Fluid Mechanics
Momentum Equation and Bernoullis Equation
1.
The water depth in a channel upstream of a sluice gate is 3 m and the flow velocity is 1.2
m/s, uniformly over the flow section. Downstream of the gate, the minimum depth of the
flow at the vena

Fluid Mechanics
Pipe Flow Pipe Network
Pipe network: Several reservoirs feeding a junction point
Reservoir A
Imaginary
piezometer
Qb
HA
Qa
Junction J
HJ
Qc
HB
Reservoir C
HC
z-datum
Reservoir B
Pipe Flow Pipe Network
Convention:
Assume flows in all pipe

Fluid Mechanics
Pipe Flow
The Problem: to pass a steady flow of fluid through a pipe
or a pipe network
power required?
change of energy (EGL) and head (HGL) along the pipe?
Not a pipe flow
Pipe flow
Driving force for flow Pressure!
Steady Pipe Flow
Steady

Fluid Mechanics
Bernoullis Equation
Momentum equation along a streamline:
Steady flow, No effect of viscosity.
What will be the changes in
pressure and velocity and
elevation when fluid flows
along a streamline, say from
P to Q?
Q
P
Bernoullis Equation
Co

Dimensional
Analysis
Introduction
Very often, real problems in fluid mechanics do not have analytical
solutions. For example, there is no analytical means of determining
the drag force acting on a ship or an airplane. Other examples
include:
Energy dissi

Fluid Kinematics
January - April 2017
A. W. Jayawardena
Introduction
Fluid Kinematics refers to the description of fluid flow without considering
forces.
In fluid flow there are 5 basic variables, namely the 3 velocity components
and 2 thermodynamic prope

January - April 2017
A.W.Jayawardena
Basic laws
Integral forms of governing equations -In fluid
mechanics, the basic laws contain integral quantities
of interest. For example,
Volume rate is the integral of velocity over area
Force is the integral of s

Dimensional Analysis
and Physical Models
Theoretical solutions are not yet available to most fluid
and hydraulic problems
Reliable solutions from experiments and physical
model testing
Experiments many parameters need ways to
reduce the variables and si

Fluid Mechanics
Integral Momentum Equation
Newtons 2nd Law applied to a Control Volume in a
Flow.
Control volume: fixed region in space through
which fluid flows.
Control volume equation:
d
dV U A
dt
dt CV
CS
dBsys
Control Volume
Control Volume Equatio

Potential
(Ideal
Fluid)Flow
January-April, 2017 A. W. Jayawardena
Velocity Potential and Stream
Function
Definition - Potential flows are irrotational flows
whose velocity components may be derived from
velocity potential functions. They apply to
incompr

January-April 2017 A. W. Jayawardena
Measurements of surface elevation
Point gauge
Hook gauge
Sonar
January-April 2017 A. W. Jayawardena
Measurement of pressure
Static pressure pressure when the velocity is
undisturbed
When the flow is parallel the pr

Department of Civil Engineering
The University of Hong Kong
January - April, 2017
Course Lecturer: A. W. Jayawardena
Course objectives
To introduce the fundamental concepts and examples of
engineering fluid mechanics
To help students to develop a sound

January-April 2017 A. W. Jayawardena
Introduction
DEFINITIONS
Fluid statics refer to the mechanics of a fluid at rest.
The main concerns in fluid statics are
pressure variation in a fluid at rest
Forces on various objects immersed in a fluid
Forces in

Fluid Mechanics
Flow Measurement
We need to measure various physical quantities in a flow:
velocity
discharge, flow rate
pressure, head
water level
Measurement is needed in the field (for monitoring and
control) and in the laboratory (for model studie

The University of Hong Kong
Department of Civil Engineering
FLUID MECHANICS (CIVL 2103)
FLUID STATICS
1.
A manometer consists of two tubes A and B, with vertical axes and uniform crosssectional areas 500 mm2 and 800 mm2 respectively, connected with a U-tu

Fluid Mechanics
Fluid flow: occurs over
space and time
- e.g. water flow in a river,
flow of ventilation air
Fluid Kinematics
Lagrangian description
- follow motions of individual fluid particles in terms
of their positions, velocities, etc. at different

Hydrostatic force on a plane surface
A surface inside a fluid is under
pressure from the fluid side.
The pressure force is a distributed
force.
The magnitude of pressure may
change from point to point on the
surface depending on the fluid head
there.
The

Fluid Mechanics
Dimensional Analysis
Dimensional analysis
Very often, we cannot have an exact solution of a physical problem. We only know or suspect
that the physical quantity (A) we require is dependent on some other physical quantities B, C,
D,. For ex

Fluid Mechanics
Flow Measurement
The determination of various quantities in a flow (e.g., velocity, discharge, flow rate,
pressure, level) is important to monitor and control many engineering processes. In
laboratory investigations and model studies, meas

Fluid Mechanics
Dimensional Analysis
1.
When a liquid of density and viscosity flows through an orifice of diameter d in a
pipe of diameter D, the pressure drop across the orifice is p. If the volume flow of
liquid Q is a function of the above variables o

Fluid Mechanics
Fluid Statics:
Forces in fluid at rest:
Only normal stress can exist in a stationary fluid.
Pressure is the only surface force in action.
Other forces are body forces (e.g. gravity, inertia)
and line forces (e.g. surface tension).
What is

Fluid Mechanics
Integral Momentum Equation
Control volume approach
In the Eulerian approach, we look at fluid flow at fixed observation points. On the bigger
scale, we look at how fluid flows through a fixed region in space. This region is a control
volum

Fluid Mechanics
Bernoullis Equation
Momentum equation along a streamline
The integral momentum equation tells us how fluid flows through a control volume under
the action of external forces on the CV. Flow follows streamlines and it is possible to
conside

The University of Hong Kong
Department of Civil Engineering
Fluid Mechanics (CIVL2013)
FLUID KINEMATICS
1.
A fluid flow is described by the velocity field
U 5 x 3 i 15 x 2 yj tk
Estimate the velocity and acceleration components at the point (1, 2, 3) at t

Potential
(Ideal
Fluid)Flow
January-April, 2017 A. W. Jayawardena
Velocity Potential and Stream
Function
Definition - Potential flows are irrotational flows
whose velocity components may be derived from
velocity potential functions. They apply to
incompr