Mechanics Of Fluids Nov2003 Rr 212101

Code No: RR-212101. II B.Tech. I-Semester Regular Examinations, November 2003 MECHANICS OF FLUIDS ( Aeronautical Engineering ) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

Set No:

1

1. a) b)

Define kinematic viscosity. How is this name attributed to this property? Lateral stability of a long shaft 15cm diameter is obtained by means of a 25cm stationary bearing having an internal diameter of 15.025cm. If the space between bearing and shaft is filled with a lubricant having a viscosity 24 Pa-s, what power will be required to overcome the viscous resistance when the shaft is rotated at a constant rate of 180 r.p.m.

2. a)

Define equipotential line and a line of constant stream function, Show that these lines intersect orthogonally. Given that u = x2 – y2 and v = - 2xy. Check whether stream function exists. If so determine the stream function and potential function for the flow.

b) 3. a) b)

What are the applications of Bernoillis equation. A conical pipe has diameter 0.40 m & 0.80 m at its two ends. The smaller end is 2m above the larger end. For a flow of 0.30 m 3 / sec of water the pressure at the lower end is 10 kPa. Assuming a head loss of 2 m and kinetic energy correction factor α = 1.1 and 1.5 at the smaller and larger ends respectively, estimate the pressure at the smaller end.

4. a)

Draw and explain the approximate flow pattern and the pressure distribution around a flat plate placed normal to a stream. A flat plate of 2.0 m width and 4.0 m length is kept parallel to air flowing at a velocity of 5 m/s. Determine the length of plate over which the boundary layer is laminar, shear at the location which boundary layer ceases to be laminar and total force on both sides on that portion of plate where the boundary layer is laminar. Take p = 1.2 kg/m3 and v = 1.47x10-5 m2/s.

b)

5. a) b) 6. a) b)

Describe Compressibility flow through a convergent and divergent nozzle. How and where does the shock occurs in the nozzle? A jet fighter travels at 500 m/s in air at 280 °C. Calculate the Mach cone, Mach cone angle and stagnation properties. Derive an expression for mean velocity of flow for laminar flow through inclined pipes. Derive the necessary condition for mean velocity for the laminar flow between parallel flat plates when both the plates are at rest. (Contd…2)

Code No: RR-212101. 7. a)

b)

8. a)

b)

.. 2..

Set No: 1

Two reservoirs are connected by three pipes laid in parallel, their diameters are d, 2d, and 3d respectively and they are of the same length l, assuming f to be the same for all pipes, determine the discharge through each of the larger pipes, if the smallest pipe is discharging 1 cumec. Three pipes of same length L, diameter D and friction factor f are connected in parallel. Determine the diameter of the pipe of length L and friction factor f which will carry the same discharge for the same head loss. Use the formula hf=fLV2/2gD. Two pressure points in a water pipe are connected to a manometer which has the form of an inversed U-tube. The space above the water in the two limbs of the manometers is filled with toluene of specific gravity 0.875. If the difference of level of water columns in the two limbs is equal to 0.12 m, what is the corresponding difference of pressure? Write short notes on piezometers.

~~~~

Set No:

Code No: RR-212101. II B.Tech. I-Semester Regular Examinations, November 2003 MECHANICS OF FLUIDS ( Aeronautical Engineering ) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1. a) b)

2. a) b)

2

Explain how liquids vaporize at normal temperature. What are the effects of vaporisation. Two large vertical plane parallel surfaces are 5mm apart and the space between them is filled with a fluid. A thin square plate of 12.5 cm falls freely between the planes along the central plane and reaches a stready velocity of 2m/sec. Determine the weight of the plate if the viscosity of the fluid filling the space is 0.02 Pa-s. Define stream function and explain its characteristics. If for a two dimensional potential flow, the velocity potential is given by φ = x (2y – 1) Determine the velocity at the point P(4,5). Determine also the value of stream function Ψ at the point P.

3. a)

Define the terms (i) Vortex flow (ii) Forced vertex flow (iii) Free vortex flow. Give suitable examples. b) A rectangular duct of width 25 cm has a two dimensional irrotational flow. It has an elbow made up of circular arcs of radius 40 cm and 65 cm for the inner and outer walls respectively. Calculate the discharge per unit width of the duct when the difference in pressure between outer and inner walls in the elbow is 30 kPa.

4. a) b)

5. a) b)

Sketch the growth of boundary layer on a flat plate and explain the different regions of it. Find the displacement thickness and wall shear stress for the velocity distribution in a boundary layer (u / U) = (y / δ) where U is the Velocity and δ is the boundary layer thickness. What is the relation between pressure and density of a compressible fluid for (i) Isothermal (ii) adiabatic process Air, thermodynamic state of which given by pressure P = 230 kN/m2 and temperature = 300 K is moving at a velocity V= 250 m/s .Calculate the stagnation pressure if (i) Compressibility is neglected (ii) Compressibility account for.

(Contd…2)

Code No: RR-212101. 6. a) b)

7. a) b)

.. 2..

Set No: 2

Prove that in a steady uniform laminar flow, the pressure gradient in the direction of flow is equal to the shear stress gradient in the normal direction. in an experiment, the details of laminar flow of fluid are as follows. Determine the discharge in the pipe. Specific gravity = 1.67 Viscosity = 1.56 poise Diameter of pipe = 15 cm Length of the pipe = 2000 m Loss of head = 0.45 m Explain the concept of flow through a long pipe along with a neat sketch. A main pipe divides into two parallel pipes which again forms one pipe. The length and diameter for the first parallel pipe are 2000 m and 1.0m respectively, while the length and diameter of second parallel pipe are 2000 m and 0.8 m. Find the rate of flow in each parallel pipe if total flow in the main is 3.0 cumecs. The coefficient of friction for each parallel pipe is same and equal to 0.005.

A pipe containing water at 172 kN/m2 pressure is connected by a differential gage to another pipe 1.5 m lower than the first pipe and containing water at high pressure. If the difference in heights of the two mercury columns of the gage is equal to 75 mm, what is the pressure in the lower pipe? G of mercury = 13.6. b) Obtain an expression for inclined manometer and explain its use.

8. a)

