Fluid Mechanics Ii Exam 2012 Essay


Answer any five (5) questions in the Answer Booklet. Start each answer on a new page. Do not bring any material into the examination room unless permission is given by the invigilator.

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Please check to make sure that this examination pack consists of: i) ii) iii) the Question Paper an Answer Booklet – provided by the Faculty a one – page Appendix 1DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO This examination paper consists of 4 printed pages © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL QUESTION 1 a) 2 EM/JAN 2012/MEC442/KJM492 Describe what happens to the velocity, static pressure, stagnation temperature, static temperature and density of an isentropic supersonic flow when it enters a converging section. (5 marks) Air enters a converging diverging nozzle at 700 kN/m2 and 27 °C with negligible velocity and experiences a normal shock at a location where the Mach number is 3.Calculate the velocity, density, static temperature, static pressure and stagnation pressure downstream of the shock. (15 marks) The following equations may be used without proof: O. S(k+)/ b) Isentropic flow: A A* „ Ma 1 { 2 Y, * – l .

, 2 Y 1+ Ma Ma . U + lA 2 J (k-l)Ma? +2 = •> 7 Shock Wave: 2 2 2kMaf-(k-l) p2 px Properties of Air: k=1. 4 1 + kMal 1 + kMa R=287 J/kg. K T2 l + Ma? (k–l)/2 Tx ~ l + Ma22(k-l)/2 Cp=1005 J/kg. K QUESTION 2 Water is pumped at the rate of 0. 55 m3/s through a centrifugal pump operating at a speed of 1750 rpm.

The impeller has a uniform blade height, b, of 60 mm with the impeller inlet and outlet radius, n = 50 mm and impeller outlet radius, r2 = 180 mm, respectively. The exit blade angle p2 is 23°. Assume ideal flow conditions and that the tangential velocity component, Vt1 of the water entering the blade is zero. Determine: a) b) c) d) the inlet blade angle, p1t the tangential velocity component, Vt2, at the exit, the ideal head rise, h, and the power transferred to the fluid, WShaft (Pwater = 1000 kg/m3, g = 9. 81 m/s2) (20 marks) © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL QUESTION 3 EM/JAN 2012/MEC442/KJM492 A liquid flows down an inclined plane surface in a steady, fully developed laminar flow of thickness h.

a) Simplify the continuity equations and Navier-Stokes equations to model this flow field. Clearly state all assumptions. Obtain expressions for the liquid velocity profile, the volume flow rate and the average velocity. Relate the liquid thickness to the volume flow rate per unit depth of surface normal to the flow. Calculate the volume flow rate in a film water h = 1 mm thick, flowing on a surface b = 1 m wide, inclined at 6 = 15° to the horizontal. b) c) ) fpwater = 1000 kg/m 3 , /u watef= 1.

0 x 10″3 kg/ms, g = 9. 81 mis2) (20 marks) h = 1 mm . 9 Width of surface = 1 m Figure Q3 QUESTION 4 a) What is the difference between skin friction drag and pressure drag? Which one is usually more significant for slender bodies such as airfoils? A small airplane has a total mass of 2200 kg and a wing area of 40 m2. Determine the lift coefficient and drag coefficient of this airplane while cruising at an altitude of 4000 m at a constant speed of 315 km/h and generating 200 kW of power.{The density of standard air at an altitude of 4000 m is = 0.

19 kg/m3} (20 marks) b) © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL QUESTION 5 4 EM/JAN 2012/MEC442/KJM492 The velocity potential for an ideal fluid flowing around long cylinder is given by {-+ * } cos (A 8=0 The cylinder has a radius R and is placed in a uniform flow of velocity U, which affects the velocity near to the cylinder. Determine the constants A and B and determine where the maximum velocity occurs. (20 marks) U Figure Q5 QUESTION 6 Air flows over the surface of a plate, forming a laminar boundary layer. The boundary layer velocity profile is approximated by the cubic olynomial expression of: U. a) b) = a + by + cy2 + dy3 Determine the constants a, b, c, and d. Show that momentum thickness, G is 39S 280 c) Given that Cf – 2 — , determine the boundary layer thickness, 8.

dG dx (20 marks) END OF QUESTION PAPER © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL APPENDIX 1 EM/JAN 2012/MEC442/KJM492 FORMULA LIST Equations of Motion in Cartesian Coordinate System. ( du du ciu Bu dp fd2u d2u d2u — + ” — + v— + w— = – — + pgx + fii—^ + —2 + Tl at dx dy dz/ dx dx” dy dz j (y direction) 2 2 2 dt dx (z direction) (dw ! w fdV p I Vu dV dV dv h V— + W— dy dz) = dp dy fd U dV d V^ + pP , + u, —r A x 6> 2 2 + ~•T 2 dx dy dz j dw dw dp fd2w dr dx dy dZ dz ** a*2 d2W 2 a>- a? , d2w^ 2 Equations of Motion in Cylindrical Coordinate System. Continuity: Convective time derivative: 3 1 Zk A Laplacian operator: _2 The r-momentum equation: i a / a , l a” _a* The 0-momentum equation: dv* 1 I dp lr-,1 VQ , 2 dvr The z-momentum equation: 6l>; + C •’ ‘”* V VK 3f ‘ v ‘ = – – dz – + fc + -? p ^ © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL