KINGS COLLEGE OF ENGINEERING

DEPARTMENT OF CIVIL ENGINEERING

Sub. Code/Name: CE 2202 –MECHANICS OF FLUIDS Year/Sem: II/III

UNIT-I: DEFINITIONS AND FLUID PROPERTIES

PART-A

1. Define the following : (i) Hydraulics (ii) Fluid Mechanics

Hydraulics

It is that branch of engineering science which deals with water (at rest

or in motion).

Fluid Mechanics

Fluid mechanics is that branch of science which deals with the behavior

of the fluids (liquid or gases) at rest as well as in motion.

Statics:- Study of fluids at rest

Dynamics: - Study of fluids in motion, Where pressure forces are considered

Kinematics: - Study of fluid in motion, Where pressure forces are not

considered

2. What is fluid? How are fluids classified?

A fluid is a substance which is capable of flowing or a fluid is a substance

which deforms continuously when subjected to external shearing force.It may be

classified as: (i) Liquid, (ii) Vapour

3. Differentiate between liquids and gases?

Liquid:- Liquid is a fluid which possesses a definite volume

(i) Liquids have bulk elastic modules when under compression and will

store up energy in the same manner as a solid.

(ii) All known liquids vaporize at narrow pressure above zero, depending

on the temperature.

Gas:- It possesses no definite volume and is compressible.

4. Explain briefly the following terms:

(i) Mass Density or Density or Specific Mass

It is defined as the ratio of the mass of a fluid to its volume. It is denoted by (ρ)

SI units: kg/m3. The value of density for water 1 gm/cm3 or 1000 kg/m3

ρ= Mass of fluid / volume of fluid in m/v.

(ii) Weight Density or Specific Weight

It is defined as the weight per volume. It is denoted by

(mass of fluid) x (acceleration due to gravity)

W = weight of fluid/volume of fluid =-----------------------------------------------------

(volume of fluid)

W = ρx g

In SI units, w = 9.81 kN/m3

In MKS units, w = 1000 kg/m3

(iii) Specific Volume

It is defined as volume per unit mass of fluid

Specific volume = volume/mass = 1/ ρ

Units : m3 / kg.

(iv) Specific Gravity (S)

It is defined as the ratio of the weight density of a fluid to the weight density of

a standard fluid. For liquids the standard fluid is taken as water and for gases the

standard fluid is air. It is also called relative density.

5. What is Viscosity or Co-efficient of dynamic viscosity?

Viscosity is defined as the property of a fluid which determines its

resistance to shearing stresses. It is primarily due to cohesion and molecular

momentum exchange between fluid layers, or the shear stress required to

produce unit rate of shear strain. Mathematically

µ = co-efficient of dynamic viscosity or only viscosity

du/dy = rate of shear strain (or) velocity gradient = shear stress

Units

M.K.S. = kgf – sec / m2

C.G.S. = poise = dyne-sec/cm2

1 poise = 1/10 N.S./m2

6. Define Kinematic Viscosity

Kinematic viscosity is defined as the ratio between the dynamic

viscosity and density of fluid. It is denoted by v

V = µ/ρ

Units

S.I. Units = m2 / sec

M.K.S. Units = m2 / sec

C.G.S. Units = stoke = cm2 / sec

1 stoke = 10-4 m2/sec

7. State Newton’s law of Viscosity and give examples of its application

It states that the shears stress (τ ) on a fluid element layer is directly

proportional to the rate of shear strain

Τ = µ – du/dy

Examples : water, kerosene, air

8. State the types of fluids?

(1) Ideal fluids, (2) Real fluids, (3) Newtonian fluids, (4) Non – Newtonian

fluids and (5) Ideal Plastic fluids.

9. Distinguish between ideal and real fluids?

A fluid, which is compressible and is having no viscosity and surface tension,

is known as an ideal fluid. An ideal fluid is only an imaginary fluid. But real

fluid possesses viscosity, surface tension and compressibility. All the fluids, in

actual practice are real fluids.

10. What is the effect of temperature and pressure on viscosity of liquid and

gasses?

The viscosity of liquids decreases but that of gases increase with increase in

temperature. This is due to the reason that in liquids the shear stress is due to the

inter – molecular cohesion which decreases with increase of temperature. The

viscosity under ordinary conditions is not appreciably affected by the changes in

pressure.

11. What is capillarity? What is the reason for this phenomenon?

Capillarity is a phenomenon by which a liquid (depending upon its specific

gravity) rises into a narrow space above or below its general level. This phenomenon

is due to the combined effect of cohesion and adhesion of liquid particles.

