SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2014/2015 ME257. Fluid Dynamics. Answer FOUR out of SIX questions

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1 s SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2014/2015 ME257 Fluid Dynamics Time allowed: TWO hours Answer: Answer FOUR out of SIX questions Items permitted: Any approved calculator Items supplied: Formulae sheet Marks for whole and part questions are indicated in brackets ( ) ME257_SEM1_2014/2015 Page 1 of 6 Printing date: 23/09/2015

2 Question 1 (a) Explain the meaning of the following terms: i) pressure ii) shear stress iii) specific volume iv) non-newtonian fluid v) gauge pressure An open tank contains oil of relative density 0.75 on top of water. If the depth of the oil is 2m and that of the water 3m, calculate the gauge and absolute pressures at the bottom of the tank when the atmospheric pressure is 1bar? (10 marks) (c) In a 0.6m diameter duct carrying air the velocity profile was found to obey the law where u is the velocity at radius r. Calculate i) the volume flow rate of the flow of the air (7 marks) ii) the mean velocity. (3 marks) ME257_SEM1_2014/2015 Page 2 of 6 Printing date: 23/09/2015

3 Question 2 a) Derive the Euler equation, without taking into account the effect of gravitation, based in the second Newton s law applied to an element of fluid (15 marks) b) A pump discharges water at 2 m 3 /s through a pipe. If the pressure difference between the inlet and outlet of the pump is equal to 10 m of water, what power is being transmitted to the water by the pump? (10 marks) Question 3 (a) Formulate the momentum equation for the flow of fluid and explain the meaning of the terms (5 marks) A jet of water 5cm in diameter and flowing at 56 litre/s impinges on a series of vanes moving at 12m/s. Before impact the jet is travelling in the same direction as the vanes, and is deflected through an angle of 135 o. Fluid resistance has the effect of reducing the relative velocity of the jet by 10% as it crosses the vanes. Determine: i) The magnitude and direction of the resultant force on the vanes. (10 marks) ii) The work done per second by the vanes. (5 marks) iii) The efficiency of the arrangement (5 marks) ME257_SEM1_2014/2015 Page 3 of 6 Printing date: 23/09/2015

4 Question 4 (a) Explain the meaning to the following terms i) pressure drag ii) skin friction drag iii) profile drag iv)drag coefficient v) lift The overall drag coefficient of a particular aircraft of weight w is given by: C D =a+b C L 2 Derive an expression for the minimum drag in horizontal flight and comment on the results (20 marks) ME257_SEM1_2014/2015 Page 4 of 6 Printing date: 23/09/2015

5 Question 5 (a) By using Newton s second law, derive the expression for Euler s head developed by a centrifugal pump: 1 E g U 2Vw2 U1Vw1 where the terms have their usual meaning. (10 marks) The inlet and outlet diameters of a centrifugal impeller of a fan running at 20 rev/s, are 50 cm and 75 cm respectively. Its width at the inlet is 10 cm and at outlet is 7.5 cm. The blade angle at the outlet is 70, the air enters the impeller radially and the air volume flow rate is equal to 800 litres/s. Calculate: i) the flow velocities at inlet and outlet (3 marks) ii) the whirl velocity at outlet (3 marks) iii) the absolute velocities at inlet and outlet (3 marks) iv) the relative velocity at inlet (3 marks) v) Euler s head (3 marks) ME257_SEM1_2014/2015 Page 5 of 6 Printing date: 23/09/2015

6 Question 6 (a) Using diagrams, describe the velocity triangles of the Pelton wheel at the inlet and outlet. (7 marks) In a Pelton wheel, the diameter of the bucket circle is 2.2 m and the deflecting angle of the bucket is 163. The jet is of 166 mm diameter, the pressure behind the nozzle is 1050 kpa and the wheel rotates at 330 rev/min. Neglecting friction, find the power developed by the wheel and the hydraulic efficiency. (18 marks) ME257_SEM1_2014/2015 Page 6 of 6 Printing date: 23/09/2015

SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2015/2016 ME257. Fluid Dynamics

s SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2015/2016 ME257 Fluid Dynamics Time allowed: TWO hours Answer: Answer TWO from THREE questions in section A and TWO from THREE