Mechanics Of Fluids May2003 Nr 220301

Set No.

1

Code No.220301 II-B.Tech. II-Semester Examination April/May 2003 MECHANICS OF FLUIDS (common to Mechanical Engineering, Metallurgical and Material Technology) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) State Newton’s law of viscosity. Distinguish between Newtonian and NonNewtonian fluids. b) A circular disc of diameter d is slowly rotated in a liquid of large viscosity µ at a small distance h from a fixed surface. Draw the sketch and derive an expression for the torque T necessary to maintain an angular velocity ω. 2.a) b)

What are the methods available for describing the fluid flow? and explain each method. A circular pipe 10 cm in diameter has 2 m length which is porous, In this porous section the velocity of exit is known to be constant. If the velocities at the inlet and outlet of the porous section are 2.0 m/sec and 1.2 m/sec respectively, estimate (i) the discharge emitted out through the walls of the porous pipe and (ii) the average velocity of this emitted discharge.

3.a) b)

What is momentum equation? Give applications of the equation. Water under a pressure of 345 kN / m2 is flowing through a 30 cm diameter pipe at the rate of 0.25 m3 / s. If the pipe is bent by 135o to the horizontal, find the magnitude and direction of the resultant force on the bend. Neglect losses.

4.a)

Draw a neat sketch showing the variation of drag coefficient for a sphere with Reynolds number and explain the salient features. A 1m x 1.2m plate moves at 13.5 m / s in still air at an angle of 12 o with horizontal. Using CD = 0.17 and CL = 0.72. Determine (i) the resultant force exerted by air on the plate (ii) the friction force (iii) the power required to keep plate moving.

b)

5.a) b) 6.a)

Explain the formation of shock waves at various section in a convergent- divergent nozzle Calculate the Mach number of an object traveling at 300 m/s in an environment of air at 200 K . Estimate also the corresponding stagnation temperature.

Sketch the Reynolds apparatus and explain how the laminar flow can be demonstrated with the help of this apparatus. b) A viscous liquid was flowing in laminar regime in a 6 cm diameter circular pipe. A pitot tube at a radial distance of 2 cm from the axis indicated a velocity of 0.6 m/sec. Calculate the maximum velocity, the mean velocity and the discharge in the pipe. Contd….2

Code No.220301

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SET- 1

7.a) How will you determine the loss of head due to friction in pipes using Darcy weisbach formula. b) An oil pipe line 60cm in diameter and roughness height 0.00005m carries a flow of 0.55 cumecs across the country. The pumping stations are located every 80km. If the pump efficiency is 85%, determine the power input required at each station when the kinematic viscosity and specific gravity of the oil are 2x10 -6 m2/sec and 0.88 respectively. 8.a) b)

What is Manometry? Explain with a neat sketch the working of single column vertical Manometer. Explain how you use U-tube manometer to find pressure difference. $$$

Set No.

2

Code No.220301 II-B.Tech. II-Semester Examination April/May 2003 MECHANICS OF FLUIDS (common to Mechanical Engineering, Metallurgical and Material Technology) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) b)

2.a) b)

Graphically represent and give one example of Newtonian fluid, pseudoplastic, dilatant, ideal plastic and thyxotropic fluid. Through a very narrow gap of height h, a thin plate of very large extent is being pulled at constant velocity V. On one side of the plate is oil of viscosity µ and on the other side oil of viscosity Kµ. Calculate the position of the plate so that the drag force on it will be a minimum. Define and distinguish between stream lines, streak lines and path line. When do these three lines coincide? For the following velocity vectors, determine the magnitude of the velocity at A(x=2, y=-3,Z =1, t = 2) i) V = (10t + xy) i + ( - yz –10t ) j + ( - yz + z2/2) k ii) V = 4x i + ( - 4y + 3t) j

3.a) b)

Define and Derive energy correction factor. A pipe 200 m long slopes down at 1 in 100 and tapers from 800 mm diameter at the higher end to 400 mm diameter at the lower end and carries 100 lps of oil (S = 0.85). If the pressure gauge reading at the higher end reads 50 kN / m2, determine, (i) Velocities at the two ends and (ii) pressure at the lower end. Neglect losses.

4.a)

How do you explain the difference between surface drag, form drag and deformation drag and give one example each. A kite weighing 12 N has an effective area of 1 m2. It is maintained in air at an angle of 10o to the horizontal. The string attached to the kite makes an angle of 45o to the horizontal and at the position the values of C D and CL are 0.6 and 0.8 respectively. Find the speed of the kite and tension in the string. Take unit weight of air = 12.5 N / m3.

b)

5.a) b)

What is meant by co-efficient of compressibility? A diffuser of area ratio 2 :1 operates at the inlet condition P1= 500 kN/m2 ,T1= 500 K , M1 = 0.6 ,ϒ= 1.4 .Estimate the following at the exit (i) velocity (ii) pressure (iii) Temperature (iv) Mach number Contd….2

Code No.220301 6.a) b)

7.a) b)

8.

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SET-2

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. Derive an expression for loss of head due to sudden contraction of a pipe. Sketch the flow pattern and show how the hydraulic gradient and total energy line vary as the flow takes place though the contraction Water flows through a 25cm diameter which is suddenly contracted to 10cm diameter . The flow through the pipe is 75lit/sec. If coefficient of contraction is 0.62, determine the head loss. The pressure of water before the contraction is 80kPa. What is the pressure after contraction Explain venturimeter in detail with diagram. Also derive an expression for finding out the actual discharge from a given venturimeter.

