Question

Prob-5 The pressure rise, Ap across a centrifugal pump from a given manufacture can be expected to depend on the angular velocity of the impeller W, the Diameter D, of the impeller, the volume flow-rate, and the density of the fluid, p. By using the method of repeating variables show that A model pump having an impeller diameter of 0.200 m is tested in the laboratory using water. The pressure rise when tested at an angular velocity of 40x rad'sec is shown on the graph. What would be the pressure rise for a geometrically similar pump with an impeller diameter of 0.30 m used to pump water operating at an angular velocity of 80x radsee and at a flow rate of 0.070 ms? Sol: # GDE

Answer 1

0 0. 200m flow rate Solution:- (5) Given that, A model pump having an impeller diameter of Similar pump with an impeller diameter = 0-30m- angular velocity = 80T7 Tad see 0.070 m/s pressure sise AP > M1?? angular velocity ws 7 diameter D - L Volume flow rate d>131 density of fluid PME By using Buckingham på Theorem There m= 5 and n=3 So, total no.of T terms m-n Ź 5-3 - 2 variables - TIM consider D, w and pas repeating Da ob o cop) Morgo – (La Gaub MCP) CHL-'13) 1990 - Mt (9-36-1 IB-2 CHI = 0 C = -1 -b-2=0 => b=-2 a-30-1=0 = a +3-1=0 = Q 5-2 TIA = DOUBSCCAP) - DX?P'CAP) . ITA ДР Sop²

2 MOC T2 - Do ob god Mel®zo - CA (7496 CHC?)$(13') H 19-30+3,5-1 c=0 -1-1=0 =) b=-1 a-3C+3 = 0 -> Q=-3 T2 = D9 WP p a Dwiga .. Tz WD 3 다. (11 , 2) =0 F C (AP a TWD² 2 WD3) ДР 3 w²2² co WD3 Gliven, DI = 0.2m, WI = LOTTradis Dz = 0.3m, W2 = 801 rady Q2 = 0.070 mp use, T2 = Q WD3 .: Q dz COID, 3 W2D2 Oz .: ai xw1 X Substitute the values, Di W2 Qi 0.070 x QOTT х SOTT Q 0.01037 ms B.) Som en

0.01037 m . s (OP), 33 •Kpa NOW, Use TI .: (Opz = Opin. C7*G using given graph, At an Opl Ople WiD,² (3) here, 8 = 22 ДР Pwp² = 1000 legimo = WiD.2 DI 2 33 x/80TI 40TT X | ()2 297 kPa pereshero Rise ho W = 8071 Nad/s D = 0.3m ell = 0.070 m/s is AP2 297 kpa