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**ANNA UNIVERSITY QUESTION BANK**

**DEPARTMENT : CIVIL**

**SEMESTER : III**

**SUBJECT CODE: CE2202**

**SUBJECT NAME: MECHANICS OF FLUIDS**

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**UNIT I- DEFINIIONS AND FLUID PROPERTIES**

PART – A (2 Marks)

1. Differentiate between specific volume and specific weight.

2. Distinguish between real and ideal fluids.

3. Define dynamic and kinematic viscosity of fluids.

4. Define fluid and fluid mechanics.

5. Distinguish between solids and fluids.

6. Define specific gravity and mass density.

7. Define capillarity and compressibility.

8. Define pressure and what are the types?

9. Calculate the capillary rise in a glass tube of 1.8mm diameter when immersed vertically in water. Take surface tension of water as 0.073 N/m.

10. What is surface tension and bulk modulus?

11. What is the effect of temperature and pressure on viscosity of liquids and gases?

12. State Newton’s law of viscosity and give examples of its application.

13. Define Newtonian and Non Newtonian fluids.

14. State the types of fluids?

15. For what range of contact angle of a fluid the following will occur (i) capillary rise and (ii) capillary fall.

16. What is a fluid? How are fluids classified?

17. Estimate the pressure inside a water droplet of size 0.3mm. Assume surface tension=0.0728 N/m.

18. A soap bubble 50mm diameter has inside pressure of 20 N/m2 above atmosphere. Calculate the tension in soap film.

19. Determine the viscosity of oil having kinematic viscosity 6 stokes and specific gravity 2.0

20. Define closed, open and isolated systems.

PART-B (16 Marks)

1. A cylindrical shaft of 90mm rotates about a vertical axis inside a cylindrical tube of length 50cm and 95mm internal diameter. If the space between them is filled with oil of viscosity 2 poise. Find power lost in friction for a shaft speed of 200rpm.

2. Determine the minimum size of glass tubing that can be used to measure water level, if the capillary rise in the tube is not exceed 0.25mm. Take surface tension of water in contact with air as 0.735 N/m.

3. i) Determine the bulk modulus of elasticity of a liquid, if as the pressure of the liquid is increased from 7 MN/m2 to 13 MN/m2 the volume of liquid decreased by 0.15%.

ii) Distinguish between dynamic and kinematic viscosity. State their units.

4. A body with gravitational force of 500 N slides downs a lubricated inclined plane making a 30o angle with the horizontal. The body has a flat surface area of 0.2m2 and slides down at a speed of 1m/s. Determine the lubricant film thickness taking viscosity as 0.1 Pa.sec.

5. i) A soap bubble 50mm diameter has an inside pressure of 20 N/m2 above atmosphere.

Calculate the tension in the soap film.

ii) The water level in a steel tank is measured with a piezometer of diameter 5mm. if the reading of water surface in the tube is 90cm. what is the true depth of water in the tank? Take surface tension of water as 0.0725 N/m.

6. Determine the bulk modulus of elasticity of a fluid which is compressed in a cylinder from a volume of 0.009 m3 at 70 N/cm2 pressure to a volume of 0.0085 m3 at 70 N/cm2 pressure.

7. Calculate the dynamic viscosity of oil, which is used for lubrication of surface between a plate of size 0.6m x 0.9m and an inclined plane with an angle of inclination 25o with horizontal. The weight of plate is 500 N and it slides down the inclined plane with a uniform velocity of 0.4 m/s. the thickness of oil film is 1.8mm.

8. A square metal plate 1.8m side and 1.8mm thick weighing 60 N is to be lifted through a vertical gap of 30 mm of infinite extent. The oil in the gap has a specific gravity 0.95 and viscosity of 3Ns/m2. If the metal plate is to be lifted at a constant speed of 0.12 m/s. find the force and power required.

9. An oil film of thickness 10mm is used for lubrication between the two square parallel plate of size 0.9 m x 0.9 m in which the upper plate moves at 2m/s requires a force of 100N to maintain this speed. Determine (i) viscosity of the oil and (ii) kinematic viscosity of oil if the specific gravity of oil is 0.95.

