This document provides an introduction to key concepts in fluid mechanics. It begins by outlining the objectives of understanding basic fluid mechanics concepts. It then discusses various fluid flow types and conditions like laminar versus turbulent flow, compressible versus incompressible flow, and internal versus external flow. Key concepts like viscosity, vapor pressure, cavitation, surface tension, and capillary effects are also introduced. Equations for hydrostatic forces on submerged surfaces are provided. In summary, the document serves as an overview of fundamental fluid mechanics topics.
Introduction to FLUID MECHANICS and its applicationkyunsoosilva14
Introduction to FLUID MECHANICS and its application.
Understand the basic concepts of Fluid Mechanics.
Recognize the various types of fluid flow problems encountered in practice.
Model engineering problems and solve them in a systematic manner.
Have a working knowledge of accuracy, precision, and significant digits, and recognize the importance of dimensional homogeneity in engineering calculations.
Mechanics: The oldest physical science that deals with both stationary and moving bodies under the influence of forces.
Statics: The branch of mechanics that
deals with bodies at rest.
Dynamics: The branch that deals with
bodies in motion.
Fluid mechanics: The science that deals with the behavior of fluids at rest (fluid statics) or in motion (fluid dynamics), and the interaction of fluids with solids or other fluids at the boundaries.
Fluid dynamics: Fluid mechanics is also referred to as fluid dynamics by considering fluids at rest as a special case of motion with zero velocity.
Hydrodynamics: The study of the motion of fluids that can be approximated as incompressible (such as liquids, especially water, and gases at low speeds).
Hydraulics: A subcategory of hydrodynamics, which deals with liquid flows in pipes and open channels.
Gas dynamics: Deals with the flow of fluids that undergo significant density changes, such as the flow of gases through nozzles at high speeds.
Aerodynamics: Deals with the flow of gases (especially air) over bodies such as aircraft, rockets, and automobiles at high or low speeds.
Meteorology, oceanography, and hydrology: Deal with naturally occurring flows.
Stress: Force per unit area.
Normal stress: The normal component of a force acting on a surface per unit area.
Shear stress: The tangential component of a force acting on a surface per unit area.
Pressure: The normal stress in a fluid at rest.
Zero shear stress: A fluid at rest is at a state of zero shear stress.
When the walls are removed or a liquid container is tilted, a shear develops as the liquid moves to re-establish a horizontal free surface.
The normal stress and shear stress at
the surface of a fluid element. For
fluids at rest, the shear stress is zero
and pressure is the only normal stress.
In a liquid, groups of molecules can move relative to each other, but the volume remains relatively constant because of the strong cohesive forces between the molecules. As a result, a liquid takes the shape of the container it is in, and it forms a free surface in a larger container in a gravitational field.
A gas expands until it encounters the walls of the container and fills the entire available space. This is because the gas molecules are widely spaced, and the cohesive forces between them are very small. Unlike liquids, a gas in an open container cannot form a free surface.
Laminar flow: The highly ordered fluid motion characterized by smooth layers of fluid. The flow of high-viscosity fluids such as oils at low velocities is typically laminar in flow.
Understand the physical mechanism of convection and its classification.
Visualize the development of velocity and thermal boundary layers during flow over surfaces.
Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers.
Distinguish between laminar and turbulent flows, and gain an understanding of the mechanisms of momentum and heat transfer in turbulent flow.
Derive the differential equations that govern convection on the basis of mass, momentum, and energy balances, and solve these equations for some simple cases such as laminar flow over a flat plate.
Non dimensionalize the convection equations and obtain the functional forms of friction and heat transfer coefficients.
Use analogies between momentum and heat transfer, and determine heat transfer coefficient from knowledge of friction coefficient.