12.For what range of contact angle of a fluid the following will occur (i)

capillary rise and (ii) capillary fall or dip

4 σ cos θ /wd.

Capillary rise, θ = 0

Capillary fall, = θ = 130 o to 150o

13.Define Newtonian and Non – Newtonian fluids. (Nov.05 (AU)

Newtonian fluid

A real fluid is one in which the shear stress is directly proportional to

the rate of shear strain which also is known as Newtonian fluid. Example :

water, kerosene, etc.,

Non-Newtonian fluid

A real fluid is one in which the shear stress is not proportional to the rate of

shear strain which is also known as Non-Newtonian fluid. Example : solutions or

suspensions (slurries), mudflows, polymer solutions.

14. What is the difference between cohesion and adhesion?

Cohesion

Cohesion means inter molecular attraction between the molecules of the

same liquid. It enables a liquid to resist small amount of tensile stresses. Surface

tension is due to cohesion between particles at the free surface.

Adhesion

Adhesion means attraction between the molecules of a liquid and the

molecules of a solid boundary surface in contact with the liquid.

15. What is surface tension?

Surface tension is defined as the tensile force acting on the surface of a liquid

in contact with a gas or on the surface between two immiscible liquids such

that the contact surface behaves like a membrane under tension. Example :1.

Raindrops, 2.rise a sap in a tree and 3. Collection of dust particles on water

surface. Unit : N/m.

16. An oil spill over a small area in sea spreads over a long area gradually. A

small drop of ink on a chalk piece spreads over a wider area. Is the reason in

both cases the same?

In the first case, it is due to surface tension. It the second case, it is due to the

capillary spread through the small pores of the chalk.

17. Define Compressibility and Bulk Modulus.

Bulk modulus (K) is defined as the ratio of compressive stress to

volumetric strain.

(Negative sign indicates decrease in volume with increase of pressure)

Compressibility is the reciprocal of the bulk modules of elasticity.

Part –B

1. What are the different types of fluids? Explain each type. (8)

2. Define capillary, surface tension and state the factors that affect them? (8)

3. Define Fluid density, specific weight and specific gravity? (8)

4. Define the term Vapor pressure and capillarity? (8)

5. What is meant by continuum concept of the system? (8)

6. What is control Volume? (8)

7. Derive an expression for continuity equation? (8)

8Calculate the capillary effect in a glass tube 5mm diameter, when immersed in 1. Water

and 2. Mercury. The surface tension of water and mercury in contact with air are 0.0725

N/m and 0.51 N/m respectively. The angle of contact of mercury is 130˚? (8)

9. A shaft rotates at a speed of 200 rpm. The power lost in the bearing for a sleeve length

of 100 mm is 250 watts. The thickness of oil film between the shaft and sleeve is 1.5 mm

and the oil has a viscosity of 10 poise. Calculate the diameters of shaft and sleeve. (8)

10. 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 0.0085m3 at 270 N/cm2

Pressure. (8)

11. Derive an expression between the surface tension in a Soap bubble. Fin the surface

tension in a soap bubble of 30 mm diameter when the intensity pressure is 2.5 N/m2

above atmospheric pressure. (8)

12. The space between two square parallel plates is filled with oil. Each side of the plate

is 75 cm. The thickness of the oil film is 10mm. The upper plate which moves at 3 m/s

requires a force of 100N to maintain the speed. Determine

(i) The Dynamic viscosity of oil

ii) The kinematic viscosity of the oil, if the specific gravity of oil is 0.9. (8)

13. One liter of crude oil weighs 9.6N. Calculate its specific weight, density, specific

volume and specific gravity.(8)

14. A rectangular plate of size 25cmx50cm and weighing 245.3N slides down a 30˚

inclined surface at a uniform velocity of 2 m/s. If the uniform 2mm gap between the plate

and the inclined surface is filled with oil, determine the viscosity of the oil.(16)

15. A cylindrical shaft of 90 mm rotates about vertical axis insides a cylindrical tube of

length 50 cm and 95 mm internal diameter. If the space between them is filled with oil of

viscosity 2 poise find the power lost in friction for a shaft speed of 200 rpm.(16)

UNIT – II : FLUID STATICS & INEMATICS

PART-A

1. Define the term : Pressure.

The force per unit area is called pressure.

Intensity of pressure, p = F/A

Where F = Force, A = Area on which the force acts.

