Code No: 07A30104

R07

Set No. 2

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II B.Tech I Semester Supplementary Examinations,June 2010 FLUID MECHANICS Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. A plate of 600mm length and 400mm wide is immersed in a fluid of specific gravity as 0.9 and kinematic viscosity = 10−4 m2 /s. The fluid is moving with a velocity of 6m/s. Determine boundary layer thickness, shear stress at the end of the plate and drag force on one side of the plate. [16]

i. ii. iii. iv.

laminar flow turbulent flow rotational flow irrotational flow.

or

2. (a) Give two examples for:

(b) Distinguish between stream line, path line and streak line.

[8+8]

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3. A venturimeter with 200 mm at inlet and 100 mm throat is laid with axis horizontal and is used for measuring the flow of oil of specific gravity 0.8. The difference of levels in the U-tube differential monometer reads 180 mm of mercury and 11.52 × 103 kg of oil is collected in 4 minutes. Calculate the discharge coefficient for the meter. Take specific gravcity of mercury as 13.6. [16]

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4. A 2.5m long pipe line tapers uniformly from 15cm diameter to 40cm diameter at its upper end. The pipe centre line slopes upwards at an angle of 300 to the horizontal and the flow direction is from smaller to bigger cross-section. The pressure gauges installed at the lower and upper ends of the pipe line read 150KPa and 200KPa respectively. Sketch the configuration. Determine the flow rate and the fluid pressure at the mid-length of the pipe line. [16]

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5. (a) A shaft of 100mm diameter rotates at 60 rpm in a 200 mm long bearing. Taking that the two surfaces are uniformly seperated at a distance of 0.5mm and taking linear velocity distribution in the lubricating oil having dynamic viscosity of 4 centipoise, find the power absorbed in the bearing. (b) A shaft of diameter 0.35 m rotates at 200 r.p.m inside a sleeve 100 mm long. The dynamic viscosity of lubricating oil in the 2 mm gap between sleeve and shaft is 8 poise. Find the power lost in the bearing. [8+8]

6. (a) Explain the phenomenon of: i. Surface tension and ii. Viscosity

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Code No: 07A30104

R07

Set No. 2

(b) Find the torque required to rotate a shaft of diameter 60mm at 1200rpm concentrically with a sleeve of 60.18mm in diameter and 12m long filled with oil. Kinematic viscosity of oil is 0.82×10−4 m2 /s. Specific gravity of oil is 0.75. [8+8]

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7. (a) An annular plate 6m external diameter and 3m internal diameter with its greatest and least depths below the surface being 4m and 2m respectively. Calculate the magnitude, direction and location of the force acting upon one side of the plate due to water pressure.

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(b) A trapezoidal plate measuring 1.5m at the top edge and 2.5m at the bottom edge is immersed in water with the plate making an angle of 300 to the free surface of water. The top and bottom edges lie at 1m and 2m respectively from the surface. Sketch the configuration. Determine the hydrostatic force on the plate. [8+8]

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8. A pipe of diameter 20 cm and length 2000 m connects two reservoirs, having difference of water levels as 20 m. Determine the discharge through the pipe. If an additional pipe of diameter 20 cm and length 1200 m is attached to the last 1200 m length of the existing pipe, find the increase in the discharge. Take f = 0.015 and neglect minor losses. [16]

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Code No: 07A30104

R07

Set No. 4

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II B.Tech I Semester Supplementary Examinations,June 2010 FLUID MECHANICS Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Show that the pressure at a point in a static fluid is equal in all directions

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(b) Bring out the advantages and disadvantages of a piezometer and a pressure gauge in measuring the pressure at a point [8+8]

2. A discharge of 2000 m3 /s is to pass over a rectangular weir. The weir is divided into a number of openings each of span 10 m. If the velocity of approach is 4 m/s, find the number of openings needed in order that the head of water over the crest is not to exceed 2 m. [16]

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3. (a) Define linear momentum and angular momentum and list out any four practical applications of each.

