06 ME 36B/ 06 ME 46B USN

III Sem B E Examination

FLUID MECHANICS [ Common to ME / IP / IM / AU / MA ] MODEL QUESTION PAPER Time: 3 Hrs.]

[Max. Marks: 100

Time : 3 hrs.

Max. Marks : 100 (Answer any FIVE questions selecting at least two from each part) PART A

1.

a) Define compressibility and derive an expression for bulk modulus of elasticity for a perfect gas undergoing isentropic process. b) Define surface tension and show that the gauge pressure within a liquid droplet varies inversely with the diameter of the droplet. c) A shaft of 0.1 m diameter rotates at 60 rpm in a 0.2 m long bearing. Taking that the two-surfaces are uniformly separated by a distance of 0.5 mm and taking linear and taking linear velocity distribution in a lubricating oil having dynamic viscosity of 4 CP, find the power absorbed in the bearing.

2. a) Derive an expression for the total pressure force & the depth of centre of pressure for an inclined surface submerged in water. b) Clearly explain how metacentric height is determined analytically. c) A uniform body of size 3 m long & 2 m wide & 1 m deep floats in water. What is the weight of the body if depth of immersion is 0.8 m. Determine the metacentric height for roll along the longitudinal axis of the body 3.

a) Define (i) Stream line (ii) Path line (iii) Rotational flow (iv) Compressible flow (v) Steady & Unsteady flow b) Define & explain briefly the velocity potential & stream function. c) Define convective & local acceleration. Find the acceleration components at a point (1,1,1) in a flow field described by u = 2x2 + 2y, v = 2xy + 3y2 + 3yz, w = 3/2 z2 + 2xz – 9y2z Describe Bucking ham’s method or p-Theorem to formulate a dimentionally homogeneous equation between the various physical quantities effecting a certain phenomenon. b) Define the following dimensionless numbers & their significance for fluid flow problems. (i) Reynold’s number (ii) Froude number (iii) Mach number

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08

06 08 06

05

07 08

4. a)

06

06

c)

The frictional torque T of a disc of dimeter D rotating at speed N, in a fluid of viscosity µ and density ? in a turbulent flow is given by  M  T = D 5 N 2 ρφ  2   D Nρ 

08

PART B

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a) Derive the Bernoulli’s equation from conservation of energy principle. b) A pump has tapering pipe running full of water. The pipe is placed vertically with the diameter at the base and the top having 1.2 m and 0.6 m respectively. The pressure at the upper end is 240 mm of Hg, while the pressure at the lower end 15 kPa. Assume the head loss to be 20% of difference in velocity head, calculate the discharge. The flow is vertically upwards and difference in the elevation is 3.9 m.

10

a) Derive Darcy Weisbach equation and deduce Chezy’s equation. b) Show that the energy transmitted by a long pipe is maximum when 1/3 rd of energy put into the pipe is lost in friction. 100 kW is to be transmitted through a pipe, the pressure at the inlet of the pipe being 70 bar. If the pressure drop per km is to be 0.44 bar and if f=0.02, find the diameter of the pipe and efficiency of transmission for 16 km.

08

a)

10

12

Derive an expression for velocity at average velocity for viscous flow between two stationary parallel plates.

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b) Glycerine (specific gravity=1.26, Viscosity=0.9 Pa.S) is pumped at the rate of 20 litres per second through straight pipe, diameter 100 mm, 45 m long and inclined upward at 15o to the horizontal. The gauge pressure at the inlet is 590 kPa. Calculate the gauge pressure at the outlet end & average shear stress at the wall.

10

8. a)

Briefly explain what is meant by boundary layer & hence define (i) Displacement thickness (ii) Momentum thickness (iii) Energy thickness b) Clearly distinguish between pressure drag and skin friction drag. c) A flat plate of 2 m x 2 m moves with a velocity of 50 kmph in air of specific weight 1.25 kg/m3. If the coefficients of lift and drag are 0.75 & 0.15 respectively. Calculate (i) Drag force (ii) Lift force (iii) Resultant force

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06 ME 36B/ 06 ME 46B USN III Sem B E Examination

FLUID MECHANICS [ Common to ME / IP / IM / AU / MA ] MODEL QUESTION PAPER Time: 3 Hrs.]