~~~~

Code No: RR-212101. II B.Tech. I-Semester Regular Examinations, November 2003 MECHANICS OF FLUIDS ( Aeronautical Engineering ) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1. a) b)

2. a) b)

3. a) b)

4. a) b)

5. a) b)

Set No:

3

Derive an expression for the torque and power required to overcome the viscous drag for a shaft running at a particular r.p.m. A hydraulic lift shaft of 500 mm diameter moves in a cylindrical sleeve the length of engagement being 2m. The interface is filled with oil of kinematic viscosity of 2.4 x 10 –4 m2/sec and density of 888 kg/m3. The drag resistance when the shaft moves at 0.2 m/sec is 267.81 N. Determine the internal diameter of the cylinder. State the basic principle of continuity equation. Obtain an expression of continuity equation for a three dimensional – steady – incompressible fluid flow. A flow is described by the stream function Ψ = 2 √3 XY. Locate the point at which the velocity vector has a magnitude of 4 units and makes an angle of 150 o with the x- axis. Derive an expression for the depth of paraboloid formed by the surface of a liquid contained in a cylindrical tank which is rotated at a constant angular velocity about its vertical axis. A U – tube contains a liquid of relative density 1.25 to a height of 25 cm in both the columns. It is rotated about a symmetrical vertical axis which is 15 cm from both the limbs. Calculate the pressures at the bottom horizontal connecting points and mid point when the speed of rotation is 240 rpm. What is an aerofoil? Explain the lift characteristics of aerofoil with a neat diagram. A wing of a small aircraft is rectangular in plain having a span of 10 m and chord of 1.2 m. In a straight and level flight at 240 km/hr. the total aerodynamic force acting on the wing is 20 kN. If the lift is 10 times the drag force, calculate the coefficient of lift and the total weight the aircraft can carry. Assume air density 1.2 kg/m3. What is mach number? Why is this parameter is so important for the study of flow of compressible fluid? A supersonic aircraft flies at an altitude of 1.8 Km where the temperature is 4 °C. Determine the speed of aircraft if its sound is heard 4 second after its passage over the head of observer. Takeϒ = 1.4 and R= 281.43 J/ Kg °K. (Contd…2)

Code No: RR-212101.

.. 2..

