module 1 properties of fluids - darshan institute of ......metre long. it contains oil of specific...

GTU Paper Analysis (New Syllabus)

Fluid Mechanics (2130602) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Module 1 – Properties of Fluids

Sr. No. Questions

De

c-1

4

Jun

e-1

5

De

c-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Write statement: Newton’s law of viscosity. 01

2. Define the terms: (1) kinematic viscosity (2) surface tension (3) specific gravity (4) specific

weight (5) Ideal fluid (6) capillarity (7) Newtonian fluid

07 03

3. Define Newtonian fluid. 01 01

4. Explain the terms Dynamic Viscosity and Kinematics Viscosity. 03

5. Explain surface tension. 01 03

6. State Newton’s law of viscosity. 01

7. Define specific gravity. 01

8. Define elasticity. 01

9. Distinguish clearly between an ideal fluid and real fluid. 01 01

10. Define dynamic viscosity of fluid. 01

11. Explain the capillary action of rise and fall of liquid columns. 01

12. Explain Compressibility and Bulk modulus. 03

13. Obtain an expression for Capillary rise of liquid. 04

14. Explain giving reasons the variation of viscosity of air and water with the temperature 03



Examples

1. Calculate capillary effect in a glass tube of 3 mm diameter when immersed in (i) water and, (ii)

mercury (specific gravity = 13.6) at temperature of 20C. The surface tension of water and

mercury at temperature of 20C are 0.074 N/m and 0.52 N/m. The contact angles water and

mercury are 0 and 130 respectively. Take specific weight of water at 20C as equal to 9.8

KN/m3.

04

2. Define compressibility of a fluid. When the pressure of liquid is increased to 7.5x103 kN/m2 from

4x103 kN/m2, its volume is found to reduce by 0.075 percent. Calculate the bulk modulus of

elasticity of the liquid.

03

3. A square plate of size 1m x 1m and weighing 500 N slides down an inclined plane with a uniform

velocity of 2 m/s. The plane makes an angle of 30 to the horizontal and has oil film of 1.5 mm

thickness. Find the dynamic viscosity of oil.

07

4. The weight of 5 m3 of certain oil is 45 kN. Calculate its specific weight, mass density and specific

gravity.

03

5. Calculate the height of capillary rise of water in a glass tube of diameter 1 mm. The air-water

surface tension at room temperature is 0.073 N/m. The contact angle for air-water-glass system

is taken as 0.

01

6. Convert 15 meters of head of water to oil of specific gravity 0.750 and mercury of specific gravity

13.6

04

7. Find the kinematic Viscosity of an oil having density 971 kg/m3. The shear stress at a point in oil

is 0.25 N/m2 and velocity gradient at that point is 0.2 per second.

04



Module 2 – Fluid Statics

Sr. No. Questions

De

c-1

4

Jun

e-1

5

De

c-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Write statement of : Hydrostatic law, Pascal’s law 2

2. Derive expressions for total force and centre of pressure on a vertical plane surface submerged

in static liquid.

7 04 07

3. Derive theoretical equation for the metacentric height of a floating body.

4. State Pascal’s law of pressure and prove it. 7 03 07

5. Write a short note on (1) piezometer & (2) inverted U-tube differential manometer with neat

sketches.

7

6. Discuss the equilibrium conditions for floating and submerged bodies with proper sketches. 7

7. State Archimede’s principle. 01 01

8. Define total pressure and center of pressure. 01 01

9. What is the value of atmospheric pressure head in terms of water column? 01

10. What is hydrostatic paradox? Explain with figure. 03 07

11. Explain construction and working of vertical and inclined single column manometer with

equation.

07

12. Explain construction and working of Bourdon tube pressure gauge. 07

13. Derive generalized equation of total pressure on inclined plane surface. 03

14. Explain possibilities of dam failure in short. 03

15. What is buoyant force? 01



16. Explain piezometer. 04

17. Derive an expression for the depth of center of pressure for inclined plane surface submerged in

the liquid.

