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## Fluid Mechanics - Jun 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 find properties and state their units:

i) Specific weight

ii) Viscosity

iii) Surface tension

iv) Specific volume.(6 marks)
**1 (a)** Define the following fluid properties and state their units: i) Specific weight ii) Viscosity iii) Surface tension iv) Specific volume(6 marks)
**1 (b)** Classify the various types of fluids with the help of a diagram and briefly explain them.(5 marks)
**1 (b)** Classify the various types of fluids with the help of a diagram and briefly explain them.(5 marks)
**1 (c)** An oil film of thickness 1.5 mm is used for lubrication between a square plate of size 0.9×0.9 m and an inclined plane having an angle of inclination 20° with the horizontal. The weight of the square plate is 392.4 N and it slides down the plane with a uniform velocity of 0.2 m/s. Find the dynamics viscosity of oil.(9 marks)
**1 (c)** An oil film of thickness 1.5 mm is used for lubrication between a square plate of size 0.9m × 0.9m and an inclined plane having an angle of inclination 20° with the horizontal. The weight of the square plate is 392.4N and it slides down the plane with a uniform velocity of 0.2m/s. Find the dynamic viscosity of oil.(9 marks)
**2 (a)** State and prove hydrostatic law.(6 marks)
**2 (a)** State and prove hydrostatic law.(6 marks)
**2 (b)** The measurements of pressure at the base and top of a mountain are 74 cm and 60 cm of mercury respectively. Calculate the height of the mountain if air has a mass density of 1.22 kg/m^{3}.(6 marks)
**2 (b)** The measurements of pressure at the base and top of a mountain are 74 cm and 60 cm of mercury respectively. Calculate the height of the mountain if air has a mass density of 1.22 kg/m^{3}.(6 marks)
**2 (c)** Derive expression for total pressure and centre of pressure for a plane surface immersed vertically in a static mass of fluid.(8 marks)
**2 (c)** Derive expressions for total pressure and centre of pressure for a plane surface immersed vertically in a static mass of fluid.(8 marks)
**3 (a)** Define the terms buoyancy, center of buoyancy, meta-centre and meta-centric height.(6 marks)
**3 (a)** Define the terms buoyancy. Center of buoyancy, meta-center and meta-centric height.(6 marks)
**3 (b)** A block of wood of specific gravity 0.8 floats in water. Determine the meta-centric height of block if its size is 3 m long. 2 m wide and 1 m height. State whether equilibrium is stable or unstable.(8 marks)
**3 (b)** A block of wood of specific gravity 0.8 floats in water. Determine the meta-centric height of bloack if its sizes is 3 m long, 2 m wide and 1m height. State wheather equilibrium is able or unstable.(8 marks)
**3 (c)** Derive continuity equation in Cartesian coordinates.(6 marks)
**3 (c)** Derive continuity equation in Cartesian coordinates.(6 marks)
**4 (a)** Derive Euler's equation of motion for ideal fluids and hence deduce Bernoulli's equation of motion. State the assumption made.(10 marks)
**4 (a)** Derive Euler's equation of motion for ideal fluids and hence deduce Bernoulli's equation of motion. State the assumptions made.(10 marks)
**4 (b)** A pipe line carrying oil of specific gravity 0.8 changes in diameter from 300 mm at position (1) to 600 mm in diameter at position (2), which is 5 m at a higher level. If the pressure at position (1) and (2) are 100 kN/m^{2} respectively and discharge is 300 lps. Determine (i) loss of head and (ii) directions of flow.(10 marks)
**4 (b)** A pipe line carrying oil of specific gravity 0.8 changes in diameter from 300mm at position (1) to 600mm in diameter at position (2), which is 5 m at a higher level. If the pressure at position (1) and (2) are 100 kN/m^{2} respectively and discharge is 300ps. Determine (i) loss of head and (ii) direction of flow.(10 marks)
**5 (a)** Derive an expression for discharge through a venturi-meter.(8 marks)
**5 (a)** Derive an expression for discharge through a venturi-meter.(8 marks)
**5 (b)** State Buckingham's theorem.(4 marks)
**5 (b)** State Buckingham's $$\pi $$ theorem.(4 marks)
**5 (c)** The frictional torque 'T' of a disc of diameter 'D" rotating at a speed of 'N' in a fluid of velocity '°' and density '?' in a turbulent flow is given by $$ T=D^2N^2 \rho \phi \left [ \dfrac {M}{D^2 n \rho} \right ] $$ . Prove this relation using Buckingham's ? theorem.(8 marks)
**5 (c)** The frictional torque 'T' of a disc of diameter 'D' rotating at a speed of 'N' in a Fluid of viscosity '$$\mu$$ and density $$\rho$$ in a turbulent flow is given by T=$$D^{2}N^{2} \rho \phi \left [ \frac{M}{D^{2}N\rho } \right ]$$ Prove this relation using Buckingham's \pi theorem.(8 marks)
**6 (a)** Derive Darcy's relation for a turbulent flow through a circle pipe.(10 marks)
**6 (a)** Derive Darcy's relation for a turbulent flow through a circular pipe.(10 marks)
**6 (b)** Find the diameter of a pipe of length 2000 m when the rate of flow of water through the pipe is 200 lps and head lost due to friction is 4,. Take the value of 'C'=50 in Chezy's formula.(10 marks)
**6 (b)** Find the diameter of a pipe of length 2000m when the rate of flow of water through the pipe is 200 $$\iota $$ps and head lost due to friction is 4m. Take the value of 'C'=50 in Chezy's formula.(10 marks)
**7 (a)** Prove that the ratio of maximum velocity a verage in a viscous flow of fluid through a circular pipe is 2.0.(10 marks)
**7 (a)** Prove that the ratio of maximum velocity to average velocity in a viscous flow of fluid through a circular pipe is 2.0.(10 marks)
**7 (b)** Lubricating oil of specific gravity 0.85 and dynamic viscosity 0.1 N-s/m^{2} is pumped through a 3cm diameter pipe. If the pressure drop per meter length of the pipe is 15 kPa. Determine