Units : In M.K.S. – kgf/m2, 1 Pascal = 1N/m2

In SI – N/m2 1 Bar = 105 N/m2

2. State Pascal’s Law and gives example where principle is is applied.

The intensity of pressure at any point in a liquid at rest, is the same in all

directions.

Examples: Hydraulic press, Hydraulic jack, Hydraulic lift and Hydraulic crane.

3. State Hydrostatic law

The pressure of any point in a fluid at rest is obtained by the hydrostatic la

which states that the rate of increase of pressure in a vertically downward direction

must be equal to the specific weight of the fluid at that point.

P p

z = -------- g = ------ z is called pressure head.

Ρ w,

4. Define the following:

Atmospheric pressure

The atmospheric air exerts a normal pressure upon all surfaces with which it

is in contact and it is known as atmospheric pressure. It is also known as Barometric

pressure.

Gauge pressure: It is defined as the pressure which is measured with the help of

a pressure measuring instrument, in which the atmospheric pressure is taken as

datum. The atmospheric pressure on the scale is marked as zero.

Vacuum Pressure

It is defined as the pressure below the atmospheric pressure (i.e., negative

pressure).

Absolute Pressure

It is defined as the pressure which is measured with the reference to absolute

vacuum pressure.

Mathematically,

1. Absolute Pressure = (Atmospheric pressure ) + (Gauge pressure).

2. Vacuum pressure = (Atmospheric pressure) – (Absolute pressure)

5.What are the methods describing of fluid flow?

Lagrangian Method

A single fluid particle is followed during its motion and its velocity,

acceleration, density, etc., are described.

Eulerian Method

The velocity, acceleration, pressure, density, etc., are described at a

point in flow field. It is commonly used in fluid mechanics.

6. What do you understand by the terms (1) Total acceleration (2) Local

acceleration (3) Connective acceleration?

Total Acceleration

Similarly for ay and az

Where u, v and w are the velocity components in x,y,z directions respectively.

Local Acceleration

It is defined as the rate of increase of velocity with respect to time at a given

point in a flow field.

Convective Acceleration

It is defined as the rate of change of velocity due to the change of position of

fluid particles in a fluid flow.

7.Define the following and give example for each:

Laminar flow

It is defined as that type of flow in which the fluid particles move along well-

defined paths. This type of flow is also called stream-line, flow or viscous flow.

Examples : Flow through capillary tube, flow of blood in veins and arteries.

Trubulent flow:

It is that type of flow in which the fluid particles move in a zig-zag way.

Compressible flow

It is that type of flow in which the density of the fluid changes from point to

point. Mathematically, ρ≠ constant.

Examples: Flow of gasses through orifices, nozzles, gas turbines, etc.

Incompressible flow

It is that type of flow in which density is constant for the fluid flow.

Mathematically ρ= constant.

Examples: subsonic, aerodynamics.

Rotational flow

It is that type of flow in which the fluid particles while following along stream

lines also rotate about their own axis.

Example : motion of liquid in a rotating tank.

Irrotational flow

It is that type of flow in which the fluid particles while flowing along stream

lines, do not rotate about their own axis.

Example: Flow above a drain hole of a stationary tank or a wash basin.

Steady flow:

It is defined as that type of flow in which the fluid character tics like velocity,

pressure, density, etc., at a point change with time, (dv/dt), at x0, y0, z0 = 0

Example: Flow through a prismatic or non-prismatic conduit at a constant flow rate.

Unsteady flow

It is that type of flow, in which the velocity, pressure and density at a point

changes with respect to time, (dv/dt) at x0, y0, z0 ≠0

Example: The flow in a pipe whose valve is being opened or closed gradually

(velocity equation is in the form u = αx2 + bxt).

Uniform flow

It is defined as that type of flow in which the velocity at any given time does

not change with respect to space, (dv/ds)t = constant = 0.

Example : Flow through a straight pipe of constant diameter.

Non-uniform flow

It is that type of flow in which the velocity at any given time changes with

respect to space.

Example: Flow through a non-prismatic conduit.

One-Two and Three dimensional flows

The flow in which the velocity is a function of time and

One space coordinates – one dimensional flow,

Two space coordinates – two dimensional flow,

Three mutually perpendicular directions – three dimensional flow

8. Distinguish between path lines, stream lines and stream lines.

Path lines:

It is the path followed by a fluid particle sin motion. It shows the

direction of particular particle as it moves ahead.

Stream lines:

It is defined as an imaginary line within the flow so that the tangent at

any point on it indicates the velocity at that point.

dx dy dz

Equation of a stream line = --- = ---- = ----

u v w

A path line gives the path of one particular particle at successive instants of

time, a stream line indicates the direction of a number of particles at the same

instant.