Report on Types of fluid flow
fluid dynamics
Introduction
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. Note that fluid flow can get very complex when it becomes turbulent. Physicists haven’t developed any elegant equations to describe turbulence because how turbulence works depends on the individual system whether you have water cascading through a pipe or air streaming out of a jet engine. Usually, you have to resort to computers to handle problems that involve fluid turbulence. Types of fluid flow:
Aerodynamic force
Cavitation
Compressible flow
Couette flow
Free molecular flow
Incompressible flow
Introduction to FLUID MECHANICS and its applicationkyunsoosilva14
Introduction to FLUID MECHANICS and its application.
Understand the basic concepts of Fluid Mechanics.
Recognize the various types of fluid flow problems encountered in practice.
Model engineering problems and solve them in a systematic manner.
Have a working knowledge of accuracy, precision, and significant digits, and recognize the importance of dimensional homogeneity in engineering calculations.
Mechanics: The oldest physical science that deals with both stationary and moving bodies under the influence of forces.
Statics: The branch of mechanics that
deals with bodies at rest.
Dynamics: The branch that deals with
bodies in motion.
Fluid mechanics: The science that deals with the behavior of fluids at rest (fluid statics) or in motion (fluid dynamics), and the interaction of fluids with solids or other fluids at the boundaries.
Fluid dynamics: Fluid mechanics is also referred to as fluid dynamics by considering fluids at rest as a special case of motion with zero velocity.
Hydrodynamics: The study of the motion of fluids that can be approximated as incompressible (such as liquids, especially water, and gases at low speeds).
Hydraulics: A subcategory of hydrodynamics, which deals with liquid flows in pipes and open channels.
Gas dynamics: Deals with the flow of fluids that undergo significant density changes, such as the flow of gases through nozzles at high speeds.
Aerodynamics: Deals with the flow of gases (especially air) over bodies such as aircraft, rockets, and automobiles at high or low speeds.
Meteorology, oceanography, and hydrology: Deal with naturally occurring flows.
Stress: Force per unit area.
Normal stress: The normal component of a force acting on a surface per unit area.
Shear stress: The tangential component of a force acting on a surface per unit area.
Pressure: The normal stress in a fluid at rest.
Zero shear stress: A fluid at rest is at a state of zero shear stress.
When the walls are removed or a liquid container is tilted, a shear develops as the liquid moves to re-establish a horizontal free surface.
The normal stress and shear stress at
the surface of a fluid element. For
fluids at rest, the shear stress is zero
and pressure is the only normal stress.
In a liquid, groups of molecules can move relative to each other, but the volume remains relatively constant because of the strong cohesive forces between the molecules. As a result, a liquid takes the shape of the container it is in, and it forms a free surface in a larger container in a gravitational field.
A gas expands until it encounters the walls of the container and fills the entire available space. This is because the gas molecules are widely spaced, and the cohesive forces between them are very small. Unlike liquids, a gas in an open container cannot form a free surface.
Laminar flow: The highly ordered fluid motion characterized by smooth layers of fluid. The flow of high-viscosity fluids such as oils at low velocities is typically laminar in flow.
Understand the physical mechanism of convection and its classification.
Visualize the development of velocity and thermal boundary layers during flow over surfaces.
Gain a working knowledge of the dimensionless Reynolds, Prandtl, and Nusselt numbers.
Distinguish between laminar and turbulent flows, and gain an understanding of the mechanisms of momentum and heat transfer in turbulent flow.
Derive the differential equations that govern convection on the basis of mass, momentum, and energy balances, and solve these equations for some simple cases such as laminar flow over a flat plate.
Non dimensionalize the convection equations and obtain the functional forms of friction and heat transfer coefficients.
Use analogies between momentum and heat transfer, and determine heat transfer coefficient from knowledge of friction coefficient.
Report on Types of fluid flow
fluid dynamics
Introduction
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. Note that fluid flow can get very complex when it becomes turbulent. Physicists haven’t developed any elegant equations to describe turbulence because how turbulence works depends on the individual system whether you have water cascading through a pipe or air streaming out of a jet engine. Usually, you have to resort to computers to handle problems that involve fluid turbulence. Types of fluid flow:
Aerodynamic force
Cavitation
Compressible flow
Couette flow
Free molecular flow
Incompressible flow
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
3. 3
Understand the basic concepts of Fluid Mechanics.