07

18. Explain the procedure of measuring vaccum pressure with the help of U-tube manometer. 07

19. Write a short note on 7

(i) U-tube Manometer, (ii) Diaphragm pressure gauge.

07

20. Define the terms metacentre, metacentric height and absolute pressure. 01 03 03

21. Explain Buoyancy and Centre of Buoyancy. 01 03 01

22. Explain equilibrium in floating bodies. 04

23. Derive an equation for time period of oscillation of floating body. 07

24. How is the atmospheric pressure measured? 01

25. Why mercury is preferred as an indicating liquid in a U tube manometer? 01

26. How is the metacentric height calculated experimentally? 01

27. Explain with a neat sketch a U-tube differential manometer. When do we use an inverted U-tube

manometer?

03

28. Draw a sketch and explain how a U tube manometer can be used for measuring vacuum pressure. 04

29. Draw a chart to explain gage pressure atmospheric pressure, vacuum pressure and absolute

zero. Define each

01 03

30. Draw sketches to explain the working of a micro manometer. Develop the expression for

measurement of differential pressure in terms of the specific gravity of the manometric marterial

and hence explain how the sensitivity of the manometer can be increased.

07

31. Explain the Pascal’s hydrostatic paradox. 07 04



Examples

1. A dam section is shown in Fig. 1. Calculate, (i) total force exerted by static water on the dam

section, (ii) inclination of the force with horizontal and, (iii) depth at which this force acts. Take

length of the dam section (perpendicular to the section given in Fig.1) equal to 1 m.

07

2. An inverted differential manometer, having an oil of specific gravity 0.8 as manometric liquid, is

connected two pipes A and B which are at same level and both carrying water. Level of the oil in

left limb is 0.2 m above centre of pipe A and, level of the oil in right limb is 0.45 m above centre of

pipe B. Calculate difference in pressure between the two pipes.

07

3. A solid cylinder having 1.5 m diameter and 2 m height is floating in water with its axis vertical. If

the specific gravity of material of cylinder is 0.85, calculate metacentric height and state whether

the equilibrium is stable or unstable.

07

4. Absolute pressure at a point is 30 kPa. Convert this pressure in terms of gauge pressure. Also

calculate the corresponding height in terms of oil of specific gravity 0.9 for both of the above

values. Take atmospheric pressure = 101.39

07

5. Rectangular lamina of size 3m x 5m is immersed vertically in water such that 5m side is parallel

and lies below 1m to the free water surface. Determine the total hydrostatic force and centre of

pressure.

07

6. Tapering pipe has diameters of 40 cm and 25 cm at two different sections. Oil of specific gravity 07



0.85 flows through it. If the velocity of flow at 25 cm section is 3 m/s and pressure is 200 kPa,

determine the pressure at the other end. Assume pipe is laid horizontal and losses are negligible

between two sections.

7. Open cylindrical tank of 15 cm diameter and 35 cm deep contains water upto the brim. Tank is

rotated at 400 rpm about its vertical axis. Determine the volume of water left in the tank.

07

8. An isosceles triangle of base 3m and altitude 6m, is immersed vertically in water, with its axis of

symmetry horizontal. If the head of water on it is 9m, Determine (i) total pressure on plate, (ii)

The position of center of pressure.

04

9. A rectangular pantoon is 5m long, 3m wide and 1.2m high. The depth of immersion is 0.8m in sea

water. If the center of gravity is 0.6m above the bottom of pantoon, determine the metacentric

height. Take density of sea water as 1025 kg per meter cube.

03

10. An open tank contains 2 m of water covered with 1 m of oil (specific gravity 0.85). Find the

pressure of the interface and the bottom of the tank.

07

11. A solid wooden cylinder of 3 m diameter and 2 m height floating in water with its axis vertical.

Find the metacentric height of cylinder. Specific gravity of wood = 0.6

07

12. A solid cylinder of diameter 4 m has a height of 4 m. Find the metacentric height of the cylinder if

the specific gravity of the material of cylinder is 0.7 and it is floating in water with its axis

vertical. State whether the equilibrium is stable or unstable.

