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Hydraulics-I chapter-one 2015/16
JIT Civil 2nd Year Page 1
CHAPTER ONE
1. INTRODUCTION
What is hydraulics?
Hydraulics is derived from a Greek Word "Hydraulikos/Hudour" which means water. It is the study of water
and some engineering fluids, which a hydraulics engineer is called upon to store, convey or pump.
Engineering fluid includes wastewater in waste disposal and oils in hydraulic control gear.
Hydraulics is often confused with the allied science of fluid mechanics because a considerable overlap occurs
between the two studies. However, fluid mechanics deals with gases, as well as the common liquids, and to
most hydraulics engineers a study of gas behavior is irrelevant to their professional needs.
The basic aim of hydraulics is to understand and control the occurrence, movement and use of water for the
benefit of society whether it is in lakes, rivers, pipes, drains, percolating through soils or pounding the
coastline as destructive waves. Therefore, the fundamentals in hydraulic engineering systems involve the
application of engineering principles and methods to the planning, control, transportation, conservation and
utilization of water.
Why do we study hydraulics?
All organized societies need adequate water supplies, drainage to dispose of waste or excess water, as well as
protection from uncontrolled water. Thus an obvious necessity for a study of hydraulics exists.
Applications of hydraulics include
 Design of a wide range of hydraulic structures (dams, canals, weirs etc.) and machinery (pumps,
turbines and fluid couplings)
 Design of a complex network of pumping and pipelines for transporting liquids.
 Power generation
 Flood protection
 Surface and ground water studies
 Flow metering like orifice meter
 Pressure measurement

General Description
atter can be distinguished by the physical form of its existence (phases) as solid, liquid and gases,
for example water appears in liquid, solid (Snow and ice), or gaseous (moisture or water vapor)
form depending on the extent of hydrogen bonding. Liquid and gaseous phases are usually
combined and given a common name of fluid.
1.1 Definition of Fluid
Fluids: Fluids are substances, which deform continuously under the application of a shear force, no matter
how small the force might be. They are characterized by their ability to flow.
Fluid is a material in which movement occurs continuously under the application of a tangential shear
stress.
A simple example is shown in figure 1.1 in which a timber board on a reservoir of water.
Figure 1.1 Use of a floating board to apply shear stress to a reservoir surface
A shear force is the force component tangent to a surface, and this force divided by the area of the
surface is the average shear stress over the area. Shear stress at a point is the limiting value of the shear
force to area as the area is reduced to the point.
1.2 Dimensions and Units
To understand hydraulics properly it is essential to be able to put numerical values on such things as
pressure, velocity and discharge in order for them to have meaning. Since just providing a number in its
own is quite meaningless, the numbers must have units to give them some useful meaning. Problem
solutions in mechanics can be greatly simplified by using consistent units of force, mass, length, time
and temperature.
Different units of measurement are used in different parts of the world. The foot, pound and second
system (known as fps) are still used extensively in USA and to some extent in the UK. The metric
M
Y

system, which relies on the centimeter, gram and second (known as cgs), is widely used in continental
Europe. But in engineering and hydraulics the most common units are those in the SI system.
The International System of Units, usually abbreviated to SI, is not difficult to grasp and has many
advantages over the other systems. All length measurements are in meters, mass is in kilograms and
time is in seconds. SI units are simple to use and their big advantage is that they can help to avoid much
of the confusion that surrounds the use of the other units. For example, it is quite easy to confuse mass
and weight in both fps and cgs units as they are both measured in pounds in fps and in kilograms in cgs.
Any mix up between them can have serious consequences for design of engineering works. In the SI
system the difference is clear because they have different units – mass is in kilograms whereas weight is
in Newton’s.
Table 1.1 Some Basic and Derived quantities and their units
Every fluid has certain characteristics by which its physical condition may be described. We call such
characteristics properties of the fluid. These properties can be divided in to two broad categories: Extensive
properties, which depend on the size of a sample of matter; and intensive properties, which are independent of
the sample size. Of the two intensive properties are the more useful because a fluid will exhibit the same
intensive property regardless of how much of it we examine. Examples of extensive property are mass and
volume as the amount of a substance increases; its mass and volume also increase. Intensive properties
include density, pressure and temperature.
In speaking of the properties of fluids, we also distinguish between physical and chemical properties. A
physical property can be specified without reference to any other fluid. Density, mass volume, color etc are all
Measurement Unit/ symbol Measurement Unit/ symbol
Length m Force N
Mass Kg Dynamic Viscosity N.s/m2
or kg/m.s
Time S Kinematic viscosity m2
/s
Area m2
Mass density kg/m3
Volume m3
Specific weight N/m3
Velocity m/s Pressure Pa or N/m2
Acceleration m/s2
Momentum kg.m/s

