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## Fluid Mechanics - Dec 2013

### Mechanical Engineering (Semester 4)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Define the following terms and mention their SI units

Capillarity

Dynamic viscosity

Weight density

Bulk modulus.(6 marks)
**1 (b)** Explain the effort of temperature variation on viscosity and gases(4 marks)
**1 (c)** Two large plane surfaces are 2.4cm apart. The space between the surface is filled with glycerine.What force is required to drag a very thin plate of surface area 0.5 square meters between the two large plane surfaces at a speed of 0.6, if the thin plate is at a distance of 0.8cm from one of the plane surface? Take μ =0.81 N-s/m^{2}(7 marks)
**1 (d)** Derive an expression for surface tension of soap bubble(3 marks)
**2 (a)** Define the following :

Gauge pressure

Vacuum pressure

centre of pressure

Hydrostatic law.(8 marks)
**2 (b)** A Caisson for closing the entrance to dry dock is of trapezoidal form 16m wide at the top and 10m wide at the bottom and 6m deep. Find the total pressure and centre of pressure on the caisson if the water on the outside is just level with the top and dock is empty.(8 marks)
**2 (c)** What is a manometer ? Hoe they are classified?(4 marks)
**3 (a)** If the a two-dimensional potential flow. The velocity potential is given by φ =x(2y -1). Determine the velocity at point p(4,5). Determine also the value of stream function at the point p(10 marks)
**3 (b)** Derive an expression for metacentric height of a floating body using analytical method(10 marks)
**4 (a)** Derive an Euler\'s equation of motion for an ideal gas(8 marks)
**4 (b)** State Bernaulis theorems for steady flow of an incompressible fluid(2 marks)
**4 (c)** A pipe line carrying oil specific gravity 0.87 changes in diameter from 200mm diameter at a position A to 500mm diameter at a position B which is 4meter at higher level if the pressure at A and B are 9.81 N/cm_{2} and 5.886 N/ cm_{2} respectively and the discharge is 200 litters determine loss of head and direction of flow.(10 marks)
**5 (a)** Derive an expression for the discharge over a triangular notch In terms of water over the crest of the notch(8 marks)
**5 (b)** A 3ocm × 15cm venturimeter is provided In a vertical pipe line carrying oil specific gravity 0.9 the flow being upwards.The difference in evaluation of the throat section and entrance section of the venturimeter is 30cm.the differential U-tube mercury manometer shows a gauge deflection 0f 25 cm.calculate

the discharge of oil

the pressure different between the entrance section and the throat section.take coefficient of meter as 0.98 and specific gravity of mercury as 13.6(9 marks)
**5 (c)** What are the method of dimensional analysis ? Describe Buckingham\'s ?-theorem for dimensional analysis(3 marks)
**6 (a)** Derive an expression for the loss of head due to sudden enlargement of pipe(10 marks)
**6 (b)** Determine the difference in the elevation between the water surfaces in the two tanks which are connected by a horizontal pipe of diameter 300mm and length 400mm. The rate of flow through the pipe is 300liter/sec.consider all losses and take f = 0.008. Also draw IIGI and TEL(10 marks)
**7 (a)** Derive an expression for Hagen-Poiseullie formulae(10 marks)
**7 (b)** An oil of velcosity 0.1 N//m_{2} and relative density 0.9 is flowing through a circular pipe of diameter 50mm and length 300m. The rate of flow of fluid through the pipe is 3.5 litre/sec.Find the pressure drop in a length of 300m and also the shear stress the pipe wall(10 marks)
**8 (a)** Define term

Drag

Lift

Displacement thickness

Boundary layer thickness

Energy thickness(10 marks)
**8 (b)** For the velocity profile for laminar boundary layer flows given as $$\dfrac{u}{U}=2\left(\dfrac{y}{\delta}\right)-\left(\dfrac{y}{\delta_2}\right)$$

Find an expression for boundary layer thickness (δ). Shear stress (?)interns of Reynolds number(10 marks)