i) The mass flow rate of oil in kg/min

ii) The shear stress at the pipe wall.

iii) Reynolds number of the flow and

iv) The power required per 40m length of the pipe to maintain the flow.(10 marks)
**7 (b)** Lubricating oil of specific gravity 0.8 and dynamic viscosity 0.1N-s/m^{2>/sup> is pumped through a 3cm diameter pipe. If the pressure drop per meter length of the pipr is 15 kPa, determine : i) The mass flow rate of oil in kg/min. ii) The shear stress at the pipe wall. iii)Reynolds number of the flow and iv) The power required per 40m length of the pipe to maintain the flow.}(10 marks)
**8 (a)** The experiments were conducted in a wind tunnel with a wind speed of 50 km/hr on a flat plate of size 2m long and 1m 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) Lift force

ii) Drag force

iii) The resultant force

iv) Direction of resultant force

v) Power exerted by air on plate.(10 marks)
**8 (a)** The experiments were conducted in a wind tunnel with a wind speed of 50 km/hr on a flat and drag are 0.75 and 0.15 respectively. Determine:

i) Lift force

ii)Drag force

iii) The resultant force

iv) Direction of resultant force.

v) Power exerted by air on plate.(10 marks)
**8 (b)** Briefly explain, what is meant by boundary layer and hence define,

i) Displacement thickness

ii) Momentum thickness(6 marks)
**8 (b)** Briefly explain, what is meant by boundary layer and hence define,

i) Displacement thickness

ii) Momentum thickness(6 marks)
**8 (c)** Define Mach number and derive an expression for the same.(4 marks)
**8 (c)** Define Mach number and derive an expression for the same.(4 marks)