07

13. A spherical sea mine of diameter 0.9 m is weighing 2300 N. It is chained to the bottom of a

harbor. What external force must the chain provide to keep the sea mine floating to the surface?

Take mass density of sea water ρ = 1025 kg/m3.

01



14. The underground oil storage tank as shown in Figure 1 has developed a leak such that water has

entered the tank. The depth of oil is 2.0 m and water depth is 0.5 m. For the dimension given,

determine the hydrostatic pressure at the (i) water –oil interface and (ii) at the base of the tank.

Take specific gravity of oil = 0.87.

04

15. State the Archemdes principle about magnitude of buoyant force. An iceberg weighing 915kg/m3

floats on sea water with a volume of 600 cubic meter above the surface. Determine the total

volume of the iceberg if the specific weight of the sea water is 1025 kg/m3

04

16. Find out the pressure on one side of a tank with vertical sides and square in plan with sides 3.5

metre long. It contains oil of specific gravity 0.9 to a depth of 1 metre floating on 0.75 meter

depth of water.

04

17. A circular annular area of 2.0 m outer diameter and 1.0 m inner diameter is immersed vertically

in water with the centre of area at 3.5 m below the water surface. Find (i) the force exerted on

one side of the area, and (ii) location of the centre of pressure.

07



18. Determine the total pressure and centre of pressure on a triangular plate of base 4 m and height

3 m when it is immersed vertically in water. The base of the plate coincides with the free surface.

If the same plate makes 600 with the free surface, calculate the total pressure and centre of

pressure.

07

19. Water is flowing through two different pipes A and B to which an inverted differential

manometer having an oil of specific gravity 0.8 is attached. Pipe A is 20 cm above pipe B. Level of

oil in both pipes A and B is 30 cm high with respect to centre of respective pipe. If the pressure

head in pipe A is 2 m of water, calculate pressure in pipe B.

07



Module 3 – Fluid Kinematics

Sr. No. Questions

De

c-1

4

Jun

e -

15

De

c-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Briefly discuss about (1) uniform and non-uniform flow (2) velocity potential function & (3) uses

of flow net.

07

2. Define circulation. 01

3. State and define different types of fluid flow. 07

4. Define the following terms:

Metacentric height, Kinematic viscosity, Surface tension,

Velocity potential function and Reynolds number.

05

5. Differentiate between the following in brief:

(i). Rotational flow and Irrotational flow

(ii). Laminar flow and Turbulent flow

(iii). Compressible flow and Incompressible flow

(iv). Uniform flow and Non-uniform flow

04 03

6. Derive continuity equation for three dimensional incompressible flow. 07

7. a) Define following terms

i) Path line, ii) streamline, iii) streak line

01 01 03 03

8. Explain Reynold’s experiment with neat sketch. 04

9. Define rotational flow. 01

10. Define steady flow. 01



11. Distinguish between laminar flow and turbulent flow in pipes. 04

12. Distinguish between a laminar and turbulent flow. 01

13. Explain the use of flow net for a two dimensional flow. 04

14. Verify whether the given stream function ψ = y2 – x2 represent ir-rotational flow. 03

15. Explain the experiment conducted by Reynolds to study laminar and turbulent flow. Hence

explain the importance of the parameters contained in the Reynolds number to categorize the

flow as laminar and turbulent flow.

07

16. Define source, sink and doublet. Give the utility of flow net in the analysis of flow fields 07

17. Define convective and temporal acceleration 04

18. Derive the theoretical expression for metacentric height of the floating body. 07

19. Discuss conditions of stability for floating bodies. 03

20. Define: Stream line, Equipotential line, Stream tube 03

21. Write brief note on Flow net. 03

22. Explain Circulation and Vorticity. 04

23. Differentiate between: Steady and unsteady flow, Uniform and non-uniform flow, Laminar and

turbulent flow, Rotational and Irrotational flow.

