## Fluid Mechanics - Dec 2015

### 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 from Q1 and Q2

**1 (a)** State and explain Newton's law of viscosity. Explain the importance of viscosity in fluid motion.(6 marks)
**1 (b)** The velocity potential function is given by an expression: $$ \phi = - \dfrac {xy^3}{3} - x^2 + \dfrac {x^3 y}{3} + y^2 $$ i) Find the velocity components in x and y directions.

ii) Show that ϕ represents a possible case of flow.(6 marks)
**2 (a)** Explain the following terms:

i) Path line

ii) Streak line

iii) Stream line and

iv) Equipotential line.(6 marks)
**2 (b)** What is metacentre and metacentric height? Explain their significance for floating and submerged bodies.(6 marks)

### Solve any one question from Q3 and Q4

**3 (a)** Define HGL and TEL. Draw a neat diagram of venturimeter and show HGL and TEL for it.(6 marks)
**3 (b)** An oil of viscosity 0.1 Ns/m^{2} and relative density 0.9 is flowing through a circular pipe of diameter 50 mm and of length 300 m. The rate of flow of fluid through the pipe is 3.5 lit/sec. Find the pressure drop in a length of 300 m and also the shear at the pipe wall.(6 marks)
**4 (a)** The inlet and throat diameter of a horizontal venturimeter are 30 cm and 10 cm respectively. The liquid flowing through the meter is water. The pressure intensity at inlet is 13.734 N/cm^{2} while the vaccum pressure head at the throat is 37 cm of mercury. Find the rate of flow. Assume that 4% of the differential heads is lost between the inlet and outlet. Find also the value of Cd for the venturimeter.(6 marks)
**4 (b)** Prove that the maximum velocity in a circular pipe for viscous flow is equal to two times the average velocity of the flow.(6 marks)

### Solve any one question from Q5 and Q6

**5 (a)** Derive Darcy Weisbach equation to calculate loss of head due to friction in pipe.(6 marks)
**5 (b)** The frictional torque T of a disc of diameter D rotating at a speed N in a fluid of viscosity μ and density ρ in a turbulent flow is given by: $$ T=D^5N^2 \rho \phi \left [ \dfrac {\mu}{D^2 N \rho} \right ] $$ Prove this relation using Buckingham's π-theorem.(7 marks)
**6 (a)** What do you mean by repeating variables? How are the repeating variables selected for dimensional analysis?(5 marks)
**6 (b)** A pipeline of length 2 km 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.(8 marks)

### Solve any one question from Q7 and Q8

**7 (a)** Explain the following terms:

i) Laminar boundary layer

ii) Laminar sub-layer and

iii) Boundary layer thickness.(6 marks)
**7 (b)** A jet plane which weighs 29.43 kN and having awing area of 20 m^{2} files at a velocity of 950 km/hr, when the engine delivers 7357.5 kW power. 65% of the power is used to overcome the drag resistance of the wing. Calculate the coefficient of lift and drag for the wing. The density of the atmospheric air is 1.21 kg/m^{3}.(7 marks)
**8 (a)** What are the different methods of preventing the separation of boundary layers?(4 marks)
**8 (b)** Explain the terms:

i) Friction drag

ii) Pressure drag.(4 marks)