10. Calculate the capillary effect in a glass tube 5mm diameter, when immersed in (i) water (ii) mercury. The surface tension of water and mercury in contact with air are 0.0725 N/m and

0.51 N/m. the angle of contact of mercury is 130o.

11. A 400mm diameter shaft is rotating at 200 rpm in a bearing of length 120mm. If the thickness of oil film is 1.5mm and the dynamic viscosity of the oil is 0.7 Ns/m2. Determine the torque required and power lost.

12. Two large plane surfaces are 120mm apart. The space between the surfaces is filled with oil of viscosity 0.92 Ns/m2. A flat thin plate of 0.6m2 area moves through the oil at velocity of 0.5 m/s. Calculate the drag force

(i) When the plate is in the middle of the two plane surfaces

(ii) When the thin plate is at a distance of 30mm from one of the planes.

13. Two large plane surfaces are 200mm apart. The space between the surfaces is filled with oil of viscosity 8 poise. A flat thin plate of 0.7m2 area moves through the oil at velocity of 0.8 m/s. Calculate the drag force

(i) When the plate is in the middle of the two plane surfaces

(ii) When the thin plate is at a distance of 70mm from one of the planes.

14. Calculate the pressure due to a column of 0.6m of (i) water, (ii) an oil of S = 0.8, and (iii) mercury of S = 14. Take density of water ρ = 1000 kg/m3.

15. The dynamic viscosity of oil used for lubricating between a shaft and a sleeve is 8 poise.

The shaft rotates at 200rpm. The power lost in the bearing for a sleeve length of 90 mm is 300 watts. The thickness of oil film is 1.8mm. Calculate the diameter of shaft and sleeve.

**UNIT II – FLUID STATICS AND KINEMATICS**

PART – A (2 Marks)

1. Distinguish between the Eulerian and Lagrangian method of representing fluid motion.

2. Define centre of pressure and centre of buoyancy.

3. Will the centre of pressure and centre of gravity ever coincide? If so, under what conditions?

4. Write the formula used to determine the Meta centric height.

5. Define stream function and state properties of stream function.

6. State Pascal’s law and give example where this principle is applied.

7. State hydrostatic law.

8. What do you understand by the terms Total acceleration, Local acceleration and Connective acceleration?

9. Distinguish between path lines, stream lines and streak lines.

10. Define metacentre and metacentric weight.

11. What are the three kinds of equilibrium of floating body?

12. Differentiate between stable, unstable and neutral equilibrium of the floating body.

13. When is mechanical pressure gauge used?

14. If the stream function is known, is it possible to determine the rate of flow between any two stream lines?

15. Write down the conditions for irrotational flow in (a) potential function (b) stream function.

16. State the condition for irrotational flow in two and three dimensional incompressible flow.

17. Define velocity potential function and stream function.

18. Define continuity equation.

19. What are the types of fluid flow?

20. What is the relation between velocity potential function and stream function?

PART-B (16 Marks)

1. Derive an expression for the force exerted and centre of pressure for a completely submerged inclined plane surface.

2. The left limb of a U tube manometer is connected to a pipe in which a fluid of specific gravity

0.8 is flowing. The right limb is open to atmosphere and manometric fluid is mercury. The difference in mercury level between the two limbs is 20cm and the center of the pipe is 12cm below the mercury level in the right limb. Find the fluid pressure in the pipe.

3. The velocity potential function for a 2- dimensional flow is given by φ = x (4xy-3).

Determine (a) the velocity at the point (2, 3), (b) stream function at the same point.

4. A hollow cylinder closed at both ends has an outside diameter of 1.25m, length 3.5m and specific weight 75 kN/m3. If the cylinder is to float just in stable equilibrium in sea water (specific weight 10 kN/m3), find the minimum permissible thickness.

5. What is a Flow net? Enumerate the methods of drawing flow nets. What are the uses and limitations of flow nets?

6. Derive the equation of continuity for three dimensional incompressible fluid flows and reduce it to one dimensional form.

7. The velocity potential function is given by an expression φ = y2 - x2 + (x3y/3) – (xy3/3). Check

continuity flow. Find the velocity components in X and Y directions.

8. The two velocity components are given by u = x2 + y2 + z2 and v = xy2 –yz2 + xy. Determine the third component of velocity such that they satisfy the continuity equation.

