## 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/cm^{2}.(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/cm^{2} 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/cm^{2}. 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/m^{3} 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)