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Set No.

3

Code No.220301 II-B.Tech. II-Semester Examination April/May 2003 MECHANICS OF FLUIDS (common to Mechanical Engineering, Metallurgical and Material Technology) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) Define mass density, specific weight, specific volume and specific gravity. Show that all these properties are inter-related. b) A hydraulic lift consists of a 25cm diameter ram which slides in a 25.015 cm diameter cylinder, the annular space being filled with oil having a kinematic viscosity of 0.025 cm2/sec and specific gravity of 0.85. If the rate of travel of the ram is 9.15m/minute, find the frictional resistance when 3.05 m long ram is engaged in the cylinder. 2.a) b)

3.a) b)

4.a) b)

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

State the continuity equation for a three dimensional flow. How is it modified for 2 dimensional and 1 dimensional flows. A pipe line 60 cm in diameter bifurcates at a Y-junction into two branches of 40 cm and 30 cm diameter. If the rate of flow in the main pipe is 1.2 m 3/s and the mean velocity of flow in the 30 cm diameter pipe is 7.5 m/s, determine the rate of flow in the 40 cm pipe. State the momentum equation. How will you apply momentum equation for determining the force exerted by a flowing liquid on a pipe bend? A nozzle at the end of a 80 mm hose produces a jet 40 mm in diameter. Determine the force on the joint at the base of the nozzle when it is discharging 1200 liters of water per minute. Give four examples in every day life where separation takes place. Draw flow pattern in each case. A jet plane, which weighs 30 kN and has a wing area of 20 m2 flies at a velocity of 1000 km/hr when the engine delivers 7350 kN. 65% of the power is used to overcome the drag resistance of the wing, calculate coefficient of lift and drag for the wing. The mass density of air is 1.2 kg/m3. Derive an expression for velocity of sound . How is it governed by the co-efficient compressibility and molecular weight of Gas? Calculate the velocity of sound (i) in air at 100° C (ii) in CO2 at 70 ° C (iii) in water. Prove that the boundary shear stress is directly proportional to the pressure gradient and the boundary spacing for the case of laminar flow between parallel flat plates when both the plates are at rest. What do you know about Couette flow? Derive the necessary equation. Contd….2

Code No.220301 7.a) b)

8.a) b)

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SET-3

For sudden expression in pipe flow, what is the optimum ratio between the diameter of the pipe before expansion and the diameter after expansion so that the pressure rise may be maximum. A pipe line 30 cm in diameter and 3200m long is used to pump up 500N/sec of an oil whose density is 9500N/m3 and whose kinematic viscosity is 2.1stokes. The centre of the pipe line at the upper end is 40m above than that at the lower end. The discharge at the upper end is atmospheric. Find the pressure at the lower end by taking f=0.015. Explain a concentric – cylinder viscometer in detail with Diagram. Also derive the expression to find the value of viscosity of a given fluid. What is hot wire Anemometer?

Set No.

4

Code No.220301 II-B.Tech. II-Semester Examination April/May 2003 MECHANICS OF FLUIDS (common to Mechanical Engineering, Metallurgical and Material Technology) Time: 3 hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) Explain in two cases of water flow, how the vaporisation takes place and its effects thereon. b) A shaft of 145 mm diameter runs in journals with a uniform oil film thickness 0.5 mm. Two bearings of 20 cm width are used. The viscosity of the oil is 19 centipoises. Determine the speed if the power absorbed is 15 W. 2.a)

A certain flow pattern has a velocity potential φ = 1/3 x3 – x2 + xy2 + y2 Determine the stream function. b) Water flows through a 15cm diameter pipeline at a mean velocity of 1.35 m/s. Calculate the ratio of flow in m3/s, liters/s, kg/s and N/s.

3.a) b)

What is the momentum equation What is its use? A jet of water is initially 12 cm in diameter and when directed vertically upwards reaches a maximum height of 20 m. Assuming the jet remains circular, determine the rate of water flowing and the diameter of the jet at a height of 10 m.

4.a)

What type of drag predominates in the following cases, (i) flight of a cricket ball (ii) air bubble rising in honey

b)

(iii) mist droplet falling in air (iv) parachute. Find the power required to tow lengthwise a plate 1.2 m wide and 3 m long at a velocity of 2.4 m/s in water. The boundary layer is changing from laminar to turbulent over the plate. Take kinematic viscosity of water 0.9x10-2 stokes and specific weight of water 9810 N/m3.

5.a) b)

Derive an expression for mass flow rate through a venturimeter. An aero plane is flying at an height of 20 km where the temperature is – 40 °C The speed of plane is corresponding to M= 1.8. Find the speed of the plane.

6.a)

What factors account for the loss of energy in laminar flow? How does the energy loss vary with velocity of flow? Derive the expression for Reynolds number.

b)

Code No.220301 7.a) b)

8.a) b)

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Contd….2 SET-4

Prove that the pressure at the summit of a siphon is always negative. Also explain negative pressure in pipe line. A pipe line of length 2000m is used for power transmission. If 110.3625kw power is to be transmitted through the pipe in which water having a pressure of 490.5 N/cm2 at inlet is flowing. Find the diameter of the pipe and efficiency of transmission if the pressure drop over the length of the pipe is 98.1N/cm2. Take f=0.0065. Define the terms (i) gage pressure (ii) vaccum pressure and (iii) absolute pressure. Explain with a sketch. Differentiate between simple and differential type of manometer.

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