Question

Project-Design Problem: A family of water pumps produced by a given pump manufacturer have performance and efficiency curves that can be characterized by the following dimensionless equations: Pump head 6 = 6.04-1616 where and 5 nD Pump efficiency n = 705-91,5006 where n = (power to water) / (elect power input) In the above equations, is the dimensionless pump head and is the dimensionless volumetric flow rate. h, is the pump head, n is the pump shaft/impeller rotation rate, and D, is the pump impeller diameter. The range of validity is 0<<<0.027. In addition, the shaft/impeller rotation rate must be no slower than 600 rpm (revolutions per minute). Now, use the above information to select a low operating-cost pump (select n and D) for the following application: Water at 20 °C is to be pumped as shown in the system in Figure 2 (next page) at a volumetric flow rate of at least 1 ft/s. Pipe friction losses in the system can be approximated by h - 27V4/(2g), where Vis the average velocity in the pipe. (Note that the operating cost is a direct function of the pump's electrical power input requirement.) 1180 Pump Figure D3

Answer 1

Here, Datum heights : 2,=50 ft. 2, 15017 pump head, ø= 6-04-1615 a Q g.hp h? í 5 = A nosp. 3. Efficiency of pump, 2=705-91,500 5 friction losses 27V2 ine 29 volumetupe flow rate ,a= 1ft²/ we know that 0= A.V - V- /A · Area A = 10² given D-6 in. ft [:: 147=12") 12 D = 0.5ft T 4 (0.5)2 v=5.094 ft /sec

given he hea 2702 27x (5.094)2 *ง 2 x 32.2 he 10.879 ft. we know from Bernoull's formular 0 21 0 2 Pe eg 123 +2 ot 2 theo hp pg 50 - 150 +10.879-hp hp = 110.879 ++ pump head is given by d=6004-1615 Dimensi onless g.hp m². Do = 6004-161 ( (open) 2 37.2 (10-879) 6.04-161 [no] 2 3570.3038 = 6.04 - 161(a) n.op given a range for 5=9 =025 20:02 7. . Let 5 =0.02 :. 3570 - 3038 .6.04-161 (0.02 ) n2 Dp²

@ 3570 3038 Bopp 2.82 esn't Do = 1266.065 a) app = 1266-065 11266.065 = 35.58 =) n.Dp = 35.58 given in must no slower than 600rpm ieen>600 rpm no 600 60 aps. nz 10925 when n = 3orps. Op = 16 186 in.

So the value of D_p=1.186 in.

Thank you.​​