Recognize the various types of fluid flow problems
encountered in practice.
Learn the history of Fluid Mechanics.
Understand the vapor pressure and its role in the occurrence
of cavitation.
Have a working knowledge of viscosity and the
consequences of the frictional effects it causes in fluid flow.
Calculate the capillary rises and drops due to the surface
tension effects.
Objective
5. 5
The development of a velocity
profile due to the no-slip
condition as a fluid flows over a
blunt nose.
A fluid flowing over a stationary
surface comes to a complete stop
at the surface because of the no-
slip condition.
Flow separation during flow over a curved
surface.
Boundary layer: The flow
region adjacent to the wall in
which the viscous effects
(and thus the velocity
gradients) are significant.
7. 7
Viscous flows: Flows in which the frictional effects are
significant.
Inviscid flow regions: In many flows of practical interest,
there are regions (typically regions not close to solid surfaces)
where viscous forces are negligibly small compared to inertial
or pressure forces.
The flow of an originally uniform
fluid stream over a flat plate, and
the regions of viscous flow (next
to the plate on both sides) and
inviscid flow (away from the
plate).
Viscous versus Inviscid Regions of Flow
8. 8
External flow over a tennis ball, and the
turbulent wake region behind.
External Flow: The flow of an unbounded fluid over a surface such
as a plate, a wire, or a pipe.
Internal Flow: The flow in a pipe or duct if the fluid is completely
bounded by solid surfaces.
Water flow in a pipe is
internal flow, and
airflow over a ball is
external flow .
The flow of liquids in a
duct is called open-
channel flow if the
duct is only partially
filled with the liquid
and there is a free
surface.
Internal versus External Flow
9. 9
Incompressible flow: If the
density of flowing fluid remains
nearly constant throughout (e.g.,
liquid flow).
Compressible flow: If the
density of fluid changes during
flow (e.g., high-speed gas flow)
When analyzing rockets,
spacecraft, and other systems
that involve high-speed gas
flows, the flow speed is often
expressed by Mach number Schlieren image of a small model of the
space shuttle orbiter being tested at
Mach 3 in the supersonic wind tunnel of
the Penn State Gas Dynamics Lab.
Several oblique shocks are seen in the
air surrounding the spacecraft.
Ma = 1 Sonic flow
Ma < 1 Subsonic flow
Ma > 1 Supersonic flow
Ma >> 1 Hypersonic flow
Compressible versus Incompressible Flow
10. 10
Laminar Flow: The highly ordered
fluid motion characterized by
smooth layers of fluid. The flow of
high-viscosity fluids such as oils at
low velocities is typically laminar.
Ttransitional Flow: A flow that
alternates between being laminar
and turbulent.
Turbulent Flow:The highly dis-
ordered fluid motion that typically
occurs at high velocities and is
characterized by velocity
fluctuations. The flow of low-
viscosity fluids such as air at high
velocities is typically turbulent.
Laminar, transitional, and turbulent
flows.
Laminar versus Turbulent Flow
11. 11
Forced Flow: A fluid is forced
to flow over a surface or in a
pipe by external means such
as a pump or a fan.
Natural flow: Fluid motion is
due to natural means such as
the buoyancy effect, which
manifests itself as the rise of
warmer (and thus lighter)
fluid and the fall of cooler
(and thus denser) fluid.
In this schlieten image of a girl in a
swimming suit, the rise of lighter,
warmer air adjacent to her body
indicates that humans and warm-
blooded animals are surrounded by
thermal plumes of rising warm air.
Natural (or Unforced) versus Forced Flow
12. 12
The term steady implies no change at a
point with time.
The opposite of steady is unsteady.
The term uniform implies no change with
location over a specified region.
The term periodic refers to the kind of
unsteady flow in which the flow
oscillates about a steady mean.
Many devices such as turbines,
compressors, boilers, condensers, and
heat exchangers operate for long periods
of time under the same conditions, and
they are classified as steady-flow
devices.