Streak Line

The streak line is a curve which gives an instantaneous picture of the location

of the fluid particles, which have passed through a given point.

9.Define Continuity Equation

The continuity equation is based on the principle of conservation of mass. It

states that in a running fluid, i.e., if no fluid is added or removed from the pipe in any

length, the mass passing across different sections shall be same, ρ1 A1 V1 = ρ2 A1 C1

for compressible fluid and A1 V1 = A2 V2 = for in compressible fluid.

For three dimensional flow

10.Explain briefly the following ; (a) Velocity potential function and (b) Stream

function.

Velocity Potential function (φ)

It is defined as a scalar function of space and time such that its negative

derivative with respect to any direction gives the fluid velocity in that direction.

Mathematically,

Φ ≠ (x,y,z,t) ------------ for unsteady flow

Φ ≠ (x,y,z,t) ------------ for unsteady flow

Where u,v,w are the components of velocity in x,y,z directions.

(1) If velocity potential (φ) exists, the flow should be irrotatinal flow. (2) if velocity

potential (φ) satisfies, the Laplace equation represents the possible steady in

compressible irrotational flow.

Stream Function (ψ)

It is defined as the scalar function of space and time, such that its partial

derivative with respect to any direction gives the velocity component at right

angles to that direction.

(1) If stream function exists, it is possible case of a fluid flow which ay be rotational or

irrotational. (2) If stream function satisfies the Laplace equation, it is a possible case of an

irrotational flow.

10. If the stream function is known, is it possible to determine the rate of

flow between any two stream lines.

Yes, from the values of ψ which are the stream function values of any two

stream lines can be found. The rate of flow between the stream lines is per unit

thickness.

11. When is Mechanical Pressure Gauge used?

Whenever a very high fluid pressure is to be measured, a mechanical gauge

is best suited.

12. What is total pressure?

The total pressure on a immersed surface, may be defined as the total

pressure exerted by the liquid on it and is given by

P = w A y.

Part – B

1. State and proof Pascal’s Law. (16)

2. Obtain an expression for continuity equation in Cartesian co ordinates. (16)

3. Derive an expression for the depth of centre of pressure from free surface of liquid of

a vertical plane Surface sub merged in the liquid. (16)

4. Derive an expression for the depth of centre of pressure from free surface of liquid of an

inclined plane Surface sub merged in the liquid. (16)

6. Determine the metacentric height with experimental determination? (8)

8. Explain in detail stream line, streak line and path line? (8)

9. Derive an expression for stream and velocity potential functions? (8)

10. How are floats used in velocity measurements? Describe the rod float and double

float? (8)

11. Explain about hot wire and hot film anemo meter used in velocity measurement?

(8)

12. Describe Laser Doppler velocimetry?(8)

13. What ids flow net? Enumerate the methods of drawing flow nets. What are the uses

and limitation of flow nets? (8)

14. The two dimensional stream function for a flow is Ψ = 9 +6x-4y+7xy. Find the velocity

potential function. (8)

15. A triangular plate of 1m base and 1.5m altitude is immersed in water. The plane of the

plate is inclined at 30° with free water surface and base is parallel to and at a depth of

2m from water surface. Find the total pressure on e plate and position of centre of

pressure. (8)

UNIT – III : FLUID DYNAMICS

PART-A

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

(i) Gravity force (Fg)

(ii) Pressure force (Fp)

(iii) Force due to viscosity (Fv)

(iv) Force due to turbulence (Fr)

(v) Force due to compressibility (Fe)

2. Write Reynolds Equation, Navier – Stokes Equation and Eulers equation of

motion.

Reynolds Equation : (Fg)x + (Fp)x + (Fv)x + (Ft)x

Navier – Stokes Equation : (Fg)x + (Fp)x + (Fv)x

Eulers Equation : (Fg)x + (Fp)x

3 Explain briefly the following heads:

Potential head or Potential energy

This is due to configuration or position above some suitable datum line. It is

denoted by Z.

Velocity head or Kinetic energy

This is due to velocity of following liquid and is measue as V2/2g where V is

the velocity of flow and g is the acceleration due to gravity (g=9.81 m/s2)

Pressure head or Pressure energy

This is due to pressure of liquid and reckoned as p/w where p is the pressure

and w is the weight density of the liquid.

Total head, H = z + V2/2g + P/w m of liquid

Total energy, E = z + V2/2g + P/w Nm/kg of liquid.