9. A cylindrical tank contains 180cm depth of water. On the top of the water is 100cm of kerosene which is open to atmosphere. If the temperature is 22oC, what is the gauge pressure at the bottom of the tank?

10. An annual ring of 2m external diameter and 1m internal diameter is immersed in water with the plate making 30o to the horizontal and the lowest edge is 5m below the water surface. Determine the total force and position of centre of pressure.

11. The x and y components of velocity in a 2-D incompressible flow are as follows: u = 3x + y and v = 2x – 3y. Derive an expression for the stream function and hence show that the flow is not irrotational. Also calculate the velocity at the point (-1, 2).

12. Show that the given stream function: ψ = (1/3x3) – x2 – xy2 + y2. Describes an irrotational

flow. Determine the stream function and the velocity vector at (1, 2).

**UNIT 3 – FLUID DYNAMICS**

PART – A (2 Marks)

1. State Bernoulli’s equation.

2. What is Moody’s diagram?

3. State a few engineering applications of the momentum equation.

4. How does turbulence affect the flow properties?

5. Differentiate stream line and path line.

6. State the assumptions used in deriving Bernoulli’s equation.

7. Explain Euler’s equation of motion.

8. Name the different forces present in a fluid flow?

9. Write Reynolds equation, Navier stokes equation and Euler’s equation of motion.

10. Explain potential energy, kinetic energy and pressure energy.

11. State advantages and limitations of manometers.

12. Differentiate between simple manometers and differential manometers.

13. What are mechanical gauges? Name four important mechanical gauges?

14. Write down the advantages and disadvantages of using orifice meter over a Venturimeter.

15. State the limitations of Bernoulli’s equation.

16. What is Pitot tube?

17. What is manometer? How they are classified?

18. Explain the principle of Venturimeter.

19. Why is coefficient of discharge of orifice meter much smaller than that of venturimeter?

20. What are the characteristics manometers liquids?

PART-B (16 Marks)

1. Derive Euler’s equations for a three–dimensional fluid flow.

2. A jet propelled boat moves at 32 km/hr in a fresh water lake. There are two jets each of diameter 20 cm. The absolute velocity of the discharged jets is 25 km/hr. Calculate the pump discharge, force of propulsion, power input and efficiency of propulsion if the inlet orifices are located at amid–ships and in bow.

3. State the practical application of Bernoulli’ theorem. Explain its application in a pitot tube.

4. A 2m long conical tube is fixed vertically with its smaller end upwards. It carries liquid in downward direction. The flow velocities at the smaller and larger end are 5m/s and 2m/s respectively. The pressure head at the smear end is 2.5m of liquid. If the loss of head in the

tube is 0.35 (V1 – V2)2/2g where V1 and V2 being the velocities at the smaller and larger end respectively. Determine the pressure head at the larger end.

5. Derive the Hagen – Poiseuille equation. Deduce the condition for maximum velocity in the circular pipe.

6. A horizontal Venturimeter with inlet and throat diameter 300mm and 100mm respectively is used o measure the flow of water. The pressure intensity at inlet is 130kN/m2 while the vacuum pressure head at throat I 350mm of mercury. Determine the rate of flow. Take Cd = 0.96.

7. Water is flowing through a pipe 300mm in diameter at a velocity of 5 m/s. The pressure at two points in the flow is 245.3 kN/m2 and 196.2 kN/m2 respectively. The datum heads at A and B are 12m and 14m. Determine the direction of flow and loss of head between A and B.

8. Prove that head loss due to friction in case of laminar flow through a circular pipe is given by hf = (32µVL) / rd2.

9. An oil of viscosity 0.096 Ns/m2 and a specific gravity of 1.59 flows through a horizontal pipe

of 50 mm diameter with a pressure drop of 6 kN/m2 per meter length of pipe. Determine the rate of low. Assume flow is laminar.

10. Derive the head loss between two sections for laminar incompressible flow in a circular pipe.

11. Derive the equation for discharge through Venturimeter. If a Venturimeter is fitted with a pipe of diameter 250mm, which carries oil of specific gravity 0.95. Calculate the rate of flow. The throat diameter is 150mm. The level difference in manometer reading is 40mm. Take Cd = 0.97.

