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 questions in Section B Items permitted: Any approved calculator Items supplied: Formula sheet Marks for whole and part questions are indicated in brackets ( ) [Code]_SEM1_2015/2016 Page 1 of 5 Printing date: 14/11/2016
Section A Attempt TWO questions in this section Question 1 Explain the meaning of the following terms: (i) Continuum concept (1 mark) (ii) Pressure at a point (1 mark) (iii) Laminar flow (1 mark) (iv) Reynolds Number (b) (i) Find gauge and absolute pressures of water at a depth of 25 m below the free surface? The density of water is 1000 kg/m 3 and the atmospheric pressure is 101 kn/m 2. (ii) The bottom of the U-tube manometer is filled with mercury which is immiscible with the water inside the tank (shown in the figure). What is the absolute pressure at point A if 10 cm, 15 cm, density of water, ͺ 1000 kg/m, density of mercury, ͺ 13600 kg/m, acceleration due to gravity, 9.81 m/s, the atmospheric pressure, ͺ 101 kn/m. [Code]_SEM1_2015/2016 Page 2 of 5 Printing date: 14/11/2016
Question 2 Water flows through a cylindrical pipe AB: diameter of the pipe, 0.8 m, velocity of the flow 2.5 m/s. It then passes through a pipe BC: 1.6 m. At C the pipe forks in two branches, CD and CE. In the branch CD: 1.5 m/s, and the flow is half of that in the pipe AB. In the branch CE: 0.5 m. Find the following: (i) the volume flow rate in AB. (ii) the velocity in BC. (iii) the diameter of CD. (iv) the velocity in CE. (b) An oil having viscosity of 0.05 kg/ m s flows through a 70 mm diameter pipe at an average velocity of 0.15 m/s. What pressure difference at the ends of the pipe is required for this uniform laminar flow if the length of the pipe is 60 m? (9 marks) Question 3 Derive the Bernoulli equation from the Euler equation: (b) A jet of water 15 cm in diameter is directed vertically up and reaches a maximum height of 10 m, acceleration due to gravity, 9.81 m/s. Assuming that the jet remains circular and neglecting the change in pressure along the jet, determine: (i) The volume flow rate of the water (ii) The jet diameter at a height of 8 m [Code]_SEM1_2015/2016 Page 3 of 5 Printing date: 14/11/2016
Section B Attempt TWO questions in this section Question 4 i) Draw the dependency of the drag coefficient on the Reynolds number for a sphere; ii) Describe three flow regimes for this flow; iii) Give the expressions for the drag coefficients in these regimes (b) A spherical solid particle of density 7.6 g/cm 3, when settling in a mixture of water and glycerol (density 1146 kg/m 3, viscosity 0.0084 Pa s) attains a terminal velocity of 1 cm/s. i) What is the Reynolds number of the falling sphere? ii) What should be the velocity of an air stream (density 1.24 kg/m 3, viscosity 1.7 10-5 N s m -2 ) in order to levitate the particle? iii) If the particle diameter is 1/4 of the diameter considered in the previous questions, what will be the new terminal velocity in the water-glycerol mixture? [Code]_SEM1_2015/2016 Page 4 of 5 Printing date: 14/11/2016
Question 5 i) Describe the principles of operation of the Francis Turbine ii) Show the velocity triangles for the inlet and outlet (6 marks) iii) Find the expression for the inlet velocity as a function of the blade angle at the inlet and the angle between the absolute fluid velocity and the blade velocity (b) The inlet and outlet diameters of a centrifugal impeller of a fan running at 18 rev/s, are 60 cm and 85 cm respectively. Its width at the inlet is 10 cm and that at the outlet is 8.5 cm. The blade angle at the outlet is 66, the air enters the impeller radially and the air volume flow rate is equal to 900 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 v) Euler s head Question 6 i) Draw a scheme of a reciprocating pump installation ii) Describe the energy balance of a reciprocating pump, in terms of the total energy and losses (b) A single acting reciprocating pump has a piston of 20 cm and stroke 30 cm. The pump discharges 120 l/min of water at 40 rpm. Calculate: i) Theoretical discharge of the pump 2) Coefficient of discharge 3) Slip and percentage of slip of the pump [Code]_SEM1_2015/2016 Page 5 of 5 Printing date: 14/11/2016