FLUID MECHANICS D203 SAE SOLUTIONS TUTORIAL 2 APPLICATIONS OF BERNOULLI SELF ASSESSMENT EXERCISE 3

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Alicia McDowell
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1 FLUI MEHNIS 0 SE SOLUTIONS TUTORIL PPLITIONS OF ERNOULLI SELF SSESSMENT EXERISE Take the density of water to be 997 kg/m throghot nless otherwise stated.. Ventri meter is 50 mm bore diameter at inlet and 0 mm bore diameter at the throat. Oil of density 900 kg/m flows throgh it and a differential pressre head of 80 mm is prodced. Given d 0.9, determine the flow rate in kg. p d r / 5 p g h 900 x 9.8 x x 0 Pa ( r ) 0.9 x π x 0.05 x x 0 m m kg ( ). Ventri meter is 60 mm bore diameter at inlet and 0 mm bore diameter at the throat. Water of density 000 kg/m flows throgh it and a differential pressre head of 50 mm is prodced. Given d 0.95, determine the flow rate in dm. g h d r 9 ( r ) 0.95 x π x 0.06 x 000 x 9.8x x 0 m or 0.55 dm ( ). alclate the differential pressre expected from a Ventri meter when the flow rate is dm of water. The area ratio is and d is 0.9. The inlet c.s.a. is 900 mm. p 0.00 d r x 900x0 p 96 Pa ( r ) p p ( ) alclate the mass flow rate of water throgh a Ventri meter when the differential pressre is 980 Pa given d 0.9, the area ratio is 5 and the inlet c.s.a. is 000 mm. r 5 p kg ( ) 000 x 0.9 x 000 x -6 x 980 m d 0 r 000( 5 ) 5. alclate the flow rate of water throgh an orifice meter with an area ratio of given d is 0.6, the pipe area is 900 mm and the d.p. is 586 Pa. (ans dm/). p r d p x 586 ( ) 900 x -6 0 x 0.6 r 000( ) 55.9 x 0 m

2 6. Water flows at a mass flow rate 0f 0.8 kg throgh a pipe of diameter 0 mm fitted with a 5 mm diameter sharp edged orifice. There are pressre tappings (a) 60 mm pstream of the orifice, (b) 5 mm downstream of the orifice and (c) 50 mm downstream of the orifice, recording pressre pa, pb and pc respectively. ssming a contraction coefficient 0f 0.68, evalate (i) the pressre difference (pa - pb) and hence the discharge coefficient. (ii)the pressre difference (pb - pc) and hence the diffser efficiency. (iii) the net force on the orifice plate. d o 5 mm d j jet diameter c 0.68 ( b / o ) (d b /5) d b.7 mm No Friction between (a) and (b) so v.0 d c v c p m od β 5/ c β π x ( ) x 0.68 p ( x 0.5 ) p p pa pb 58 Pa 8 Note the same answer may be obtained by applying ernolli s eqation between (a) and (b) Now apply ernolli s eqation between (b) and (c) p b + b / p c + c / + loss loss ( b - c ) / m 0.8 b m b 997 x π x 0.07 / m 0.8 c.5 m loss 997 ( ) / 5 Pa c 997 x π x 0.0 / p c - p b (997/)( ) 5 67 Pa η 5./.58 7% Energy recovered 6.7/.58 9% Force π x 0.0 / x N (on the control section)

3 7. The figre shows an ejector (or jet pmp) which extracts x 0 - m of water from tank which is sitated.0 m below the centre-line of the ejector. The diameter of the oter pipe of the ejector is 0 mm and water is spplied from a reservoir to the thin-walled inner pipe which is of diameter 0 mm. The ejector discharges to atmosphere at section. Evalate the pressre p at section, jst downstream of the end of pipe, the velocity in pipe and the reqired height of the free water level in the reservoir spplying pipe. (-.8 kpa gage,.9 m, 6. m). It may be assmed that both spply pipes are loss free. π x 0.0 /. x 0-6 m π x 0.0 / 56 x 0-6 m x 0-6 m / 0.00 x 0-6 /0.98 x 0-6. m pply ernolli from to h + + z h + + z g g. h z. m p gh -.8 kpa g g Next apply the conservation of momentm between the points where and join and the exit at. This reslts in the following. p a b p c x x0.56 x 0 + c 7.8x0 a + b + c x x 56 x x 0 b ± - b a -6 ac.87 ±.87 + x 86 x 0.06 x ± or m x 86 /.9 m pply ernolli between E and point z h + /g 6.8 m + ( x 0 )

4 8. iscss the se of orifice plates and ventri-meters for the measrement of flow rates in pipes. Water flows with a mean velocity of 0.6 m in a 50 mm diameter pipe fitted with a sharp edged orifice of diameter 0 mm. ssming the contraction coefficient is 0.6, find the pressre difference between tappings at the vena contracta and a few diameters pstream of the orifice, and hence evalate the discharge coefficient. Estimate also the overall pressre loss cased by the orifice plate. It may be assmed that there is no loss of energy pstream of the vena contracta. d o 0 mm d j jet diameter d b c 0.6 ( b / o ) (d b /0) d b mm 0.6 x π x 0.05 / m No Friction between (a) and (b) so v.0 d c v c p od β 0/ c β ( ) π x x 0.6 p ( x 0.6 ) p.06 p pa pb 00 Pa 7 Note the same answer may be obtained by applying ernolli s eqation between (a) and (b) Now apply ernolli s eqation between (b) and (c) p b + b / p c + c / + loss loss ( b - c ) / b.6 m b π x 0.0 / q c 0.6 m loss 997 (.6 0.6) / 000 Pa π x 0.05 / c

5 9. The figre shows an ejector pmp designed to lift x 0- m of water from an open tank,.0 m below the level of the centre-line of the pmp. The pmp discharges to atmosphere at. The diameter of thin-walled inner pipe mm and the internal diameter of the oter pipe of the is 5 mm. ssming that there is no energy loss in pipe and there is no shear stress on the wall of pipe, calclate the pressre at point and the reqired velocity of the water in pipe. erive all the eqations sed and state yor assmptions. π x 0.0 /. x 0-6 m π x 0.05 / 9 x 0-6 m x 0-6 m / 0.00 x 0-6 /77.8 x m pply ernolli from to h + + z h + + z g g 5.9 h z.9 m p gh -. kpa g g Next apply the conservation of momentm between the points where and join and the exit at. This reslts in the following. p a x x0 b 8.9 9x 0 p c + c x 0 a + b 8.9 ± - + c or m / 0.95 m - 00 x 9x b ± b a x 6805 x x ac + ( x 0 )

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA. PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3 OUTCOME 3 - HYDRODYNAMICS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 3 NQF LEVEL 3 OUTCOME 3 - HYDRODYNAMICS TUTORIAL - PIPE FLOW CONTENT Be able to determine the parameters of pipeline