UNIT 4 – BOUNDARY LAYER AND FLOW THROUGH PIPES

PART – A (2 Marks)

1. What is meant by the term ‘‘Piezometric head’’?

2. A pipe has D = 40 cm, L = 100 m, f = 0.005. Compute the length of an equivalent pipe which has D = 20 cm and f = 0.008.

3. Define displacement thickness and boundary layer thickness.

4. The velocity of water in a pipe 200mm diameter is 5 m/s. The length of the pipe is 500m.

Find the loss of head due to friction, assuming friction factor as 0.02.

5. What is meant by hydraulic gradient line?

6. Define energy thickness and Momentum thickness.

7. List the various classifications of boundary layer thickness.

8. What is meant by laminar sub layer?

9. Define an Equivalent pipe.

10. Give four examples in everyday life where formation of boundary layer is important.

11. Give the Von-karman Momentum integral equation.

12. What are the different methods of preventing the separation of boundary layers?

13. What is an equivalent pipe?

14. What do you understand by (a) pipes in series, (b) pipes in parallel?

15. Under what conditions does a minor loss become a major loss?

16. Differentiate between laminar boundary layer and turbulent boundary layer?

17. Define Total energy line and Hydraulic gradient line.

18. How will you determine the major energy loss by using (i) Darcy formula and (ii) Chezy’s formula?

19. Define major energy loss and minor energy loss in pipe.

20. What are the applications of momentum equation?

PART-B (16 Marks)

1. Water flows through a 10cm diameter, 30m long pipe at a rate of 1400 lpm. What percent of head would be gained by replacing the central one third length of pipe by another pipe of 20 cm diameter. Assume that the changes in section are abrupt and f = 0.008 for all pipes. Neglect entrance and exit losses but consider all other losses.

2. For the laminar boundary layer, the velocity distribution is given by u/U = 2(y/δ) – 2(y/δ) 3 + (y/δ) 4. Compute the displacement thickness.

3. A plate 450mm x 150mm has been placed longitudinally in a stream of crude oil (specific gravity 0.925 and kinematics viscosity of 0.9 stoke) which flows with velocity of 6m/s. calculate the friction drag on the plate, thickness of the boundary layer at the trailing edge and the shear stress at the trailing edge.

4. Two pipe of diameter 400mm and 200mm are 300mm long. Where the pipes are connected in series, the discharge through the pipe line is 0.10m3/s. Find the loss in head. What would the loss of pipeline is 0.10m3/s. Find the loss in head. What would the loss of head in the system to pass the same total discharge when the pipes are connected in parallel? Assume Darcy’s friction factor a 0.03.

5. The diameter of a horizontal pipe which I 300mm is suddenly enlarged to 600mm. The rate of flow of water through this pipe is 0.4m3/s. If the intensity of pressure in the smaller pipe I125kN/m2, determine the loss of head, due to sudden enlargement and the power lost due to enlargement.

6. Derive expressions for displacement thickness and momentum thickness.

7. What is separation of boundary layer? When it occurs? Discuss the methods for the control of boundary layer separation.

8. Two reservoirs 1 km apart are connected by two pipes in parallel. One is 30 cm in diameter and the other is 20 cm in diameter. If the combined flow is 1 m3/s, find the discharge in each pipe. Assume friction factor is same for both the pipes.

9. An old water supply distribution pipe 25 cm diameter of a city is to be replaced by two parallel pipes of smaller diameter having equal lengths and identical friction factor values. Find out the new diameter required?

10. Describe Nikuradse’s experiment on the resistance of artificially roughened pipes. Discuss the characteristics features of the results obtained.

11. Derive Von-karman momentum integral equation for flow past a flat plate.

12. Derive the expression for head loss due to friction for a pipe flow.

13. Two reservoirs are connected by a pipe line which is 160 mm in diameter for the first 7 m and 260 mm in diameter for the remaining 15 m length. The water level difference between upper and lower reservoir is 8 m. calculate the rate of flow considering major losses only and considering minor losses also.

14. Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 450 m, 255 m and 315 m respectively are connected in series. The difference in water surface levels in two tanks is 18 m. Determine the rate of flow of water if coefficient of friction are 0.0075, 0.0078 and 0.0072 respectively considering minor losses and neglecting minor losses.