07

Examples

1. A stream function for a two dimensional flow is given by ψ = 2xy, calculate the velocity at point P

(2,3). Find the velocity potential function ϕ.

04

2. For a fluid flow, velocity components in x and y directions are u = 2xy and v = x2 – y2 + 4

respectively. Show that the components represent a possible case of fluid flow. Derive stream

function and the flow rate between the stream lines corresponding to points (1, 0) and (1, 1).

07

3. A tank is 1.5m x1.5m square in plan and contains 1 meter depth of water up to the brim. How 04



high must the sides be so that no water is spilled when the acceleration parallel to one of the

sides is 5 m/s2.

4. A rectangular sluice gate of size 2m x 2m whose plane is inclined at an angle of 45 degree with

the horizontal has its horizontal upper edge 1.5 meter below free surface of water. Find out the

magnitude of the force parallel to the plane of gate required to pull it, given that the coefficient

of friction between the gate and gate groove is 0.15. Neglect self-weight.

04

5. A stream function is given by Ψ = 6x – 5y. Calculate the velocity components and also magnitude

and direction of resultant velocity at any point.

04

Module 4 – Fluid Dynamics

Sr. No. Questions

De

c-1

4

De

c-1

5

Jun

e-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Define Bernoulli’s theorem. 01 01

2. Derive Bernoulli’s equation for incompressible fluid flow. State assumptions made in the

derivation.

07 03 07

3. Give derivation of Bernoulli’s equation from Euler’s equation of motion. Enumerate assumptions

made in derivation and explain the meaning of each term of Bernoulli’s equation.

07 07 07

4. What is pressure head? 01

5. Derive Euler’s equation of motion along streamline. 07

6. What do you meant by TEL and HGL 01 04

7. What is the difference between Euler equation and Bernoulli’s equation? 03

8. Write the Bernoulli’s equation for ideal fluid and real fluid. Also list the applications where 04



Bernoulli’s equation is used.

9. Justify the use of energy correction factors and momentum correction factors in piped and open

channel flow analysis.

03

Module 5 – Flow Measuring Devices

Sr. No. Questions

De

c-1

4

Jun

e -

15

De

c-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Derive equation for rate of flow through the venturimeter. 07 04 07 07 07

2. Derive equation for discharge over a rectangular weir. Also explain significance of velocity of

approach.

07

3. Derive the equation for determining the discharge from Borda’s mouthpiece running full. 07

4. Define various hydraulic coefficients. How to determine coefficient of velocity experimentally? 07 04 07

5. Classify various types of notches. Derive the equation for discharge through a rectangular notch. 07 04

6. Define co-efficient of discharge. 01 01

7. What is Pitot tube? Derive equation of velocity for flow of fluid through it. 03 03

8. Explain working of rotameter with figure. 03

9. Derive equation of discharge through a convergent-divergent mouthpiece. 07

10. Derive darcy-weisbach equation for friction loss in the pipe. 07 07

11. Discuss relative merits and demerits of venturimeter with respect to orifice meter. 04

12. What are the advantages of triangular notch over a rectangular notch? 04

13. What is weir? How it different from a notch. 03

14. What are the advantages of providing mouth piece? 04



15. How volumetric flow rate can be measured by pitot tube? 03

16. Classify various types of notches. 03

17. Write the working principle of a Pitot tube. 01

18. Explain the components of a venturimeter with a neat proportionate sketch. 04

19. What is the difference between a mouthpiece and an orifice? 03

20. Explain with neat sketches the Convergent-Divergent mouthpiece and the Borda’s mouthpiece 04

21. Explain with neat sketches the contracted rectangular notch and Cippoleti notch. 04

22. Derive the equation for time (T) required to empty a rectangular tank filled with liquid. The tank

has an orifice at its bottom. The initial depth of water in the tank is H1.

07

23. Define a sharp crested, narrow crested and a broad crested weir. 03

24. Define sensitivity of a notch. Explain giving the properties of a triangular notch why it is

preferred over rectangular and other shapes of notches for flow measurements in open channels.