examples of physical properties. A chemical property on the other hand states some interaction between
chemical substances.
The way fluid (water) behaves under various conditions encountered in practice depends primarily on its
fundamental and physical properties, which are briefed as follows.
1.3 Fluid Properties
An understanding of fluid behavior and application of its basic laws through experimentation advances the
subject of hydraulics. Fluid properties play principal roles both in open channel and pipe flow.
The principal physical properties of fluids are described as follows.
1. Mass density or density, denoted by  (Greek, rho)
It is defined as the mass per unit volume.
density =
v
m
v
occupied
Volume
m
fluid
of
Mass


,
)
(
)
(
 SI unit Kg/ m3
 Dimensionally ML-3
 For an incompressible fluid, ‘’ is constant
 For water,  is 1000 kg/ m3
at 40
c and standard pressure (760 –mm Hg)
(There is a slight decrease in density with increasing temperature, but for normal practical
purposes the value is constant)
 Generally, the density of liquids is only slightly dependent on either temperature or pressure and
the variation can be ignored but for gases, it significantly varies with both temperature and
pressure.
2. Specific weight / unit weight / unit gravity force /, designated by  (Gk, gamma)
It is defined as the weight per unit volume.

g
g
v
mg
V
W








W = weight = mass x gravitational acceleration (g)
 SI unit N/m3
(usually KN/ m3
)
 Dimensionally (ML –2
T-2
)
 At 40
c ‘’ for water is 9.806 / 9.81 KN /m3
/
 It changes with location on the earth’s surface depending upon g.
3. Specific gravity (S) or relative density
It is defined as the ratio of mass of a body to mass of an equal volume of a substance taken as a standard (for liquids water
at 40
c)
water
of
density
fluid
of
density
water
of
volume
equal
of
mass
fluid
of
mass
density
lative


Re
 It is a pure no (dimensionless parameter)
Typical values of specific gravities:
 Relative density of water is 1.00 (S water = 1.00, standard for measuring relative density of other
liquids).
 S mercury = 13.6, commonly used secondary fluid in manometers for pressure measurement.
 Oils usually have a relative density less than one and they float on water.
 If relative density of a given oil is 0.8 its density is 0.8 (1000 kg / m3
) = 800 kg/ m3
Note: It is clear that density, specific weight, and specific gravity are all interrelated and from knowledge of
any one of the three the others can be calculated.
4. Specific Volume (Vs)
It is the volume occupied by a unit mass of fluid or simply the reciprocal of density.


1


m
v
Vs
 Commonly applied to gases
5. Bulk modulus of elasticity or Compressibility, K (kappa)
For most practical purposes liquids may be regarded as incompressible. However, there are certain cases, such
as water hammer, where the compressibility should be taken into account. If water were not compressible,
then closing a valve on a pipeline could be a dangerous task. Imagine trying to stop suddenly a solid column
of water several kilometers long. The force involved would be immense. Fortunately water is compressible
and compresses like a spring to absorb the energy of the impact as the valve is closed. Water hammer
pressures are quite large. Therefore, engineers must design piping systems to keep the pressure within
acceptable limits. This is done by
 Installing an accumulator near the valve and/or operating the valve in such a way that rapid
closure is prevented. Accumulators may be in the form of air chambers for relatively small
systems, or surge tanks.
 Installing pressure-relief valves at critical points in the pipe system.
Analysis of water hammer is beyond the scope of this course.
If the pressure of a volume of fluid is increased by dp, it will cause a volume decrease dv, then the bulk
modulus of elasticity is defined as
Bulk modulus (K) = (stress change in pressure) / (volumetric strain)
K = -
v
dv
dp
/
v = original fluid volume
The negative sign indicates a decrease in volume with the increase in pressure.
 = m/v , Mass of a certain volume is constant, differentiating .
v
dv
v
dv
v
m
v
dv
m
v
md
v
m
d
d 
 


















 2
1
v
dv
d






Substituting:

