Fluid Mechanics - Dec 2016

Mechanical Engg (Semester 3)

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.

Solve any one question fromQ.1(a,b) and Q.2(a,b)

1(a) Distinguish between:
i) Simple manometer and differential manometer
ii) Real fluids and ideal fluids
iii) Specific weight and specific volume.(6 marks) 1(b) Determine the total pressure and cenre of pressure on an isoceless triangular plate of base 6 m when it is immersed vertically in an oil of sp. Gr 0-8. Take altitude as 4 m and base of the plate concides with the tree surface of oil.(6 marks) 2(a) State and prove Pascal's law.(6 marks) 2(b) The stream function for a two dimensional flow is given by ψ = 8xy. Calculate the velocity at the point P(4,5). Find also velocity potential function φ(6 marks)

Solve any one question fromQ3(a,b) and Q.4(a,b)

3(a) State Bernoulli's theorem for steady flow of an incompressible fluid. Derive an expression for Bernoulli's theoremfrom first principle and state assumptions made for such a derivation.(6 marks) 3(b) Find the discharge of water flowing through a pipe 30 cm diameter placed in an inclined position where a verturimeter is inserted, having a throat diameter 18 cm. The difference of pressure between the main and thorat is measured by a liquid of sp gr. 0.7 in an inverted V-tube which gives a reading of 30 cm. The loss of head between the main and thorat is 0.2 times the kinetic head of pipe.(6 marks) 4(a) State the operating principle of pitot tube and derive the equation for measurement of velocity at any point for it.(6 marks) 4(b) The water is flowing through a tapper pipe of length 80 m having diameters 600 mm at the upper end and 400 mm at the lower end at the rate of 50 litres/second. The pipe has a slope of 1 in 30. Find the pressure at lower end if the pressure at the higher level is 20.72 N/cm².(6 marks)

Solve any one question fromQ5(a,b) and Q.6(a,b)

5(a) A pipe line of length 2000 m is used for power transmission. If 110.3625 KW power is to be transmitted through the pipe in which water having a pressure of 490.5 N/cm² at inlet is flowing. Find the diameter of the pipe and efficiency of transmission if the pressure drop over the length of pipe is 98.1 N/cm². Take f = 0.0065.(7 marks) 5(b) Define and explain the terms:
i) Hydraulic gradient line
ii) Total energy line.(6 marks) 6(a) Using Buckingham's π theorem, show that the velocity through a circular orifice is given by: $V=\sqrt{29H}\phi\left [ \frac{D}{H},\frac{\mu }{\rho VH} \right ] $/
where H is head causing flow, D is diameter of orice μ is coefficient of viscosity,ρ is mass density and g is gravitational acceleration.(7 marks) 6(b) An old water supply distribution pipe of 250 mm diameter of a city is to be replaced by two parallel pipes of smaller equal diameter having equal lengths and identical friction factor values. Find out new diameter required.(6 marks)

Solve any one question fromQ.7(a,b) and Q.8(a,b)

7(a) Find the difference in drag force exerted on a flat plate of size 2 m ×2 when the plate is moving at a speed of 4 m/s normal to its plane in:
i) water
ii) air of density 1.24 kg/m³ coefficient of drag is given as 1.15.(7 marks) 7(b) Deefine the terms:
i) Lift
ii) Drag
iii) Angle of attack
iv) Camber.(6 marks) 8(a) Define displacement thickness and momentum thickness. Derive an expression for displacement thickness.(6 marks) 8(b) Find the displacement thickness, the momentum thinkness and energy thickness for the velocity distribution in the boundary layer given by:$$\frac{u}{U}=2\left ( \frac{y}{\delta } \right )-\left ( \frac{y}{\delta } \right )^2.$$(7 marks)