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## Fluid Mechanics - Dec 2014

### Mechanical Engineering (Semester 4)

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)** Define the following fluid properties

i) Density ii) Specific volume iii) Specific gravity iv) Kinematic viscosity v) Capillarity(5 marks)
**1 (b)** The pressure outside the droplet of water of diameter 0.04 mm is 10.32 N/cm^{2} (atmospheric pressure). Calculate the pressure within the droplet if surface tension is given as 0.725 N/m of water.(5 marks)
**1 (c)** Calculate the capillary effect in mm in a glass tube of 4mm diameter, when immersed in Hg. The temperature of liqiud is 20°C and surface tension of Hg at 20°C in contact with air is 0.51 N/m. Angle of contact is 130° (specific gravity of Hgis 13.6).(5 marks)
**1 (d)** Determine the specific gravity of fluid having viscosity 0.05 poise and kinematic viscosity 0.035 stokes.(5 marks)
**2 (a)** State and prove Pascal's law(5 marks)
**2 (b)** The right limb of a simple U tube manometer containing Hg is open to the atmosphere while the left limb is connected to a pipe in which a fluid of specific gravity 0.9 is flowing. The center of pipe is 12 cm below the level of Hg in the right limb. Find the pressure of fluid in the pipe if the difference of Hg level in two limbs is 20cm.(5 marks)
**2(c)** A caisson for closing the entrance to a dry dock is of trapezoidal form 16 m wide the top and 10m wide at bottom and 6 m deep. Find the total pressure and center of pressure on the caisson, if the water on the outside is just level with the tap and dock is empty.(10 marks)
**3 (a)** Define : i) Buoyancy, ii)Centre of buoyancy , iii) Path line, iv) Laminar flow, v) Turbulent flow.(5 marks)
**3 (b)** A body of dimension 1.5m× 1.0m × 2m weight 1962 N in water. Find its weight in air. What will be its specific gravity?(5 marks)
**3 (c)** A 25 cm diameter pipe carrier oil of specific gravity 0.9 at a velocity of 3 m/s. At another section the diameter is 20 cm. Fine the velocity at this section and mass rate of flow of oil.(10 marks)
**4 (a)** What is Euler's equation of motion? How will you obtain Beroulli's equation from it?(10 marks)
**4 (b)** The water is flowing through a taper pipe of length 100 m having diameters 600mm at the upper end and 300 mm at the lower end, at the rate of 50. The pipe has slope of 1 in 30. find the pressure at the lower end if the pressure at the higher level is 19.62 N/cm^{2}.(10 marks)
**5 (a)** Sketch and derive yhe equation relation for actual discharge through an orifice meter.(10 marks)
**5 (b)** State Buckingham's $$\pi $$ theorem. The efficiency $$\eta$$ of a fan depends on density $$\rho $$, dynamic viscosity $$\mu $$ of the fluid , angular velocity $$\varpi $$, diameter D, discharge Q. Express $$\eta$$ in term of dimensionless parameters.(10 marks)
**6 (a)** Derive the Darcy-Weisbach equation for the loss of head due to friction in pipr.(10 marks)
**6 (b)** Find the head lost due to friction in a pipe of diameter 300 mm and length 50 m through which water is flowing at a velocity of 3 m/s using : i) Dancy's formula ii) Chezy's formula for which C=60.(10 marks)
**7 (a)** Define Reynold's number. What is its significance?(4 marks)
**7 (b)** Derive Hagen Poisoulle's equation for viscous flow through a circular pipe.(10 marks)
**7 (c)** An oil of viscosity 10 poise flows between two parallel fixed plates which are kept at a distance of 50 mm apart. Find the rate of flow of oil between the plates if the drop of pressure in a length of 1.2 m be 0.3/cm^{3}. The width of plates is 200mm.(6 marks)
**8 (a)** Explain terms: i) Lifts ; ii) Drag: iii) Displacement thickness; iv) Momentum thickness.(8 marks)
**8 (b)** Define the terms subsonic flow and supersonic flow.(4 marks)
**8 (c)** A flat plate 1.5m × 1.5 m moves at 50 km/hr in stationary air of density. 1.15 kg/m^{3}. If the co efficient of drag and lift are 0.15 and 0.75 respectively. Determine : i) lift force; ii) drag force; iii) resultant force.(8 marks)