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(b) A converging pipe of 30 cm and 15 cm diameter carrying water is positioned inclined whose inlet and outlet are at 6 m and 1 m above the datum. The pressure at inlet is 1.5 bar and velocity is 5 m /sec. Find the pressure of water at the outlet of the pipe. Neglect the losses. [8+8] 4. (a) A steady flow of oil of Specific gravity = 0.85 occurs in a 0.1 m diameter pipe which has a downward slope of 1 in 100. If the discharge measured is 2 litres per second. Find the pressure drop between two points on the pipe 200 m apart. Take µ for oil as 1.2 poise. [16]

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(b) Using Hagen-Poiseuille equation derive an expression for the head loss in a pipe of diameter D and length L in terms of Reynolds number and velocity head. [8+8]

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5. (a) A flow field is represented by a velocity potential function as given below: φ = c(2x2 -3y2 ) Verify whether it is a valid function or not? If valid, then find out the corresponding stream function. (b) Define:

i. stream function and ii. velocity potential function. Describe their physical and mathematical concepts. Also list out the properties. [8+8]

6. (a) Cite any six examples where surface tension effect play a prominent role. (b) Derive the dimensions of: i. Dynamic viscosity and

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Code No: 07A30104

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Set No. 4

ii. Kinematic viscosity Also obtain their units in MKS, FPS and SI systems. [6+10]

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7. Air flows at 10m/s past a smooth rectangular flat plate 0.3m wide and 3m long. Assuming that the turbulence level in the oncoming stream is low and that transition occurs at Re = 5×105 , calculate the total drag force, when the flow is parallel to the length of the plate. [16]

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8. A pipe of diameter 0.4 m and of length 2000 m is connected to a reservoir at one end. The other end of the pipe is connected to a junction from which two pipes of lengths 1000 m and diameter 300 mm run in parallel. These parallel pipes are connected to another reservoir, which is having level of water 10 m below the water level of the above reservoir. Determine the total discharge if f = 0.0l5. Neglect minor losses. [16]

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Code No: 07A30104

R07

Set No. 1

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II B.Tech I Semester Supplementary Examinations,June 2010 FLUID MECHANICS Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. For the velocity profile for laminar boundary layer u/U = 3/2 (y/δ) -1/2(y/δ)2 . Find the boundary layer thickness, shear stress, force and co-efficient of drag in terms of Reynolds number. [16]

or

2. Petrol of specific gravity 0.8 is flowing through a pipe inclined at 300 to the horizontal in upward direction. A venturimeter is fitted in this 25 cm diameter pipe; the ratio of areas of main and throat is 4 and the throat is at a distance of 1.2 m from inlet along its length. The U-tube differential manometer connected to the inlet and throat section registers a steady reading of 5 cm of mercury ; the tubes above the mercury being full of water. Find the discharge and pressure difference in kPa between the throat and entrance section. The meter has a discharge coefficient of 0.95 and relative density of mercury is 13.6. [16] 3. (a) Distinguish between rotational and irrotational flows.

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(b) Show that the velocity components given by u=2x/t v=-y/t and w=z/t represent a possible fluid flow. Mention whether the flow is rotational or not. [8+8]

4. (a) State Newton’s law of viscosity and give any four examples of its applications.

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(b) An oil of viscosity 8 poise is used for lubrication between a shaft and sleeve. The diameter of shaft is 0.4m and it rotates at 180rpm. Calculate the horse power lost in the oil for a sleeve length of 120mm. The thickness of the oil film is 1.3mm. [8+8]

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5. (a) A rectangular plate 0.5m wide and 1.6m deep is submerged in water in an inclined position. The maximum and minimum depths of the plate are 1.8m and 0.75m from the free surface. Calculate the hydrostatic force on one face of the plate, and the depth of centre of pressure. (b) A triangular plate of base width 3m and height 4m is immersed in water with its plan making an angle of 500 with the free surface of water. Determine the hydrostatic pressure force and the position of centre of pressure when the apex of the triangle lies 5m below the free water surface. [8+8]