4. State Bernoulli’s Equation

It states that in a steady ideal flow of an incompressible fluid, the total energy

at any point of the fluid is constant. The total energy consists of pressure energy,

kinetic energy and potential energy.

Mathematically, p/ρ g + V2/wg + z = constant.

5. State the assumptions in Bernoulli’s Equation

(i) The fluid is ideal, i.e., viscosity is zero

(ii) The flow is steady and continuous

(iii) The flow is compressible

(iv) The flow is irrotational

(v) The flow is along the streamline.

6. State the limitations of Bernoulli’s Equation

1. Velocity of flow is assumed to be constant whereas it is not so in actual practice.

2. For viscous flow, the loss of energy due to shear forces, has to be accounted for.

3. For the flow of liquid in a curved path, the energy due to the centrifugal force must

be taken into account.

4. In the case of unsteady flow, the changes on the kinetic energy are to be

accounted for.

7. What is the difference between venturimeter and an orficemeter.

1. The venturimeter can be used for measuring the flow rates of all incompressible

flows (gases with low pressure variations as well as liquids), whereas orficemeter

can be generally used for measuring the flow rates of liquids.

2. Venturimeter is installed in pipeline only, and the accelerated flow through the

apparatus, is subsequently decelerated to the original velocity at the outlet of the

venturimeter. The flow continues through the pipeline. In the orficemeter the entire

potential energy of fluid is converted to kinetic energy and the jet discharges freely

into the open atmosphere.

8. Write down the advantages and disadvantages of using orficemeter over a

venturimeter.

Advantages

Advantage of orinficemeter over venturimeter is that its length is short and

hence it can be used in a wide variety of application whereas a venturimeter has

excessive length.

Disadvantages

The disadvantage of orinficemeter is that a sizeable pressure loss is

increased because of the flow separation down stream of the plate. In a venturimeter

the gradual expanding section keeps boundary layer separationto a minimum,

resulting in good pressure recovery across the meter.

9. what is Pitot tube?

It is a device used for measuring the velocity of flow at any point in a pipe or in

a channel. It is basedo n the principle that if the velocity of flow at a point becomes

zero, the pressure there is increased due to the conversion of the kinetic energy into

pressure energy. In its simplest form, the pitot tube consists of a glass tube is bent at

right angles and its placed in flow such that one leg is vertical and the other leg is

horizontal.

10. Explain the principel of Venturimeter

The basic principle on which a venturimeter works is that by reducing the

cross sectional area of the flow passage, a pressure difference is created and the

measurement of the pressure difference enables the determination of the discharge

through the pipe.

11. Why is coefficient of discharge of orifice meter much smaller than that of

venturimeter?

The coefficient of discharge for an orifice meter is much smaller than that for a

venturimeter. This is because in the case of an orifice meter there are no gradual

converging and diverging flow passages as in the case of a venturimeter, which

results in a greater loss of energy and consequent reduction of the coefficient of

discharge for an orifice meter.

12. What is manometer? How they are classified?

Manomeer are defined as the devices used for measuring the pressure at a

point in a fluid by balancing the column of fluid by the same or another column of the

fluid.

They are classified as:

(a) Simple manometers (b) Differential Manometers

1. Piezometer 1. U-tube differential manometer.

2. U-tube manometer 2. Inverted U-tube differential manometer

3. Single column manometer

13. Differentiate between simple manometers and differential manometers.

Simple manometers are used to measure pressure of fluid at a point in a pipe

whereas differential manometers are used to measure the difference in pressure

between any two points in a pipeline or in any two pipes.

14 What are mechanical gauges? Name four important mechanical gauges?

Mechanical gauges are defined as the devices used for measuring the

pressure by balancing the fluid column by the spring or dead weight.

(a) Diaphragm pressure gauge (b) Bourdon – tube pressure gauge (c) Dead –

weight Pressure gauge and (d) Bellows pressure gauge.