Set No: 3

6. a) b)

Derive Hazen-Poiseuille equation for laminar flow in the circular pipes. Glycerin of viscosity 1.5 pascal-sec and mass density 1200 kg/m3 flows at a velocity of 5 m/sec in a 10 cm diameter pipe. Check whether the flow is laminar in pipe line. Find the boundary shear stress in the pipe.

7. a)

Sketch and explain the hydraulic gradient and total energy line for an inclined pipe and horizontal pipe discharging freely in atmosphere. A siphon of diameter 20cm connects two reservoirs having a difference in elevation of 15m. The total length of the siphon if 600 m and the summit is 4 m above the water level in the upper reservoir. If the separation takes place at 2.8 m of water absolute, find the maximum length of siphon from upper reservoir to the summit. Take f=0.004 and atmospheric pressure 10.3 m of water.

b)

8. a)

b)

A 150 mm x 75 mm venturimeter with Cd = 0.98 is to be replaced by an orifice meter having a value of Cd = 0.6. If both the meters are to give the same differential mercury manometer reading for a discharge of 100 lps and the inlet dia. to remain 150 mm, what should be the diameter of orifice. What is the necessity of ventilation of weirs?

~~~~

Code No: RR212101. II B.Tech. I-Semester Regular Examination November 2003 MECHANICS OF FLUIDS ( Aeronautical Engineering ) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1. a) b) 2. a) b)

3. a) b)

4. a) b) c)

5. a) b)

Set No:

4

Define compressibility and bulk modulus of elasticity. Obtain an expression for the bulk modulus of elasticity K of a fluid in terms of the pressure p and the mass density. Determine the pressure increase required to reduce the volume of water by 1.5%, if its bulk modulus of elasticity is 2.2 x 10 9 Pa. Define and derive the equation of rotation for a fluid particle in a flow field about any axis. A fluid flow field is given by V = xy i+ 2yz j – (yz +z2) k Determine whether this is a possible steady incompressible fluid flow. If so, determine the value of rotation at the point P (1,2,3). Name the different forces present in a fluid flow. For the Euler’s equation of motion, which forces are taken into considerations. A closed vertical cylinder 400 mm in diameter and 500 mm height is filled with oil of relative density 0.9 to a depth of 340 mm, the remaining volume containing air at atmospheric pressure. The cylinder rotates about its vertical axis at such a speed that the oil just begins to uncover the base. Calculate (i) the speed of rotation for this condition. Distinguish between the friction drag and pressure drag. Which type of drag predominates in the motion of following bodies. (i) Blunt body (ii) Stream lined body (iii) Aerofoil (iv) Small sphere moving in a highly viscous fluid with very low velocity Find the ratio of skin friction drag on the front two third and rear one third of a flat plate kept in a uniform stream at zero incidence. Assume the boundary layer to be turbulent over the entire plate. Differentiate between compressible and incompressible flows. A large vessel fitted with a nozzle, contains air at pressure of 2500 kN/m 2 and a temperature of 20 °C. If the pressure at the outlet of the nozzle is 1750 kN/m2. Find the velocity of air flowing at the outlet of the nozzle?

(Contd…2)

Code No: RR212101. 6. a) b)

.. 2..

Set No: 4

Explain the velocity and shear stress distribution for laminar flow in a circular pipe with a neat sketch. A fluid of mass density 1790 kg/m3 and viscosity of 2.1 pascal-sec flow at a velocity of 3 m/sec in a 6 cm diameter pipe. Estimate the head loss in a length of 12 m of pipe.

7. a) b)

Explain different laws of fluid friction in detail? A siphon of diameter 20 cm connects two reservoirs having a difference in elevation of 20 m. The length of the siphon is 500m and the summit is 3 m above the water level in the upper reservoir. The length of the pipe from upper reservoir to the summit is 100 m. Determine the discharge through the siphon and also pressure at the summit by neglecting minor losses and taking coefficient of friction as 0.005.

8. a)

The rate of flow of water in a 150mm diameter pipe is measured with a venturimeter with a 50mm dia. throat. When a mercury manometer is connected across the converging section reads 8mm, the flow rate is 2.7 kg/s. What is the coefficient of discharge at that flow rate and what is permanent loss of head? Specific gravity of mercury = 13.6 What is the device used for measuring fluid pressure? Explain briefly the principle of an inclined manometer.

b)

~~~~