15. Find the head lost due to friction in pipe of diameter 300 mm and length 75 mm through which water is flowing at a velocity of 4 m/s using (i) Darcy formula, (ii) Chezy’s formula for which C = 55. Take kinematic viscosity for water 0.03 stokes.

UNIT 5 – SIMILITUDE AND MODEL STUDY

1. What is Dimensional analysis?

2. State Buckingham’s π-theorem.

3. What is meant by dimensional homogeneity?

4. What are distorted models?

5. What is meant by repeating variables?

6. Define Reynolds model law.

7. How are hydraulic models classified?

8. Write short notes about Moody’s diagram.

9. Define non-dimensional numbers.

10. What are their significances for fluid flow problems?

11. What is meant by Geometric, Kinematic and Dynamic similarities?

12. What are the advantages and applications of model testing?

13. What is Model analysis?

14. What do you mean by fundamental units and derived units? Give examples.

15. What is the limitation of Rayleigh’s method of dimensional analysis?

16. Explain the significance of Froude model law.

17. What are the conditions for hydraulic similitude?

18. What are the advantages of Buckingham’s π-theorem?

19. What do you understand by Reynolds number and Froude number?

20. What are the types of models?

PART-B (16 Marks)

1. Explain distorted and undistorted models.

2. Using Buckingham’s π-theorem, show that the drag force FD of an aircraft is given by FD = ρ L2 V2 φ (Re, M) in which Re = ρ V L / µ; M = V/C; ρ = fluid mass density; L = chord length; V

= velocity of aircraft; µ = fluid viscosity; C = sonic velocity = (K / ρ)1/2 where K = bulk modulus of elasticity.

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3. State the reasons for constructing distorted models of rivers and discuss the various types of distortion in models. What are the merits and demerits of distorted models as compared to undistorted models?

4. The resistance ‘R’ experienced by a partially submerged body depends upon the velocity ‘V’, length of the body ‘L’ viscosity of fluid ‘µ’, density of the fluid ‘ρ’ and gravitational acceleration ‘g’; obtain a dimensionless expression for R.

5. The discharge Q over a weir depends on the head of water H, the acceleration due to gravity g, the density ρ, the viscosity µ and surface tension σ. Obtain an expression for the discharge.

6. The spillway model is to be built to a geometrically similar scale of 1:50 across a flume of 60 cm width. The prototype is 1.5 m high and the maximum head on it is expected to be 1.5 m. What height of model and what head on the model should be used. If the flow over the model at a particular head is 12 lps, what flow per meter length of the prototype is expected? If the pressure in the model is 14 cm, what is the negative pressure in prototype? Is it practicable?

7. The frictional loss of pressure head depends on the length of pipe ‘L’, diameter of pipe d, mass density of fluid ρ, dynamic viscosity of fluid µ, roughness projections k, velocity of fluid

V. find the relationship between pressure loss due to friction and the various parameters cited, using Buckingham’s π-theorem.

8. A ship 150 m long moves in fresh water at 36 km/hr. A 1:100 model of this ship is to be tested in a towing basin containing a liquid of gravity 0.90. What viscosity must this liquid should have for both Reynolds and Froude model laws to be satisfied? Also find the speed which the model must be towed. µ of water = 1.13x10-3 Ns/m2.

9. A 1:50 scale model of a proposed dam is used to predict prototype flow conditions. If the design floods discharge over the spillway is 20000 m3/s. What is the water flow rate should be established in the model to similitude this flow?

10. Obtain an expression for capillary rise through a small diameter tube D, immersed in a liquid of specific weight ‘γ’ with a surface tension ‘σ’ using Rayleigh’s method.

11. Obtain the form of equation for torque by performing dimensional analysis if the torque depends on the rate of flow q, head h, angular velocity of rotator ω, specific weight of water ‘γ’ and efficiency?

12. It is assumed that the stability of laminar flow depends on ‘ρ’, dynamic viscosity ‘µ’ of the fluid, velocity gradient ‘i’ and the distance from the boundary ‘L’. Obtain a dimensional relationship using Rayleigh’s method.

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