## Fluid Mechanics - May 2016

### 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.

### Solve any FOUR

**1(a)** Define a fluid and explain Newton's law of viscosity(5 marks)
**1(b)** Explain boundary layer separation and methods to control it(5 marks)
**1(c)** A two dimensional flow is described in the Lagrangian system as

x = x_{0}e^{-kt} + y_{0} (1-e^{-2kt}) and y = y_{0}e^{-kt}.

Find the equation of a fluid particlein the flow field(5 marks)
**1(d)** Explain Induced drag(5 marks)
**1(e)** Draw a sketch of an Orifice meter(5 marks)
**2(a)** Find the magnitude and direction of resultant pressure acting on a curved face of a dam which is shaped according to the relation y = x^{2}/9 as shown in the figure. The height of the water retain by the dam is 10m. Consider the width of the dam as unity.

**2(b)**The stream lines is represented by Ψ = x

^{2}+y

^{2}

(i) Find its corresponding velocity potential

(ii) Determine the velocity and its direction at (2,2)

(iii) Sketch the streamlines and also show the direction of flow.(10 marks)

**3(a)**Starting from Navier stoke equation for incompressible laminar flow; derive an equation for velocity profile for Couette flow. State the assumptions made.(10 marks)

**3(b)**360 lit/sec of water is flowing in a pipe. The pipe is sent by 120°. The pipe bend measure 360 mm × 240 mm and volume at the bend is 0.14m

^{3}. The pressure at the entrance is 73 KN/m

^{2}and exit is 2.4m above the entrance section. Find the resultant force and the direction on the bend(10 marks)

**4(a)**If velocity distribution, u in laminar boundary layer over a flat plate is assumed to be given by second order polynomial

u = a + by + cy

^{2}

where y is the perpendicular distance measured from the surface of the flat plate, and a, b and c are constant. Determine the expression of velocity distribution in dimensionless form as, U is main stream velocity at boundary layer thickness δ. Further also find boundary layer thickness in terms of Reynolds number.(10 marks)

**4(b)**A pipe 60 mm diameter and 450 m long slopes upwards at 1 in 50 an oil of viscosity 0.9 Ns / m

^{2}and sp. gr. 0.9 is required to be pumped at the rate of 5 liters/s

(1) Is the flow laminar?

(2) What pressure difference is required to attain this condition?

(3) What is the power of the pump required assuming overall efficiency 65%?

(4) What is the centre line velocity and the velocity gradient at pipe wall?(10 marks)

**5(a)**Foe a normal shock wave in air Mach number is 3. If the atmospheric pressure and air density are 26.5 KN/m

^{2}and 0.413 kg/m

^{3}respectively, determine the flow conditions before and after the shock wave. Tank γ = 1.4(10 marks)

**5(b)**Derive an expression of 'critical pressure ratio' for compressible fluid flow(10 marks)

**6(a)**A pipe pf diameter 0.4 m and of length 2000 m is connected to a reservoir at one end. The other end of the pipe is connected to a junction from which two pipes of length 1000m and diameter 30 cm runs parallel. These parallel pipes are connected to another reservoir which is having a level of water 10m below the water level of the above reservoir. Determine the total discharge, if coefficient of friction f=0.015.neglect the minor losses.(10 marks)

**6(b)**Explain

(i) Moodys Diagram

(ii) Major and Minor losses in pipes.(10 marks)