Question

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1. As shown in the figure, using a 6-m-long, 100 mm diameter pipe and assuming a friction factor f-0.02, investigate the likelhood of cavitation if h-4 m and h = 3m Water temperature is 25 degrees Centigrade, 5101325 KP kinematic viscosity =156 m2/sec, flow velocity = 4 m/sec, neglect minor losses using 2. At the deign flow rate read the pump characteristics if the 6 in impeller is used (power, efficiency, head) 3. If the angular speed is doubled find the changes in power, head, NPSHA NPSHR flow rate 4. Repeat 3 If the Diameter of the impeler is reduced to 4 in

Answer 1

d = 100mm=0.1 m Flow rate in pipe is given by, Q = AV Q==x0.1° x4 Q=0.031416 m/s 4 The friction factor for the pipe is f=0.02 Total head loss = Major loss + minor loss h = (h; +hm) h; fLV? +0 2gd +O ) 0.02x6x42 hi 2x9.81x0.1 hı = 0.9786 m For h= 4 m hp = 4+0.9786 = 4.9786 m

30 20 B (NPSH)roq 65% 70% 75% 173) 6-india 80% 80% Head (ft) 150 5.5-in. dia 125 5-india 100 75 - 1750 rpm 75% 70% 65% 50 25 bhp 20 bhp 18 bhp 10 bhp 25 100 200 300 337 400 470 500 600 Flow Q(gal/min) 700 800 From graph, for 500 GPM NPSH R is 18 ft (5.4864 m) The condition for pump operation without cavitation is,

NPSH, S NPSH 4 Vapour pressure of water at 25 C is 3.16 kPa. Available head is given by the relation, P --Z, -H(suction) NPSH P, 7 Substituting the values, we get 101.325x10 3.16x1000 NPSHA = -4-0.9786- 1000 x 9.81 9.81x1000 NPSHA = 10.33-4-719.06-0.322 NPSHA = 5.028 m Hence, cavitation will occur for 4 m. For h= 3 m Available head is given by the relation, NPSHA --- P -2, -H(suction) 7 Substituting the values, we get

101.325x103 3.16x1000 NPSHA = -3-0.9786- 1000 x 9.81 9.81x1000 NPSHA = 10.33--719.06 -0.322 NPSHA = 6.028 m Hence, cavitation will not occur for 3 m. 2)

30 20 B TO (NPSH) 175/6-india 65% 70% 75% 80% 80% Head (ft) 150 5.5-india 125 3-india 7100 75 wh - 1750 rpm 75% 70% 65% 50 25 bhp 20 bhp 18 bhp 10 bhp 25 100 200 300 337 400 470 500 600 Flow Q (gal/min) 700 800 In black point, Head =137.5 ft, Efficiency=83% and power 22 bhp. 3)

Diameter of the impeller is same of 6 in. To find the NPSH A and NPSH R. The pump for the doubled angular speed is required. The dimensionless pump parameters are given by, Capacity coefficient(Ce), V OD =( OD OD 500 OD 20D V = 1000GPM Head coefficient(CH), gH CH oʻD gH gH m’D? (20)’D

gH, gH, 0²D2 40²D H = 137.5x 4 = 550 ft Here, impeller rotational speed iso, Diameter of the impeller blades is D, and net head with gravity is gH. Power coefficient(Cp), bhp po:D bhp bhp po’DS poºd bhp, bhp2 po Dp8oD bhp2 = 22x8 = 176bhp Diameter of the impeller is same of 4 in. To find the NPSH A and NPSH R. The pump for the doubled angular speed is required. The dimensionless pump parameters are given by, Capacity coefficient(C),

V OD V OD OD? 500 V 204 V = 296.3GPM Head coefficient(CH), C = gH O D2 gH gH 062 (26)* 4 gH gH O 36 40 16 H = 244.44 ft Power coefficient(Cp), bhp Ср = ρωD bhp bhp pod pod bhp: bhp2 ρω65 p8m2 43 bhp2 = 23-18bhp