HYDRAULICS ENGINEERING
AGE 403
Engr. Dr. J. K. ADEWUMI
DEPARTMENT OF AGRICULTURAL ENGINEERING.
UNIVERSITY OF AGRICULTURE, ABEOKUTA
OGUN STATE
Office Location: Postgraduate Building
Email: jkadewumi@yahoo.com
CONTENT
• Basic definition of terms
• Types of flow
• Basic equations in hydraulics
continuity
Energy
Momentum equation
• Flow: Devices for flow measurement
Venturimeter
Pitot tube
Orifice
Weirs
 Pipe flow
-
Osborne Reynolds Experiment
Laminar flow
Transitional flow
Turbulent flow
Turbulent flow in pipes: friction
factor, head loss, moody
Form losses in pipes
Pipe flow problems: Use of charts
 Open Channel flow
 Definition of open channel flow
 Equations governing open channel flow
- Chezy
- Manning equations
 Features of open channel flow: velocity, discharge, roughness etc.
 Problems in open channel flow
 Specific Energy: Concept e.g critical depth, hydraulic jump e t c.
INTRODUCTION
 DEFINITION: a fluid is a substance which deforms continuously
under the application of shear stress. Gas and liquid are classified as
fluids while solids are not classified as fluids because it returns some
shear stress and there is finite deformation.
 PROPERTIES AND CHARACTERISTICS OF FLUIDS
 Density (): mass per unit volume
• Specific volume: This is the reciprocal of density that is
• Specific weight (): weight per unit volume
• Specific gravity: Ratio of density fluid to that of water
 Viscosity: ability to resist flow.
 Types of viscosity
 Absolute viscosity ()
 Kinematic viscosity ()
Mathematically we have
Where  is the shear stress (force per unit area)
 Pressure: force per unit area (kPa)
 Surface tension: Force per unit length on surface of liquid
(N/m)
 Stress: For a liquid in motion, there are 2 types of stress
 Normal stress ()
 Shear stress ()
TYPES OF FLOWS
Definitions:
i)
Stream line – A streamline is a line drain of any instance across which there is no flow component so that at any
point on it, the resultant velocity is in direction tangential to the streamline. Streamlines are therefore, imaginary
lines traced out by successive fluid particles through the flow stream. Streamlines concept has neglected
secondary fluctuations superimposed by turbulence.
ii)
Stream tube: - A stream tube may be regarded as a bundle of streamlines. It is a tube whose walls are made up
of continuous, streamlines and across which there can be no flows. Streamlines and streamtubes have no physical
(significant) substance. They are geometric figures which the observer images to be drawn within the flowing
fluid.
In general, 4 types of flow exist viz:a.)
Laminar/turbulent flow
b)
Rotational/Irrotational flow
c)
Steady/unsteady flow
d)
Uniform/Non Uniform flow
LAMINAR / TURBULENT FLOW

In laminar flow all fluid Particles proceed along parallel paths and there is no transverse component of velocity.
The orderly progressions of movement is such that each particle follow exactly a path preceeding it flunctuations.
Laminar flow is associated with low-velocities and sluggish viscious fluids. If a dye is injected, the filament of dye
will remain or stay without diffusion. In laminar flow the motion is close to rectilinear. There is much greater
transverse velocity gradient in laminar flow than in turbulent flow.
d/dr (laminar) > dv/dr (turbulent)
( )
For a pipe, the ratio of mean velocity, V and the maximum velocity Vmax = 0.5 (V/Vmax = 0.5)

In turbulent flow, the progression of fluid particles is irregular and haphazard interchange of motion.
Individual particles are subjected to fluctuating transverse velocities. The motion can be described as eddying and
sinuous.
Steady and Unsteady Flows
• Flow is steady when conditions at any point are constant with
respect to time. Examples are constant discharge in a conduit
or open channel. Depth does not change during time interval
• Flow is unsteady when conditions vary with respect to time.
Example is varied discharge in a conduit or open channel,
wave motions, floods and rising and falling hydrographs
Uniform and Non-uniform flow
• Space is an important criteria for classifying flows into
uniform or non-uniform
• Flow is uniform when there is no variation in the magnitude
and direction of the velocity vector from one point to
another along the path of flow
• Flow is non-uniform when velocity vector varies with
location. Example is flow between converging and diverging
boundaries
Rotational and Irrotational Flow
 Are applicable to flow adjacent to a straight boundary.
 Flow is rotational if each fluid particle has an angular velocity
about its own mass centre
 Flow is Irrotational if the velocity is inversely proportional to
the radius, r. The two axes rotate in opposite directions
Dynamics of Fluid flows and laws of
fluid flow
 Continuity Equation: A1V1 = A2V2
 Energy Equation: Most powerful tool used to analyze fluid flow problems.
Flow assumed to be steady and fluid frictionless and incompressible.
 Momentum Equation:
Devices for flow Measurement
 Venturimeter- Device for measuring discharge of a pipe. Constriction in pipes
cross section which causes an increase in velocity at the throat.
 Pitot tube- device for measuring the velocity of flow of a fluid usually when
a free water surface exists.
 Orifices-used to measure flows Q=AV
 Notches and Weirs- Obstructions to flow intended to cause the fluid to backup behind
the weir or notch and flow through it in a regular fashion.
 Triangular Notch and V-Notch: Used when it is required that the
coefficient of discharge should remain constant over a wide range of head.
Pipe Flow
 Steady turbulent
Form losses in Pipe Flow
• In pipe flow, the main energy loss is carried by boundary
friction. There may be other losses.
Examples are:
– sudden enlargement- movement of water from a smaller
diameter pipe to a bigger diameter pipe.
– Sudden contraction- movement from bigger size pipe to one of
smaller size. HL = CV22/2g
HL  (V 1  V 2)2 / 2 g
– Entry loss- the discharge of water from a reservoir into the distribution
system (mains) can be considered as a special case of sudden contraction.
Form losses in Pipe Flow (Contd)
- Exit loss- the discharge of water into a reservoir from a pumping main
station. It is a special case of sudden enlargement.
Complex Network
 Pipe connection in a complex network is frequently a combination of series and
parallel.
 Flow in pipe is analogous to current flow through resistors
 Pipes in series: Q1=Q2, HL = HL1 + HL2 current is equal in both pipes
 Pipes in Parallel: Q = Q1 +Q2 HL1 = HL2 voltage is equal in both pipes
Open Channel Flow