PART-B

1 Derive the Euler’s equation of motion and finally derive the Bernoulli’s equation and

clearly state its assumption.(16)

2. Draw the sectional view of Pitot’s tube and write its concept to measure velocity of the

fluid flow? (8)

3 Differentiate between Venturimeter and Orifice meter?(8)

4. Derive the Hagen poiseuille’s equation to show the head loss

for a laminar flow. (16)

5. A swimming pool of 8m x 15m is to be filled to a depth of 2.5m. Determine the inflow

required in m cube per second for a filling time of 90 minutes. If 40mm pipes are available

and the water velocity in each ho se is limited to 2m/s, determine the number of hoses

required? (16)

6. A 400mm dia meter pipe branches into two pipes of diameters 200mm and 250mm

respectively. If the average velocity in the 400 mm diameter pipe is 2.2m/s, find the

discharge in the pipe. Also determine the velocity in 250mm pipe, if the average velocity in

200mm diameter pipe is 2.6m/s? (16)

7. A jet of water from a nozzle of diameter 15mm is directed vertically upwards

with a velocity of 12m/s. If the jet remain circular, workout its diameter at a point 3m

above the nozzle tip. Neglect any loss of energy? (16)

8 Water flows through h a pipe AB of diameter 50mm, which is in series with pipe BC of

diameter 75 mm in which the velocity is 2m/s. At c the pipe forks and one branch CD

is of unknown diameter such that the velocity is 1.5 m/s. The other unknown dia meter

such that the velocity is 1.5 m/s. The other branch CE is of diameter 2 5mm and condition

are such that the discharge in pipe BC divides so that the discharge in the pipe CD is equal

to two times of discharge in CE.

Calculate

1. Discharge in pipe AB and CD.

2. Velocity in pipe AB and CE.

3. Diameter of pipe CD. (16)

9 A vertical tube of 1m dia meter and 20 m long has a pressure head of 5.5m of water at

the upper end. When water flows through the pipe at a n average velocity of 4.5m/s,

calculate the head at the lower end of the pipe when the flow is upward. (16)

10 Water is flowing through a tapering pipe having diameters 300mm and 1 50mm at

sections 1 and 2 respectively. The discharge through the pipe is 40lit/s. The section 1 is

10m above datum and section 2 is 6m above datum. Find the pressure at the section 2, if

that at section 1 is 400kN/m square? (16)

11 The discharge through a horizontal tapering pipe is 60lit/s. The diameter at inlet and

outlet are 25cm and 15cm respectively. If the water enters at a pressure of

1kgf/centimeter cube, Determine the Pressure at which it leaves. (16)

12 Oil of specific gravity of 0.90 flows in a pipe 300mm diameter at the rate of 120 lit/s and

the pressure at a point A is 25kPa. If the point A is 5.2m above the datum line, calculate

the total energy at point A in terms of m of oil? (16)

13. A 300 mm x 100 mm Venturimeter is provided in a horizontal pipeline to measure the

flow of water. The pressure intensity at inlet is 125 KN/meter square while the vacuum

pressure head at the throat is 360mm of mercury? Assuming that 4% of head is lost in

between the inlet and throat, find the co-efficient of discharge and rate of flow through

Venturimeter. (16)

14. Derive an expression for discharge of Venturimeter. (16)

UNIT – 4 : BOUNDARY LAYER AND FLOW THROUGH PIPIE

1. Define the terms : Major Energy loss and minor energy loss in pipe?

The loss of head or energy due to friction in a pipe is known as a major

loss while the loss of energy due to change of velocity of the flowing fluid in

magnitude or direction is called minor loss of energy.

2. What do you understand by (a) Total energy line (b) Hydraulic gradient

line?

Total energy line

It is defined as the line which gives the sum of pressure head, datum

head and kinetic head of a flowing fluid in a pipe with respect to some

reference line.

Hydraulic gradient line

It is defined as the line which gives the sum of pressure head, datum

head of a flowing fluid in a pipe respect to some reference line. Sometimes the

hydraulic grade line is also known as piezometric head, (p/w+z).

3. What is an equivalent pipe?

An equivalent pipe is defined a the pipe of uniform diameter having loss

of head and discharge equal to the loss of head and discharge of a compound

pipe consisting of several pipes of different lengths and diameters.

L L1 L2 L3

---- + ---- + ---- + ----- +….

D5 D51 D

52 D

53

The above equation is also known as Dupits equation.

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

Pipes in series

Pipes in series or compound pipes is defined as the pipes of different

lengths and of different diameters are connected end to end (in series) to form

a pipe line.

Pipe in parallel

Pipes are said to be parallel, when a main pipe divides into two or more

parallel pipes which again joint together downstream and continues as a

mainline. The pipes are connected in parallel in order to increase the

discharge passing through the main.

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

In long pipes, minor losses are insignificant in magnitude compared to

friction losses which is justifiably treated as major loss. If the pipe is short,

minor losses may be come the major component of the total head loss.

