SREENARAYANAGURU MEMORIAL EDUCATIONAL TRUST’SK R GOURIAMMA COLLEGE OF ENGINEERING FOR WOMENValamangalam South P.O, Thuravoor, Alappuzha, Kerala

SECOND SERIES B.TECH.EXAMINATION – SEPT 2011

FLUID MECHANICS – I

Time: 1.00 hour Max. Marks: 50 Part-A Answer all questions. (5*4marks = 20)

1. Define the terms : ( i ) Metacentre ( ii ) Metacentric height 2. Define the terms : ( iii ) Buoyancy ( iv ) Centre of buoyancy. 3. What do you understand by the term Pressure diagram? With the help of pressure diagram derive the equation for total force & centre of pressure for vertical plane surface submerged in liquid ? 4. Determine the total pressure and centre of pressure on an isosceles triangular plate of base 4 m and altitude 4 m when it is immersed vertically in an oil of specific gravity 0.9 . The base of the plate coincides with the free surface of oil.

Part – B Any Two (15*2marks = 30)

1. (a) Discuss the conditions of stability of floating and submerged bodies? (6 marks)

(b) An annular plate 3 m external diameter and 1.5 m internal diameter is immersed in water with its greatest and least depths below water surface as 3.6 m and 1.2 m respectively. Determine the total pressure and the position of the centre of pressure on one face of the plate. (9 marks)

OR

2. (a) A wooden cylinder of circular section and uniform density. specific gravity 0.6 is required to float in oil of specific gravity 0.8 .If the diameter of the cylinder is d and its length is l , show that l cannot exceed about 0.817d for cylinder to float with its longitudinal axis vertical. (5 marks)

(b) In finding the metacentre of a ship of 98.1 MN (10000 tonnes) displacement, a weight of 490.5 KN (50 tonnes ) at a distance of 6 m from the longitudinal centre plane causes the ship to heel through an angle of 3. What is the

metacentric height? Hence find the angle of heel and its direction when the ship is going ahead and 2.8336 MW (3850 metric H.P.) is being transmitted to a single propeller shaft which is rotated at a speed of 3 rad/s ( 90 r.p.m). (5 marks)

(c)Derive the expression for experimental method for determination of metacentric height. (5 marks)

OR

3. (a) Derive the expression for hydrostatic forces acting on a vertical plane surface submerged in liquid. (6 marks)

(b) The figure given below shows the cross-section of a tank full of water under pressure. The length of the tank is 2 m.An empty cylinder lies along the length of the tank on one corner as shown in the figure. Find the magnitude and location of the horizontal and vertical components of the force acting on the curved surface ABC of the cylinder. Also compute the magnitude of this force and locate its line of action as well as point of application. (9 marks)