04

25. Develop an expression for measurement of velocity of flow in a pipe with the help of a pitot tube,

explain stagnation pressure.

07

26. Explain why ventilation of weirs is necessary. 03

27. Give classification of Orifices. 03

28. Derive an expression for the discharge through triangular notch. 07

29. What is mouthpiece? Briefly explain Borda’s mouthpiece. 03



Examples

1. A sharp-edged orifice of 125 mm diameter is fixed on vertical side of a tank under a constant

head of 9 m. The orifice is discharging water at a rate of 105 liters/sec. A point on the jet has

horizontal and vertical coordinates of 4.25 m and 0.55 m respectively, which are measured from

the vena contracta. Calculate coefficient of velocity, coefficient of discharge and coefficient of

contraction. Also estimate area of the jet at the vena contracta.

07

2. A tank has two identical orifices in one of its vertical side. The upper and lower orifices are 3m

and 5 m below the water surface respectively. Determine the point of intersection of two jets if

coefficient of velocity is 0.92 for both the orifices.

07

3. A reservoir discharges through a sluice 0.915m wide by 1.22m deep. The top of the opening is

0.65m below the water level in the reservoir and the downstream water level is below the

bottom of the opening. Calculate (i) the discharge through the opening if Cd= 0.6 and (ii) % error

if the opening is treated as a small orifice.

04

4. A circular tank of diameter 5 m contains water up to a height of 4.5 m. the tank is provided with

an orifice of diameter 0.5 m at the bottom. Find the time taken by water (i) to fall from 4.5 m to

1.5 m (ii) for completely emptying of tank. Take Cd= 0.62

07

5. A projectile is traveling in air having pressure and temperature as 9 N/cm2 and -5C. If the mach

angle is 35, find the velocity of projectile. Take k=1.4 and R=287 J/kg K

04

6. A 200 m long pipe is laid on a slope of 1 in 50. It has 1 m diameter at the high end and reduces to

half of its diameter at lower end. Water is flowing at a rate of 60 liter/sec. If the pressure at the

high end is 35.72 kN/m2. Find pressure at the low end. Neglect losses.

07

7. Water is flowing in a rectangular channel of 1.2 m width and 0.08 m depth. Find the discharge if

the crest length is 50 cm, if the head of water over the crest of weir is 18 cm and water from

07



channel flows over weir. Take Cd= 0.62. Neglect end contraction. Take velocity of approach in to

consideration.

8. Sketch the jet trajectory from a small circular orifice located on the side wall of a liquid container.

Show the vena contracta. What do you understand by coefficient of contraction? Give typical

values of Cc for small circular orifice.

07

9. A pitot tube is inserted in a pipe of 30 cm diameter. The static pressure of the tube is 10 cm of

mercury, vacuum. The stagnation pressure at the centre of the pipe recorded by the pitot tube is

1.1 N/cm2. Calculate the rate of flow of water through the pipe if mean velocity of flow is 0.85

times centre line velocity. Take coefficient of pitot tube = 0.98.

07

10. Estimate the discharge over a 90 triangular notch having head over crest as 45 cm. The

coefficient of discharge Cd = 0.62. If the head over crest becomes 55 cm calculate the percentage

increase in discharge.

07

11. Calculate the discharge for flow passing through a trapezoidal notch having base width of 0.75 m

and side slope of 1:1. Take the head over crest of notch = 50 cm. The coefficient of discharge Cd=

0.63.

03

12. The head over a rectangular notch is 90 cm. The discharge is 0.3 m3/s. Find the length of the

notch when coefficient of discharge is equal to 0.62.

04

13. A horizontal venturimeter with inlet and throat diameters 30 cm and 15 cm respectively is used

to measure rate of water. The reading of differential manometer connected to the venturimeter

is 20 cm of mercury. Determine the rate of flow. Take coefficient of discharge equal to 0.98.