6. Define : Water hammer in pipes.

In a long pipe, when the flowing water is suddenly brought to rest by

closing the valve or by any similar cause, there will be a sudden rise in

pressure due to the momentum of water being destroyed. A pressure wave is

transmitted along the pipe. A sudden rise in pressure has the effect of

hammering action on the walls of the pipe. This phenomenon of sudden rise in

pressure is known as water hammer or hammer blow.

7. Define boundary layer.

When a solid body is immersed in a flowing fluid, there is a narrow

region of the fluid in the neighborhood of the solid body, where the velocity of

fluid varies from zero to free stream velocity. This narrow region of fluid is

called boundary layer.

8. Differentiate between laminar boundary layer and turbulent boundary

layer?

The boundary layer is called laminar boundary layer, if the Reynolds

number of the flow as Re = U x X/v is less than 3 x 105

If the Reynolds number is more than 5 x 105, then the boundary layer is

called turbulent boundary.

Where

U = free stream velocity of flow

X = distance from leading edge

And v = kinematic viscosity of fluid.

9. Define laminar sub layer?

In turbulent boundary layer region, adjacent to the solid boundary

velocity for a small thickness variation is influenced by viscous effect. This

layer is called as laminar sub layer.

10. Define boundary layer thickness (δ).

It is defined as the distance from the boundary of the solid body

measured in the y – direction to the point where the velocity of the fluid is

approximately equal to 0.99 times the free stream (v) velocity of the fluid.

11. Define displacement thickness (δ)

It is defined as the distance measure perpendicular to the boundary of

the solid body, by which the boundary should be displaced to compensate for

the reduction in flow rate on account of boundary layer formation.

δ* = ∫ δ (I – u/v) dy, u – velocity of fluid at the elemental strip.

0

12. Define Momentum thickness (θ).

It is defined as the distance, measured perpendicular to the boundary

of the solid body, by which the boundary should be displaced to compensate

for the reduction in momentum of the flowing fluid of boundary layer for

motion.

θ = ∫ δ (I – u/v) dy, u

13. Define Energy thickness (δ**)

It is defined as the distance, measured perpendicular to the boundary of

the solid body, by which the boundary should be displaced to compensate for

the reduction in kinetic energy of the flowing fluid on account of boundary

layer formation.

θ = ∫ δ u/v(I – u2) dy

T0 = shear stress at surface

U = free stream velocity

This equation applicable to laminar, transition and turbulent boundary layer

flows.

14. What are the different methods of preventing the separation of

boundary layers?

1. Suction of the slow moving fluid by a suction slot.

2. Supplying additional energy from a blower.

3. Providing a bypass in the slotted wing.

4. Rotating boundary in the direction of flow.

5. Providing small divergence in a diffuser.

6. Providing guide – blades in a bend.

0

PART-B

1.. Write short notes on 1) Laminar boundary layer 2) Turbulent boundary layer 3)

Displacement thickness. Energy thickness 5) Momentum thickness 6) Drag coefficients?

(16)

2. Derive and expression for Darcy Weisbach formula? (16)

3. Find the head lost due to friction in a pipe of diameter 300mm and length 50mm, through

which water is flowing at a velocity of 3 m/s using (i) Chezy’s formula (ii) Darcy formula

for which C=60 (16)

3. An oil container in a truck has a horizontal crack in its end wall which is 400mm wide

and 40mm thick in the direction of the flow. The pressure difference between two ends of

the crack is 12kPa and the crack area has a gap of 0.3mm between the parallel surfaces.

Calculate: 1. Volume of the oil leakage per hour through the crack.

2. Maximum leakage velocity

3. Shear stress a nd velocity gradient at the boundary. (16)

4. Find the displacement thickness, momentum thickness and energy thickness for the

velocity distribution in the boundary layer is given by u/U =2 (y/ δ)-( (y/ δ)2 (16)

5. Define and derive the momentum thickness (8)

UNIT 5 : SIMILITUDE AND MODEL STUDY

PART-A

1. What is Dimensional analysis?

Dimensional analysis is a mathematical technique which makes use of

the study of the dimensions for solving several engineering problems.

Uses

1. Testing the dimensional homogeneity of any equation of fluid motion.

2. Deriving equations expressed in terms of non – dimensional parameters

to show the relative significance of each parameter.

3. Planning model tests and presenting experimental results in a

systematic manner in terms of non-dimensional parameters; thus

making it possible to analyses the complex fluid flow problems.

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

examples.

The several of physical quantities used in fluid phenomenon can be

express in terms of fundamental or primary quantities. The fundamental

quantities are mass, length, time. (M, L,T). The quantities which are

expressed in terms of the fundamental or primary quantities are called

derived or secondary quantities.