 /
d
dp
k 
 The concept of the bulk modulus is mainly applied to liquids, since for gases the compressibility
is so great that the value of K is not a constant
 For water, k is approximately 2150 N/ mm2
at normal temperatures and pressures.
 For steel k = 215000 N/ mm2 (i.e. water is 100 times more compressible than steel)
6. Viscosity: is a measure of the friction force/ resistance to deformation or flow under an
applied shear stress. Viscosity is primarily due to interaction between fluid molecules and,
generally, there are two types of viscosity.
a) Absolute / (Dynamic) Viscosity ( = mu): According to Newton’s law of viscosity for a
given rate of angular deformation (the slope of velocity distribution) of fluid, the shear
stress is directly proportional to the absolute viscosity.
A fluid with greater absolute viscosity would require a greater applied shear stress in order to achieve
an identical rate of deformation. The resistance of fluid to shear depends upon its cohesion and upon its
rate of transfer of molecular momentum. A liquid, with its molecules much more closely spaced than a
gas, has cohesive forces much larger than a gas. Cohesion appears to be the predominant cause of
viscosity in a liquid, and since cohesion decreases with temperature, the viscosity does likewise. A gas
on the other hand, has very small cohesive forces. Most of the resistance to shear stress is the result of
the transfer of molecular momentum.
Consider a fluid confined between two plates which are situated a very short distance y- apart. The lower
plate is stationary whilst the upper plate is moving at a velocity v. Hence; the fluid in immediate contact with
the moving plate has a velocity v and with the stationary plate has zero velocity. (The experimental
observation that the fluid “sticks” to the solid boundary is very important one in fluid mechanics and is
usually referred to as the no slip condition. All fluids satisfy this condition.

Hydraulics-I Chapter-one 2015/16
A F
Fig 1.2 Viscous deformation
‘F’ is the force required to move the surface at constant velocity. If distance y and velocity V are not
great, the velocity variation (gradient) will be a straight line. Experiments show that, F is directly
proportional to A and V and inversely proportional to thickness Y.
- Similarity of triangles
dy
dv
y
v
dy
dv
A
Y
AV
F 


- A = area of upper plate
or 
A
F
dy
dv
A
F
  (tau) = shear stress
dy
dv


If proportionality constant, called absolute (dynamic) viscosity, is introduced.
dy
dv
or
dy
dv 


 

This expression was first postulated by Newton and is known as Newton’s equation of viscosity.
 Heavy oils have greater viscosity than water and water is more viscous than air.
 All real fluids posses' viscosity, though to varying degrees.
 There can be no shear stress in a fluid, which is at rest
 The SI unit of  is N.s /m2
or Pa.s (kg/ m.s),
 Or in cgs system
s
cm
gm
.
termed as poise
Y
V

 One poise = 0.1 kg m-1
s-1
= 0.1 Pa.s
 Dimensionally = (ML-1
T-1
) (FL-2
T)
b) Kinematic viscosity (ν): is the ratio of viscosity to mass density ( ) and has units of m2
/s.
Values of μ and ν for different fluids vary with temperatures.
Kinematic viscosity =






e
i
density
mass
ity
vis
absolute
.
)
(
)
(
cos
 SI unit of  is m2
/s in cgs system cm2
/s called stoke.
 For water,  = 1.14 mm2
/s at 150
c
 For heavy air  may be as high as 900mm2
/s.
 Viscosities (absolute of dynamic) of liquids decrease with increasing temperature but are not
affected appreciably by pressure changes.
Viscometer
It is an instrument to measure viscosity. It measures some quantity which is a function of viscosity. The
quantity measured is usually the time taken to pass a certain volume of liquid through an orifice fitted in
the bottom of viscometer. The temperature of liquid while it is being passed through the orifice should be
maintained constant.
Effect of Temperature on Viscosity
The viscosity of a gas increases with temperature, but the viscosity of a liquid decreases with
temperature.
The liquid molecules are closely spaced, with strong cohesive forces between molecules, and the
resistance to relative motion between adjacent layers of fluid is related to these intermolecular forces. As
the temperature increases, the cohesive forces are reduced with a corresponding reduction in resistance to
motion, since viscosity is an index of this resistance, it follows that the viscosity is reduced by an increase
in temperature.
A gas, on the other hand, has very small cohesive forces. Most of its resistance to shear stress is the result
of molecular interaction. As the temperature of the gas increases, the random molecular activity increases
hence viscosity increases with temperature.
The effect of temperature on viscosity is approximated by;

For gases,
S
T
T
C


2
/
3
 Where C and S empirical constant, T = absolute temperature
(Sutherland equation)
For liquids,
T
B
e
D /