04



Module 6 – Flow Immersed Past Bodies

Sr. No. Questions

De

c-1

4

Jun

e-1

5

De

c-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Differentiate between a stream lined body and a bluff body. Prove that the coefficient of drag for

the drag on sphere is given by CD = 24/Re, when Re (Reynolds’ number) ≤ 0.2.

07

2. Briefly discuss about drag force and lift force. Explain the types of drag. 07

3. Define drag and lift. 01

4. Derive the equation of pressure at the bottom of the container when liquid in it is subjected to

uniform acceleration in vertically upward and downward direction.

07

5. Define various parts of an aerofoil. 03

6. Explain characteristics of airfoil. 04

7. Briefly discuss about drag force and lift force. 04

8. Explain free and forced vortex with suitable examples. 03

9. Explain the terms Total drag, Frictional drag, pressure drag with suitable examples. 04

10. Explain the Magnus effect in lift generation around a body 01 03

11. Explain chord length, angle of attack and stall point for airfoils and explain the development of

circulation around them.

07

12. Differentiate between: (i) Stream line body and Bluff body (ii) Friction drag and Pressure drag 04

13. Discuss Drag on a sphere for various range of Reynold’s number. 07



Examples

1. Experiments on a flat plate of 1 m length and 0.5 m width were conducted in a wind tunnel in

which wind was blowing horizontally at a speed of 60 Km/hour. The plate was kept at such an

angle that the coefficients of drag and lift were 0.2 and 0.88 respectively. Calculate, (i) drag and

lift forces, (ii) resultant force and its direction and, (iii) power exerted by the air stream on the

plate. Take specific weight of air equal to 11.28 KN/m3.

07

2. An aero plane weighing 40 kN is flying in a horizontal direction at 360 km/hr. The plane spans

15m and has a wing surface area of 35 m2. Determine the lift coefficient and the power required

to drive the plane. Assume drag coefficient =0.3 and for air ρ = 1.20 kg/m3. Also work out the

theoretical value of the boundary layer circulation.

07

3. An open cylindrical tank of 0.9 m in diameter and 2 m high contains water up to 1.5 m depth. If

the cylinder rotates about its vertical axis what maximum angular velocity can be attained

without spilling any water?

07

4. A car has frontal projected area of 1.5 m2 and travels at 55 km/h. Calculate the power required to

overcome wind resistance if coefficient of drag is 0.35. If the drag coefficient is reduced by

streamlining to 0.25 what speed of the car is possible? Take ρair = 1.2 kg/m3

07

Module 7 – Compressible Flow

Sr. No. Questions

De

c-1

4

Jun

e-1

5

De

c-1

5

Jun

e-1

6

Jan

-17

Jun

e-1

7

No

v-1

7

Ma

y-1

8

Theory

1. Derive equation for sonic velocity of sound wave in a compressible fluid in terms of the bulk

modulus of elasticity of the fluid medium.

07 07



2. Define Mach number. Give classification and explanation of the type of flow based on Mach

number.

07

3. Prove that velocity of sound wave is square root of the ratio of change of pressure to the change

of density of the fluid

07

5. What is sonic flow? 01

6. What is stagnation point? 01

7. Define Mach Number. 01

8. Define Mach number. Give classification and explanation of the type flow based on Mach number. 04 07

9. What do you understand by stagnation pressure? 01

10. Distinguish between subsonic and supersonic flow. 03

11. Draw sketches to explain the propagation of pressure waves by an object moving in a

compressible fluid with supersonic motion. Mark Mach cone and zone of silence.

07

Examples

1. An aeroplane is flying at 950 Km/hour through still air having an absolute pressure of 80 KN/m2

and temperature -7C. Calculate stagnation pressure, stagnation temperature and stagnation

density, on the stagnation point on the nose of the plane. Take R = 287 J/ Kg K and γ = 1.4 for air.

07

2. Define Mach number. A supersonic plane in its flight has a Mach angle of 40 and is flying in air

with -20 C. Calculate the speed of plane. Assume k = 1.4 and R = 287 J/Kg.K

07

module 1 properties of fluids - darshan institute of ......metre long. it contains oil of specific...

Documents