6. (a) A pipe 250m long has a slope of 1 in 100 and tapers from 1.5m diameter at the higher end to 0.7m at the lower end. The quantity of water flowing is 700litres/second. If the pressure at the higher end is 60KPa, find the pressure at the lower end. (b) Mention any eight practical applications of Bernoulli‘s energy theorem. [8+8] 5

Code No: 07A30104

R07

Set No. 1

7. Three pipes of the 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 LV 2 . will carry the same discharge for the same head loss. Use the formula hf = 4f2gD [16]

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8. A pipe of diameter 20 cm and length 10,000 m is laid at a slope of 1 in 200. An oil of Specific gravity = 0.9 and µ = 1.l5 poise is pumped up at the rate of 20 litres per second. Find the head lost due to friction. Also find the power required to pump the oil. [16]

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Code No: 07A30104

R07

Set No. 3

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II B.Tech I Semester Supplementary Examinations,June 2010 FLUID MECHANICS Civil Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. A pressure gauge is fitted at the bottom of a closed vessel to which a simple manometer is also fitted as shown in figure 1. Determine the reading indicated by the pressure gauge if manometric liquid is mercury. [16]

Figure 1

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2. For the velocity profile for laminar boundary layer u/U = 2(y/δ)- (y/δ)3 + (y/δ)4 , obtain expression for boundary layer thickness, shear stress, drag force on one side of the plate and co-efficient of drag in terms of Reynold number. [16] 3. (a) Derive the equations for head loss due to sudden enlargement and due to sudden contraction.

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(b) At a sudden enlargement of a water main from 240 mm to 480 mm diameter, the hydraulic gradient rises by 10 mm. Estimate the rate of flow. [10+6]

4. (a) If A is the cross-sectional area of a stream filament, establish the equation of continuity in the form (δ/δt)(ρA) + (δ/δs)(ρAV) = 0 Where s is measured along the filament in the direction of flow and V is the speed. Further show that for steady incompressible flow the equation reduces to AV = constant. (b) What are the different types of fluid flow? Explain.

[8+8]

5. (a) Mention the advantages and limitations of an orifice plate as a flow metering device. 7

Code No: 07A30104

R07

Set No. 3

(b) An orifice plate of orifice diameter 10 cm has been fitted into a 25 cm diameter pipe that conveys oil of specific gravity 0.8. The pressure differential on the two sides of the orifice plate is messured by a mercury-oil differential manometer. If the gauge shows a deflection of 80 cm of mercury, calculate the oil discharge in litres per second. Take coefficient of discharge Cd = 0.65. [8+8]

(a) Flush with the water surface

[16]

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(b) 3m below the water surface. Also comment on the results.

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6. A rectangular plate 3.5m × 8m is immersed vertically in water such that the 3.5m side is parallel to the water surface. Determine the hydrostatic force and the centre of pressure if the top edge of the surface is:

or

7. Lubricating oil of specific gravity 0.82 and dynamic viscosity 12.066 × 102 N.s/m2 is pumped at a rate of 0.02 m3 /s through a 0.15 m diameter 300m long pipe. Calculate the pressure drop, average shear stress at the wall of the pipe and the power required to maintain flow, if the pipe is inclined at 15 degree with the horizontal and the flow is in upward direction. [16]

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8. (a) Water is pumped at the rate of 0.7m3 /s through a 25cm diameter pipe upto a hill top. Hill top has an elevation of 45m, and the diameter of the pipe line reduces to 25cm. If the pump maintains a pressure of 9810N/m2 at hill top, determine the pressure at the foot of the hill. What is the power required to pump the water? (b) A pipe of 350mm diameter conveying 0.43m3 /s of water has a right angled bend in a horizontal plane. Find the resultant force exerted on the bend if the pressure at inlet and outlet of the bend are 30N/cm2 and 27N/cm2 . [8+8]

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