No. of Printed Pages : 6 BME-028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) Term-End Examination December, 2011 00792 BME-028 : FLUID MECHANICS Time : 3 hours Maximum Marks : 70 Note : Answer any seven questions. Use of scientific calculator is permitted. 1. (a) The specific gravity of a liquid is 3.0, what 5+5 are its specific weight, specific mass and specific volume? (b) An iceberg weighing 8976 N/m 3 floats in the ocean with a volume of 600 m 3 above the surface. Determine the total volume of the iceberg if specific weight of ocean water is 10055 N/m 3. BME-028 1 P.T.O.
2. (a) For a two dimensional flow 5+5 431 = 3 xy and (y2 x2 ) 2 Determine the velocity components at the points (1, 3) and (3, 3). Also find the discharge passing between the streamlines passing through the points given above. (b) Calculate the unknown velocity components so that they satisfy continuity equation : u = 2x2 ; v = xyz ; w =? 3. (a) Define and distinguish between (any two) : 5+5 (i) steady and unsteady flow ; (ii) uniform and non-uniform flow ; and (iii) rotational and irrotational flow ; (b) Determine which of the following velocity fields represent possible case(s) of an irrotational flow. (i) u = Cx v= Cy (ii) u = C Y v =C log (xy) BME-028 2
4. (a) Calculate the velocity components u and v 5+5 for the following velocity potential function = sin x sin y. Does this velocity potential function is satisfy the continuity equation? (b) If the expression for the stream function is described by = x3 _ 3xy2, indicate whether the flow is rotational or irrotational. If the flow is irrotational, determine the value of the velocity potential. 5. (a) A venturimeter is to be fitted in a pipe of 5+5 0.25 m diameter where the pressure head is 7.6 m of flowing liquid and the maximum flow is 8.1 m3 per minute. Find the least diameter of the throat to ensure that the pressure head does not become negative. Take K =0.96. (b) State and derive Bernoulli's theorem, mentioning clearly the assumptions underlying it. BME-028 3
(a) A jet of water issues from a sharp edged 5+5 vertical orifice under a constant head of 0.51 m. At a certain point of issuing jet, the horizontal and vertical coordinates measured from the vena-contracta are 0.406 m and 0.085 m respectively. Determine Cv, if Cd = 0.62. Also find Cc. (b) Explain the terms hydraulic gradient line and total energy line. 7. (a) What do you understand by displacement 5+5 thickness and momentum thickness? (b) Oil of viscosity 0.1 Pas and specific gravity 0.90, flows through a horizontal pipe of 25 mm diameter. If the pressure drop per metre length of the pipe is 12 kpa, determine (i) (ii) the rate of flow the shear stress at the pipe wall (iii) the Reynolds number of the flow ; 8., (a) What do you understand by 5+5 hydrodynamically smooth and rough boundaries? BME-028 4 P.T.O.
(b) Explain the terms : (i) (ii) Force of buoyancy, and Centre of buoyancy. 9. (a) Assuming that rate of discharge Q of a 5+5 centrifugal pump is dependent upon the mass density p of fluid, pump speed N(rpm), the diameter of impeller D, the pressure p and the viscosity of fluid show using the Buckingham's Tr-theorem or Rayleigh's method that it can be represented by g (2--- ( -(ND3) (I)[(N2HD2 N1)2 A where H = head, and V = kinematic viscosity of the fluid. (b) Show that the centre of pressure of any lamina immersed under liquid is always below its centroid. 10. (a) A circular disc 3 m in diameter is held 5+5 normal to a 26.4 m/s wind of density 1.2 kg/m3. What force is required to hold it at rest. Assume co-efficient of drag of disc to be 1.2. BME-028 5 P.T.O.
(b) The velocity distribution in the boundary layer is given as u = 3 y_ 11y12 U 2 6 ) 2 6 ) Compute (w 6* ) and I 0 where 6* = Displacement thickness, and 0 = Momentum thickness. BME-028 6