Question

Water is pumped from a reservoir to a large receiver vessel which is maintained at p3 = 6 bar 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 pipe is 6 inch SCH 80 commercial steel (roughness height ε = 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. 1. (15 Marks) What head rise across the pump, H, is required to deliver a flow of Q = 0.15 m’s-1 from the reservoir to the receiver vessel with conditions as shown? 10 H₂O 20°C Nz Pabbar 4 7m 5 IN₂ Figure 1: Schematic of the piping system. 2. (5 Marks) What is the relationship between the system head (the head rise required across the pump) and the flow rate? 3. (5 Marks) Is the TACOTC080622 pump in figure 2 suitable for the present configuration? What impeller size would you choose?

In regards to question 3, will cavitation occur based on the NPSH available vs NPSH required?

Answer 1

Please refer the following images for the solution.

Given P₂ = 6 bar Kgv = 0.15 Ksy=2 Diameter of Ginch SCH 80 d d = 16.3mm = 0.1463m &= 0.05mm L = 135m Q- 0.15 ot/s Solution 0-15 Ixd² & 1) Relative roughness of the pipe, 0.05x103 3-4 X16 d 0.1463 velocity of water in the pipe, Ve 8.923 m/s Ix 0.1463² Reynolds number of the flow 8.923 0.1463 1302439.29 1.00 23x150 (1.0023x1oʻmys. at 206) Using Moody's diagram for = 3.4x1.79 Re=1302439.29 Friction factor of the pipe is, f=0.01587 Re=vd and papse gordet 4 2g Applying Bernouli's equation at the reservoir levelci) and +2, + Hp = PA Z gt V the sg 2g sg where, P1 = 1-01325 bar = Atmospheric pressure Zu-Z, = 10m 로 o C constant Jered in the reservoirs) zg zg P4= 6 bar head 2 Hp- pump

h = total head loss. major loss + minor loss Above equation becomes 1 Pi Hp P4 (24-2, the sg eg .: Hpa (P4- Po) (26-2) + hl lo sg Hp. (6x108–1:013254105) 10 + fly² + 998% 9.8) gd EKL y² zg Hp = C 6010- 1.01325x105 +10 + (0-01587x135x8.9233) 99879.81 2x 9.81% 0.1463 + (ki +3Kgv + Kev+ Skel) x 8.923² 2x9.81 where, ki = entrance loss coefficient = 0.5 kg ve gate valve coefficient = 0.15 (3 numbers) Ksra swing check valve coefficient = 2 Kel = 30 elbow coefficient = 0.3 (5 numbers +10+ Hp - (67105- 1:01329x109) 0.01587x135x8.9239 99 879.8) 2x 9.81 0.1463 + (0.5+(3X0-15.)+2 + (5X0-3))x 8.9233 2x 9.81 Hp = 138.42m be re

The relationship between the system head and the flow rate Hp = (P4 - P.) (24-2) + hi sg + 10+ Hp = (62109-1101325X101) (0.01587*135*132 998 x 9.81 2x 9,818 0.1463 +(0.5+(3x0.15)+2+(5 40.3))x v2 2x9.81 2 .. Hp - 60.9352+0.9732 v where, velocity ve 7 + 0.14632 59.487 Q Id Hp = 60.9352+ 0.9732* (59.487Q)? Hp = 60.9352+ 3443-866 Q? 26667 Hp is in 'm' and Q is in m/s (3) Using above system curve equation and plotting on the given pump curve the operating point is Q- 2680 gem a 0.169082 mays Hp = 159.39m n = 73% NPSHR = 18 ft = 5.4864m For marimum pump efficiency of 734, the impeller 21.6 or 548mm 7 size would be

4) Checking for cavitation NPSHA = HA+Hs - Hf - Hup 2 HA - Atmospheric pressure head - 10,34m Hs= static head HE= head loss in suction pipe = f Ls V2 + ZK LV² agd zg As suction pipe length is not given, assu assuming it is 3m. He=0.01587x3x 0-169082 Tro.14633 (0.5+0.15x 0.169082 2 x 98| xo.14 63 700-1463² 2x9.81 Hp = |-678 +3,3515 =5.03 m and Hup = vapor pressure head - Pup 2.348183 -0.24m 38 99879.81 + NPSHA = HA+Hs - Hf - Hup = 10.34+4-5.03-0.24 INPSHA =9.07m As NPSHA > NPSHR there will be no cavitation. No cavitation

Q(m3/s) Q (gpm) Hp (m) Hp (ft) 0 이 60.9352199.9186 0.031545 500 64.36217| 211.162 0.06309 1000 74.64307 244.892) 0.094635 1500 91.77791 301.1086 0.12618 2000 115.7667 379.812) 0.157725 2500 146.6094 481.002 0.189271 3000 184.306 604.6786 0.220816 3500 228.8566 750.8419 0.252361 4000 280.2611 919.4919 0.283906 4500 338.5196| 1110.629 0.315451 5000 403.632 1324.252

NPSHR Taco seres MODEL 080622 TC/TS Series 75 100 125 FREQUIRED NPSH- 1760 RPM March 25, 2019 175 200 225 Curve no. 2540 Min. Imp. Dia. 17.72" Size 8 X 6 X 22 250 275 300 KPa L/SEC 25 50 150 750 25 20 15 10 5 0 LO 75 60 45 30 15 O 1750 625 L-21.6"(548mm) 175 500 1500 150 20.10"(510mm) HEAD IN FEET 125 1250 Figure 2: TACOTC080622 pump performance chart 18.90" 480mm) AHHHHHH 375 F17.72" (450mm) No HA 600HP(450.OKW) XXX) 1500HP(375.0KW) 450HP(337.5KW) 400 HP C300.0KW) (350HP (262.5kw). 300HP (225.0KW) HEAD IN METERS HEAD IN KILOPASCALS 100 E 1000 250 75 750 50 500 125 25 - 250 CURVES BASED ON CLEAR WATER WITH SPECIFIC GRAVITY OF 1.0 0 0 0 0 500 1000 4000 4500 5000 1500 2000 2500 3000 3500 FLOW IN GALLONS PER MINUTE MS 3-25-2019 PC-2540 Revc