mm 17.72"250mm) 375 125 1250 SOOHP(373.0KW (450. OM HEAD IN METERS HEAD IN KILOPASCALS 100 3 1000 250 300 OK JSONO 2.5KW SOOHP(225 KW) 75 750 125 50 500 CURVES BASED ON CLEAR WATER WITH SPECIFIC GRAVITY OF 1.0 25 250 0 0 500 0 1000 1500 2000 2500 3000 3500 4000 4500 5000 FLOW IN GALLONS PER MINUTE Figure 2: Pump characteristic curve. Intersecting point is shown in black point. Yes, TACO pump suitable for the given configuration. Impeller size is 510 mm (20.10”)