[Max. Marks: 100

Time : 3 hrs.

Max. Marks : 100 (Answer any FIVE questions selecting at least two from each part)

PART A 1 (a) Recognize the following substances a fluids or solids and if fluids, classify them further. The values are obtained from isothermal tests. Substance A Substance B Substance C Substance D Substance E

du / dy = 0 =0 du / dy = 0 =1 du / dy = 0 =0 du / dy = 0 =0 du / dy = 0 =0

1 2 1 2 0.5 1.0 0 0.5 1 0

2 4 2 3 1.0 2.5 0 1 2 0

3 6 3 4 1.5 4.0 0 1.5 3 0

4 8 4 5 2.0 6.0 0 2 4 0

10 (b) Define the term vapour pressure. How does it very with temperature. 02 ( c ) A cylinder of 100mm diameter and 300mm length rotates about a vertical axis inside a fixed cylindrical tube of 105mm diameter and 300mm length. If the space between the tube and the cylinder is filled with liquid of dynamic viscosity of 0.125 N-S/m² determine the speed of rotation of the cylinder which will be obtained if an external torque of 1 N-m is applied to it. 08 2 ( a ) State and prove Pascal’s law 07 ( b ) A differential manometer is connected at the two point A and b as shown in fig. At B air pressure is 7-848 N/Cm² (abs). Find the absolute pressure at A.

Oil of sp. Gravity = 0.8 AIR WATER

B

A

50 cm 12

10

cm

cm

Mercury Sp – gravity = 13.6 ( c ) Explain in brief the conditions of equilibrium of floating and submerged bodies.

04 09

3 ( a ) Derive an equation for the continuity equation for three dimensional flow in Cartesian Co-ordinate System. 10 ( b ) The velocity potential in a 2-dimensional flow is ? =y+ x²-y². Find the stream function for this flow. 10 4 ( a ) Explain the physical significance of the following non-dimensional number : ( I ) Reynolds number ( ii ) Froude number 9 iii ) Euler number ( iv ) Weber number ( v ) Mach number. 10 ( b ) The pressure drop ? P in a pipe of diameter D and length l depends on the density P, viscosity V of flow and average height of perturbance show that the pressure drop can be expressed in the form. ? P= ?V2 ? [ l/D, µ/ eVD, t/D]

10

5 ( a ) Derive the Eulers equation of motion for ideal fluids and hence deduce Bernoulli’s equation of motion. Mention the assumptions made. 10 ( b ) A pipe line carrying oil of specific gravity 0.8 changes in diameter from 300 mm at position 1 to 600 mm diameter at position 2 which is 5 meters at a higher level. If the pressures at position 1 and 2 are 100 KN/m² and 60KN/ m² respectively and the discharge is 300 liters/ Sec. Determine ( i ) Loss of head and ( ii ) Direction of flow. 10 6 ( a ) Derive an expression for the discharge through an orifice meter.

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( b ) In a pipe of diameter 400 mm and length 100 mm water is flowing at a velocity of 3.5 m/ sec.. Find the head loss due to friction using ( i ) Darcy – weisbach formula ( ii ) Chezy’s – formula for which c=55 10

7 ( a ) Define Reynolds number and clearly distinguish between laminar and turbulent flows.

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( b ) Derive an expression for the maximum discharge through a round pipe for a fully developed laminar flow using usual symbols. 10 ( c ) Water at 15º C flows between two parallel plates at a distance of 1.6 mm apart. Determine ( a ) The maximum velocity ( b ) The pressure loss per unit length, if the average velocity is 0.2 m/s. The Viscosity of water at 15º C is given as 0.01 poise. 08 8 ( a ) Derive an expression for velocity of sound in a compressible fluid and express in terms of K, for isothermal and adiabatic flow. 14 ( b ) Find the velocity of bullet fired in standard air if the Mach angle is 300 C. Take R=287.14 J/kg K and ?=1.4 for air. Assume the temperature of air as 15º C. 06