3.12 Velocity and Acceleration in Steady and
One dimensional flow means
that the flow velocity is a
function of one coordinate
V = f( X or Y or Z )
Two dimensional flow means that
the flow velocity is a function of
V = f(
(Chap # 02)
Fluid will be static or moving in such a way that there is no relative motion between particles
(rigid body motion of fluids).
Only pressure, its distribution within the fluid and the fluid weight will be considered.
Hydrostatic Force on an Inclined Plane Surface
Hydrostatic forces always act on objects that are
submerged in a fluid.
For a static fluid these forces always act perpendicular to
the surface since the shear forces are absent.
Fluid Mechanics-I (ME-204)
(Course Instructor Dr. Murtuza)
Fundamentals of Fluid Mechanics (4th Edition)
Munson, Young & Okiishi
Sessional Marks Distribution
1) Mid term Exam = 20 marks
2) Assignments/Reports/Tests = 15 marks
3) Class behavio
Buoyancy force (FB) is due to the
fact that pressure increases with
the depth therefore, if a body is
fully or partially immersed in a
liquid a net upward force acts on
Buoyancy force can either be
represented by an upward vertical
Elementary Fluid Dynamics
(The Bernoulli Equation)
The equation was developed by a physicist named Daniel Bernoulli (1700-1782).
Bernoulli equation is only used for inviscid ( = 0), incompressible ( = constant), steady state
(time independent) and irrot
Pressure Distribution in Rigid Body Rotation of a Fluid
Centrifuge (used for the separation of immiscible substances e.g. liquid & air bubbles).
Rotation of air in the core region of the tornado/cyclone.
Accretion disks (orbital motion of
The Dimensional Analysis
Experimentation is a widely used technique in fluid mechanics.
In an experiment, effect of independent variables can be investigated on an output variable.
Dimensional Analysis (DA) is a tool that can help us in reducing the nu
Solutions Manual Chapter
Properties of Reinforced Concrete
Flexural Analysis of Reinforced Concrete Beams
Flexural Design of Reinforced Concrete Beams
Deflection and Control of Cracking
Development Length of Reinforcing Bars
Stability of Submerged &
Stability can be defined as the ability (by virtue of the
design) to withstand applied disturbance to the
All floating as well submerged objects can be in 1)
Stable equilibrium 2) Unstable e
Lagrange Method of Describing Fluid Motion
Path of individual fluid particle is tracked w.r.t time only.
Hence all flow properties becomes function of time. V=V(t), S=S(t) & p=p(t).
Newtons laws and conservation of mass & energy directly applies to eac
MEHRAN UNIVERSITY OF ENGINEERING AND TECHNOLOGY,
SECOND TERM THIRD YEAR (6TH TERM) B.E.(MECHANICAL) REGULAR
EXAMINATION 2009 OF 07-BATCH.
Time Allowed: 03 Hours.
NOTE: ATTEMPT ANY
Water pumps are devices designed to
convert mechanical energy to hydraulic
energy. All forms of water pumps may be
classified into two basic categories:
Turbo-hydraulic pumps are:
Shear and diagonal tension
When a beam is loaded, bending moments and shear
forces develop along the beam.
To carry the loads safely, the beam must be designed
for both types of forces.
Flexural design is considered first to est
ABDUL BASIT SHAIKH 1
Name: Abdul Basit Shaikh
Roll Number: CE-091
Year: Third Year
Department: Civil Engineering
Topic: Singly Reinforced Beams
Course Code: CE-304
Subject: Reinforcement Concrete Design
Derivation of Energy Equation
The total energy (e) of the system consist of all forms of internal energies (on microscopic
level), and kinetic & potential energy (on macroscopic level).
From first law of thermodynamics we know that the rate of change of
Vapor Pressure (pv )
All liquids and solids exert a pressure above their free surface known as the vapor pressure due
This pressure is dependent on the operating temperature as shown in the figure below.
The pressure is due to the escap
QUESTION # 4.1(b)
0.9 7.6200293 0.0132292 0.6309896
USE 8#9 bars
if b(min) b then section
7. Steady Flow through Pipes
Synthetic Hydrological Cycle
1. Supply pipeline
The flow of water, oil and
gas in pipes is of immense
practical significance in
2. Water treatment plant
3. Ringmain distribution
3. Fluid Kinematics
(classification of types of
Fluid dynamics is the analysis of fluid in motion.
If a fluid flows through pipes and channel or around
bodies such as aircraft and ships, the shape of the
boundaries, the externa
5. Momentum-Impulse Principle
Consider a duct and
identify the control
volume on which to
conduct a force
The inner passage is filled with fluid with pressure p1
Consider pressures of the fluid measured relative to
4.7 Venturi meter
- The Venturi meter is a
device for measuring
discharge in a pipe.
- It consists of a rapidly
converging section, which
increases the velocity of
flow and hence reduces
- It then returns to the original dimensions of the
EXAMPLE: Spraying Water into the Air
Water is flowing from a hose attached to a
water main at 400 kPa. A child places his thumb
to cover most of the hose outlet, causing a thin
jet of high-speed water to emerge. If the hose is
held upward, what is the max
4.3 Ways to express Bernoulli equation
- conservation of energy (no friction loss)
Energy per unit volume:
Energy per unit mass:
Energy per unit weight:
p z V 2 constant (along streamline )
gz V constant (along streamline )
4. Energy Considerations in Steady Flow
Energy may be neither created nor destroyed.
It can be transformed from one guise to another (e.g.
potential energy can be transformed into kinetic energy),
but none is actually lost.
Engineers sometimes loosely
EXPRESSION FOR MAXIMUM PERCENTAGE OF STEEL
Let us consider the case of a balanced
section, which determines that at
ultimate load strain in concrete is equal
to 0.003 and strain in steel is equal to the
yield stress divided by modulus of
elasticity of ste