 Where D and B constant, (Andrade’s equation)
Types of Fluids
1. Newtonian fluids
A fluid, which obeys Newton’s law of viscosity, is known as a Newtonian fluid and they will have a
certain constant viscosity. For these fluids the plotting of shear stress against velocity gradient is a straight
line passing through the origin. The slope of the line gives viscosity. Examples of Newtonian fluids are
water, air, gasoline and light oils. (Under normal condition)
2. Non-Newtonian Fluids
In a non- Newtonian fluid there is a non -linear relation between the magnitude of applied shear stress and
the rate of angular deformation. Examples of non - Newtonian fluids are human blood, butter, printers ink
etc….
 Gases and most common liquids tend to be Newtonian.
 Newtonian and Non - Newtonian fluids are real fluid.
3. Ideal fluid
For purposes of analysis, the assumption is frequently made that a fluid is non -viscous (frictionless) and
incompressible (inelastic). Such an imaginary fluid is called ideal or perfect fluid.
Ideal fluids with zero viscosity always have zero stress and hence the plotting coincides with the x -axis.
No real fluid fully complies with this concept, but some liquids, including water, are near to an ideal fluid
and the assumption is useful and justified.
4. Real fluid
A Fluid which possesses viscosity is known as real fluid. All the fluids, in actual practice, are real fluids.

5. Ideal plastic
Sustain a certain amount of shearing stress without deformation and thereafter it would deform in
proportion to the shearing stress. If not proportion they are called thyxotropic fluid.
Shear stress, 
Velocity gradient (rate of deformation), dv/dy
Fig 1.3 Plot of  versus dv/dy
7. Surface tension denoted by  (Gk. Sigma) and Capillarity
Considering the behavior of molecules at the interior & along the surface of a fluid mass can give us a
clear understanding of surface phenomena. Take molecules in the interior of a fluid mass. They are under
attractive forces in all directions and the vector sum of these forces is zero. However, at the surface
between liquid and air or two immiscible liquids the upward and downward attraction are unbalanced
(acted on by a net in ward cohesive force that is perpendicular to the surface) which causes the surface to
behave as if it were a ‘skin’ or elastic membrane stretched over the fluid mass giving rise to the
phenomenon of surface tension. Actually such a skin doesn’t present, but this conceptual analogy allows
as to explain several commonly observed phenomenon. This is demonstrated schematically in the
following figure for water with a free surface.
Newtonian
Non-Newtonian
Ideal plastic
Ideal solid
Ideal fluid

Fig 1.4. Surface tension due to molecular attraction
Generally, surface tension is a force which exists on the surface of a liquid when it is in contact with
another fluid or a solid boundary. Its magnitude depends up on nature of the liquid, and the surrounding
matter which may be a solid, liquid or a gas, kinetic energy and hence the temperature of liquid molecules
(or the relative magnitude of cohesive and adhesive forces.)
Surface tension effect enables:
 An isolated drop of liquid to take nearly a spherical shape.
 A drop of water to be held in suspension at a tap.
 Birds to drink water from ponds.
 A vessel to be filled slightly above the brim.
 Dust particles and needle to float on the surface of liquids.
 Capillary rise and depression in thin-bored tubes.
Capillarity or meniscus effect
When a tube of small diameter called capillary tube is inserted in to a container of liquid, the level will
rise or fall within the tube depending up on the relative magnitudes of the cohesion of the liquid and the
adhesion of the liquid to the wall of the containing vessel. Liquids rise in tubes they wet (adhesion >
cohesion) and fall in tubes they do not wet (cohesion > adhesion) see the following figure.
 The phenomenon of rise and fall of liquid in a capillary tube is known as capillarity. Capillarity
is important in capillary tubes, monometer or open pores in the soil. (Tubes  10 mm diameter).
Air
Water

σ


σ σ
Fig 1.5 a) Rise of column of liquid for wetting liquid b) Depression or fall of column for non-wetting
liquid. The magnitude of the capillary rise (or depression), h, is determined by the balance of adhesive
force between the liquid and solid surface and the weight of the liquid column above (or below) the liquid
free surface. For Fig 1.5 a), the gravitational force on the column of liquid elevated must be supported by
surface tension acting around the periphery of the tube.
  0
Fy
Component of forces = weight of volume due to surface tension (ABCD)  neglecting pressure forces.
 h =
d
gd 




 cos
4
cos
4
 , h=
d


 cos
4
Where: h – height of capillary rise (or depression)
γ – Specific weight of liquid
σ – Surface tension
 – wetting angle
r – Radius of tube
It is to be noted that for 0 ≤  ≤ 900
‘h’ is positive (concave meniscus and capillary rise) and that for 90 ≤
 ≤ 1800
h is negative (convex meniscus and capillary depression).
 For pure water and clean glass  = 00
 6 for water = 0.0735 N/m
h
A
B C
D

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