Example: Velocity, area density

Velocity = distance / unit time = L/T

3. Explain the term: Dimensional Homogeneity

Dimensional Homogeneity means the dimensions of each term in an

equation on both sides equal.

4. State Buckingham’s π– theorem.

If there are n variables (dependent and independent variables) in a

dimensionally homogeneous equation and if these variables contain m

fundamental dimensions.

5. What is Model Analysis?

Model analysis is an experimental method of finding solutions of

complex flow problems. The model is the small scale replica of the actual

structure or machine. The actual structure or machine is called prototype.

The study of models of actual machine is called model analysis.

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

Advantages

1. The model tests are quite economical and convenient (because the

design, construction and operation of a model may be changed several

times if necessary, without increasing much expenditure, till most

suitable design is obtained).

2. The performance of the hydraulic structure or hydraulic machine can be

easily predicted, in advance, from its model.

3. The merits of alternative design can be predicted with the help of model

testing.

4. Model testing can be used to detect and rectify the defects if an existing

structure which is not functioning properly.

Applications

1. Civil Engineering structures such as dams, spillways, weirs, canals etc.

2. Turbines, pumps and compressors.

3. Design of harbors, ships and submarine.

4. Aero planes, rockets and missiles

5. Flood control, investigation of silting and scour in rivers, irrigation

channels.

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

Similitude is defined as the similarity between the model and prototype

in every respect

Geometric Similarity

The ratio of all linear dimensions of the model and of the

prototype should be equal.

Lr = Lm/Lp = Bm/Bp = Hm/Hp = Dm/Dp, Lr

Kinematic similarity

Kinematic similarity means the similarity of motion between model

and prototype.

Dynamic similarity

Dynamic similarity means the similarity of forces between the

model and prototype.

8. How are hydraulic models classified?

(i) Undistorted models (such as M,L,T etc), then the variables are

arranged into (n-m) dimensionless terms. These dimensionless terms are

called π– terms.

PART-B

1. Explain briefly Rayleigh’s Method? (8)

2. Explain briefly Buckingham Pi Method? (8)

3. What is Similitude and explain different similarities in model and prototype analysis? (8)

4. Explain in detail about model or similarity laws? (8)

5. What are the types of models? Explain them? (8)

6. What is scale effects in model and also explain the scale ratio for distorted models? (8)

7. What are repeating variables? How are these selected by dimensional analysis? (16)

8. Using Buckingham Pi Method The head loss in a horizontal pipe in turbulent flow is

related to the pressure drop p, and is a measure of the resistance to flow in the pipe. It

depends on the diameter of the pipe D, the viscosity and density ,

The length of the pipe l, the velocity of the flow v and the surface roughness . (16)

9. The variables controlling the motion of a floating vessel through water are the drag force

F, the speed V, the L, the density ρ, dynamic viscosity µ of water and acceleration due to

gravity g. Derive an expression for by Buckingham Pi theorem. (16)

10. The resisting force R of a supersonic plane during flight can be considered as

dependent upon the length of the air craft L, velocity V, air viscosity µ, air density ρ and bulk

modulus of air K. Express the functional relationship between these variables and the

resisting force. (16)

11. The efficiency η of a fan depends on density ρ, dynamic viscosity µ of the fluid, angular

velocity ώ, diameter D of the rotor and the discharge Q. Express η in terms of

dimensionless parameters. (16)

12.The pressure difference ∆p in a pipe of diameter D and length L due to turbulent flow

depends on the velocity V, viscosity µ,density ρ and roughness k. Using Buckingham’s Π-

theorem, obtain an expression for ∆p. (16)

13. In an aero plane model of size (1/10) of its prototype, the pressure drop is 7.5kN/m2.

The mode is tested in water. Find the corresponding pressure drop in the prototype.

Assume density of air = 1.24kg/m3 density of water = 1000kg/m3: viscosity of air = 0.00018

Poise; viscosity of water = 0.01 Poise. (16)

14. Explain Reyond’s law of similitude and Froude’s law of similitude. (8)

15. It is desired to obtain the dynamic similarity between a 30 cm diameter pipe carrying

linseed oil at 0.5 m3/s and 5 m diameter pipe carrying water. What should be the rate of

flow of water in lps? If the pressure loss in the model is 196 N/m2, what is the pressure loss

in the prototype pipe? Kinematic viscosities of linseed oil and water are 0.457 and 0.0113

stokes respectively. Specific gravity of linseed oil = 0.82. (16)