## Fluid Mechanics - Jun 2014

### 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.
**1 (a)** Give reasons:

i) Dynamic viscosity of gases varies with temperature.

ii) Cavitation must be avided in most of the flow systems.(4 marks)
**1 (b)** Derive the relation for pressure intensity and the surface tension, in case of soap bubble.(4 marks)
**1 (c)** Determine the density and mass of air in a room whose dimensions are 4m × sm× 6m at 100kPa and 25°C. Take R=287J/kg K.(4 marks)
**1 (d)** The viscosity of the fluid to be measured by a viscometer constructed of two 75cm long concentric cylinders. The outer diameter of the inner cylinder is 15cm, and the gap between the two cylinder is 1mm. The inner cylinder is rotated at 300rpm, and torque is measured to be 0.8 N-m. Determine the viscosity of the fluid.(8 marks)
**2 (a)** Differentiate between absolute, gauge and vacum pressure. Represent these pressures on a chart(4 marks)
**2 (b)** Derive the expression for total pressure force and depth of center of pressure for a vertical plane surface submerged in liquid.(10 marks)
**2 (c)** A differential manometer is connected at the two points A and B of two pipes as shown in the fig Q2(c). The pipe A contains a liquid of Ap. Gravity=1.5 while pipe B contains a liquid of specific gravity=0.9. the pressure at A and B are 9.81N/cm^{2} and 17.66 N/cm^{2>} respectively. Find the difference in mercury level in the differential manometer. Take sp. Gravity of mercury=13.6

img(6 marks)
**3 (a)** Differentiate between

i) Steady and uniform flow.

ii) Laminar and turbulent flow.

iii) Compressible and incompressible flow.

iv) Centre of buoyancy and centre of gravity.(8 marks)
**3 (b)** A wooden block of size 6m × 5m× 3m height floats in fresh water. Find the depth of immersion and the distance between centre of Buoyancy and centre of gravity (BG). Specific gravity of wood is 0.7.(4 marks)
**3 (c)** An idealized flow is given by V=2x^{3}i-3x^{2}yj. Is the flow steady or unsteady? Determine the resultant acceleration of the fluid particle at point P(x,y,x)=(2,1,3).(8 marks)
**4 (a)** State and drive Bernoulli's equation for fluid flow. State the limitation on the use of Bernoulli's theorem(12 marks)
**4 (b)** Water is flowing through a pipe having diameters 30cm and 15 cm at the bottom and upper end respectively. The intensity pf pressure at the bottom end is 29.43 N/cm^{2} and the pressure at the upper end is 14.715 N/cm^{2}. Determine the difference in datum head if the rate of flow through pipe is 0.05m^{3}/s.(8 marks)
**5 (a)** Sketch and derive the relation for actual discharge through a venturimeter.(8 marks)
**5 (b)** Find the discharge over a triangular notch of angle 60° when the head over the triangular notch is 0.2m. Take C_{d}=0.6(4 marks)
**5 (c)** The variable controlling the motion of a floating vessel through water are the drag force F, the speed V, the length L, the density \delta , the dynamic viscosity u of water and acceleration due to gravity g. Derive an expression for F by dimensional analysis. Use Buckingham \pi theorem.(8 marks)
**6 (a)** Derive the Darcy-Weisbach equation for the loss of head due to friction in a pipe.(10 marks)
**6 (b)** Sketch the TEL and HGL for a pipeline connecting two reservoirs.(4 marks)
**6 (c)** A 5cm diameter pipe takes off from a large tank and runs 8m, then suddenly expands to 10cm diameter and runs 45m, and next discharge directly into atmosphere with a velocity of 1.5 m/s. Compute the necessary height of water surface in the tank above the point of discharge. Consider all the monitor losses. Take f=0.0065 in the Darcy equation.(6 marks)
**7 (a)** What do you mean by viscous flow>(2 marks)
**7 (b)** Prove that, in a laminar flow through pipr, velocity distribution across the section of the pipe is parabolic. Also sketch the velocity distribution and shear stress distribution across a section of pipe.(10 marks)
**7 (c)** Determine i) The pressure gradient ii) The shear stress at the two horizontal parallel plates and iii) Discharge per meter width for the laminar flow of oil with a maximum velocity of 2m/s between two horizontal parallel fixed plate which are 100mm apart, Given \mu =2.4525 Ns/m^{2}(8 marks)
**8 (a)** Experiments were conducted in a wind tunnel with a wind speed of 50km/hr on a flat plate of size 2m long and 1 m wide. The density of air is 1.15 kg/m^{3}. The coefficients of lift and drag are 0.75 and 0.15 respectively. Determine i)the lift force; ii) the drag force; iii) the resultant force; iv) the direction of resultant force; v) power exerted by air on the plate.(10 marks)
**8 (b)** Differentiate between i) Sonic flow, subsonic flow, supersonic flow ii) Match number, mach angle mach cone.(6 marks)
**8 (c)** Determine the match number and mach and match angle, if a projectile travels in air of pressure 10.1043 N/cm^{3} at 10°C at a speed of 1500 km/hr. Take K=1.4 and R=287 J/kg K.(4 marks)