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# pro00033 - Pipe Flow Problems-III Example 1 A centrifugal...

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Pipe Flow Problems-III Example 1 A centrifugal pump has a 100 mm diameter suction pipe and a 75 mm diameter delivery pipe. When discharging 15 l/s of water, the inlet water mercury manometer with one limb exposed to the atmosphere recorded a vacuum deflection of 198 mm; the mercury level on the suction side was 100 mm below the pipe centerline. The delivery pressure gauge, 200 mm above the pump inlet, recorded a pressure of 0.95 bar. The measured in put power was 3.2 kW. Calculate the pump efficiency. (See fig.1) Solution; Manometric head = rise in total head ) 2 . 60 ( 602 . 0 2 . 3 09 . 13 015 . 0 2 . 3 ) ( 3200 ) ( power input power output ) ( Efficiency 13.09m 0.186) (-2.793 - 0.2 0.588 9.69 Hm Then 186 . 0 2 ; / 91 . 1 588 . 0 2 ; / 39 . 3 65 . 9 198 . 10 * 95 . 0 water of 10.198m 1bar 2 2 2 1 1 2 2 2 2 2 1 1 2 2 2 percent watts watts gQHm m g V s m V m g V s m V water of m g p g V g p z g V g p Hm = × × = = = = + + + = = = = = = = = + - + + = η ρ η ρ ρ ρ Fig 1.

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Example 2 (Pipeline selection in pumping system design) As existing pump, having the tabulated characteristics is to be used to pump raw sewage to a treatment plant through a static lift of 20 m. An uPVC pipeline 10 km long is to be used. Allowing for minor losses totaling 10 V 2 /2g and taking an effective roughness of 0.15 mm because of sliming, select a suitable commercially available pipe size to achieve a discharge of 60 l/s. Calculate this power consumption. Discharge (l/s) 0 10 20 30 40 50 60 70 Total head (m) 45 44.7 43.7 42.5 40.6 38 35 31 Overall efficiency 35 50 57 60 60 53 40 (per cent) Solution; At 60 l/s, total head = 35.0 m, therefore the sum of the static lift and pipeline losses must not exceed 35.0 m. Try 300 mm diameter: A=0.0707 m 2 V=0.85 m/s Re = 2.25*100000 ; k/D = 0.0005 λ =0.019= f Friction head loss m 32 . 23 62 . 19 3 . 0 85 . 0 10000 019 . 0 2 = × × × =
Hs + h f = 43.32 (> 35) pipe diameter too small Try 300 mm diameter: A=0.0962 m 2 V=0.624 m/s; Re = 1.93*100000 ; k/D = 0.00043 λ =0.0185 H f =10.48m; hm Hs + h f + hm =30.68 (< 35 m) O.K The pump would deliver approximately 70 l/s through the 350 mm pipe and to regulate the flow to 60 l/s an additional head loss of 4.32 m by valve closure would be required.

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pro00033 - Pipe Flow Problems-III Example 1 A centrifugal...

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