## Fluid Mechanics - Dec 2012

### 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.

### Attempt any **four**:-

**1 (a)** Define a fluid and distinguish between:

(i) Ideal and real fluids

(ii) Compressible and incompressible fluids(5 marks)
**1 (b)** State and explain the principle of floatation. How does it differ from the principle of buoyancy?(5 marks)
**1 (c)** Differentiate between Eulerian and Lagrangian method of representing fluid motion. (5 marks)
**1 (d)** Write a note on major and minor losses in pipes.(5 marks)
**1 (e)** Discuss the phenomenon of boundary layer separation.(5 marks)
**2 (a)** Starting from Navier Stokes equation for an incompressible Newtonian fluid derive Bernoulli's equation stating the assumptions.(10 marks)
**2 (b)** A large thin plate is pulled at a constant velocity 'U' through a narrow gap of height 'h' on one side of plate is oil of viscosity '�' and on the other side of the plate 'α�' where α is constant. Calculate the position of plates so that the drag force will be minimum.(10 marks)
**3 (a)** A sliding gate 3m wide and 1.5 m high situated in vertical plane has a coefficient of friction between itself and guide of 0.18. If the gate weight is 19 kN and if its upper edge is at a depth of 9m. What vertical force is required to raise it? Neglect buoyancy force on gate. (10 marks)
**3 (b)** Derive Darcy-weisbach equation and its utility.(10 marks)
**4 (a)** Using the laminar boundary layer velocity distribution:

Check if boundary layer separation occurs. Also determine in terms of Reynold's number.

(i) Boundary layer thickness.

(ii) Shear stress at surface.

(iii) Local coefficient of drag.

(iv) Average coefficient of drag.(12 marks)
**4 (b)** Write a note on Prandtl's mixing length theory.(4 marks)
**4 (c)** Two horizontal plates are placed 1.25 cm apart, the space between them being filled with oil of viscosity 14 poise. Calculate the shear stress in oil if upper plate is moved with a velocity of 2.5 m/s.(4 marks)
**5 (a)** Consider a two dimensional viscous incompressible flow of a Newtonian fluid between two parallel plates, separated by a distance 'c'. One of the plates is stationary and other is moving with a uniform velocity V. There is no pressure gradient in the flow. Obtain the governing equations from the general Navier stokes equations. Discretize the equation. Specify the boundary condition for a CFD solution. (15 marks)
**5 (b)** A stream function is given by Ψ=5x-6y. Calculate the velocity components and also magnitude and direction of the resultant velocity at any point.(5 marks)
**6 (a)** Explain the Reynold's transport theorem with its proof. (12 marks)
**6 (b)** A lubricating oil of viscosity 1 poise and specific gravity 0.9 is pumped through a 30mm diameter pipe. If the pressure drop per meter length of pipe is 20KN/m^{2}, determine:

(i) Mass flow rate in kg/min.

(ii) Shear stress at the pipe wall.

(iii) Reynold's number of flow.(8 marks)
**7 (a)** Derive the continuity equation in Cartesian coordinates. The diameter of a pipe at the sections 1 and 2 are 10cm and 15cm respectively. Find the discharge through a pipe if the velocity of water flowingthrough the pipe at section 1 is 5m/s. Also determine the velocity at section 2. (8 marks)
**7 (b)** State and derive hydrostatics law.(6 marks)
**7 (c)** Define path lines, stream lines and streak lines.(6 marks)