## Fluid Mechanics - May 2014

### Mechanical Engineering (Semester 4)

TOTAL MARKS: 80

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

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

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1(a)** What do you mean by boundary layer and boundary layer thickness?(5 marks)
**1(b)** What is pitot tube? On what principle does it works?(5 marks)
**1(c)** Two horizontal plates are placed 1.25 cm apart, the space between them being filled with with oil of viscosity 14 poise.calculate the shear stress in oil if upper plate is moved with a velocity of 2.5m/s(5 marks)
**1(d)** The barometric pressure at sea level is 760 mm of mercury while that on a mountain top is 725mm, if the density of air is assumed constant at 1.19 kg/m^{3},what is the elevation of the mountain top.(5 marks)
**2(a)** A sliding gate 3m wide and 1.5m hgh situated in a vertical plane has a coefficient of friction between itself and guide of 1.18.if the gate weight is 19kN and if its upper edge is at a depth of 9m,what vertical force is required to raise it? Neglected buoyancy force on gate(10 marks)
**2(b)**

Using the laminar boundary layer velocity distribution: $\dfrac{u}{V}=2\left(\dfrac{Y}{\delta}\right)-\left(\dfrac{Y}{\delta}\right)^{2}$

i) Check if boundary layer separation occurs.

ii) Determine Boundary layer thickness(In terms of Re)

(10 marks)
**3(a)** Derive Euler's equation for three dimensions.(12 marks)
**3(b)** An oil of specific gravity 0.8 flows upwards through a vertical pipe.A & B are two points in the pipe,B being 30cm higher than A.Connections are led from A &B to a U-tube containing mercury.If the difference of pressure between A & B is 0.18kg/cm^{2}. Find the reading shown by the differential manometer(8 marks)
**4(a)** Starting from Navier stokes equation for incompressible laminar flows derive an equation for velocity profile for Couette flow.state the assumption made(10 marks)
**4(b)** Derive Darcy-Weisbach equation and state its utility(10 marks)
**5(a)** Explain Reynold's transport theorem with its proof(10 marks)
**5(b)** A liquid of viscosity of 0.88 poise is filled between two horizontal plates 10mm apart.If the upper plate moving at 1.1 m/s with respect to lower plate is stationary and pressure and pressure difference the two section 60m apart is 60 KN/m^{2},determine:

i) Velocity distribution

ii) Discharge per unit width, and

iii) shear stress on the upper plate.
(10 marks)
**6(a)** Three pipes of diameter 300mm,200mm,&400mm and length 450m,250m,& 315m respectively are connected in series.The difference in water surface levels in two tanks is 18m.Determine the rate of flow of water if coefficient of friction are 0.0075,0.0078 & 0.0072 respectively(Consider minor losses)(10 marks)
**6(b)** A uniform flow of velocity 6m/s is flowing along x axis over a source & sink which are situated along x axis.the strength of source and slink is 15m^{2}/s and they are at a distance of 1.5m apart.Determine

i) Location of stagnation points

ii) Length & width of the ranking oval

iii) Equation of profile of the Rankine body
(10 marks)

### Distinguish between (any three).

**7(a)(i)** Streamlined and Buff bodies(4 marks)
**7(a)(ii)** Implicit and Explicit schemes(4 marks)
**7(a)(iii)** Structured and untrusted and unstructured grid.(4 marks)
**7(a)(iv)** Finite Volume Method and finite Difference Method(4 marks)
**7(b)(i)** Write Short note on the following - Elbow Meter(4 marks)
**7(b)(ii)** Write Short note on the following - Moody's Diagram(4 marks)