Oscillating wake of a blunt-based
airfoil at Mach number 0.6. Photo (a)
is an instantaneous image, while
photo (b) is a long-exposure (time-
averaged) image.
Steady versus Unsteady Flow
13. 13
A flow field is best characterized by its
velocity distribution.
A flow is said to be one-, two-, or three-
dimensional if the flow velocity varies
in one, two, or three dimensions,
respectively.
However, the variation of velocity in
certain directions can be small relative
to the variation in other directions and
can be ignored.
The development of the velocity profile in a circular pipe. V = V(r,
z) and thus the flow is two-dimensional in the entrance region,
and becomes one-dimensional downstream when the velocity
profile fully develops and remains unchanged in the flow
Flow over a car antenna is
approximately two-dimensional
except near the top and bottom
of the antenna.
One-, Two-, and Thee- Dimensional Flow
15. 15
Segment of Pergamon pipeline. Each
clay pipe section was 13 to 18 cm in
diameter.
A mine hoist powered
by a reversible water
wheel.
16. 16
The Wright brothers take flight at Kitty
Hawk.
The Oklahoma Wind Power Center
consists of:
68 turbines, 1.5 MW each.
17. 17
Saturation temperature Tsat: The temperature
at which a pure substance changes phase at a
given pressure.
Saturation pressure Psat: The pressure at
which a pure substance changes phase at a
given temperature.
vapor pressure (Pv): The pressure exerted by
its vapor in phase equilibrium with its liquid at
a given temperature. It is identical to the
saturation pressure Psat of the liquid (Pv = Psat).
Partial pressure: The pressure of a gas or
vapor in a mixture with other gases. For
example, atmospheric air is a mixture of dry air
and water vapor, and atmospheric pressure is
the sum of the partial pressure of dry air and
the partial pressure of water vapor.
Vapor Pressure and Cavitation
18. 18
There is a possibility of the liquid
pressure in liquid-flow systems
dropping below the vapor
pressure at some locations, and
the resulting unplanned
vaporization.
The vapor bubbles (called
cavitation bubbles since they
form “cavities” in the liquid)
collapse as they are swept away
from the low-pressure regions,
generating highly destructive,
extremely high-pressure waves.
This phenomenon, which is a
common cause for drop in
performance and even the
erosion of impeller blades, is
called cavitation, and it is an
important consideration in the
design of hydraulic turbines and
Cavitation damage on a 16-mm by
23-mm aluminum sample tested at
60 m/s for 2.5 h. The sample was
located at the cavity collapse
region downstream of a cavity
generator specifically designed to
produce high damage potential.
19. 19
COMPRESSIBILITY AND SPEED OF SOUND
Speed of sound (sonic speed): The speed at which an infinitesimally small
pressure wave travels through a medium.
Propagation of a small
pressure wave along a duct.
Control volume moving with the
small pressure wave along a duct.
For an ideal gas
For any fluid
20. 20
The speed of sound changes with
temperature and varies with the fluid.
Gas Constant
R = 0.287 kJ/kgK for air
R = 2.0769 kJ/kgK for helium
22. 22
Viscosity: A property that represents the internal resistance of
a fluid to motion or the “fluidity”.
Drag force: The force a flowing fluid exerts on a body in the
flow direction. The magnitude of this force depends, in
part, on viscosity
A fluid moving relative to a
body exerts a drag force on
the body, partly because of
friction caused by viscosity.
23. 23
The behavior of a fluid
in laminar flow
between two parallel
plates when the upper
plate moves with a
constant velocity.
Fluids for which the rate of
deformation is proportional to the
shear stress are called Newtonian
fluids.
Shear Stress
: is the Dynamic Viscosity kg/m s or N s/m2 or Pa s
1 poise = 0.1 Pa s
)
m
/
N
(
dy
dV 2
)
N
(
A
dy
dV
A
F
Shear Force
dy
dV
or
dt
)
(
d
22
y
X
y
Force F
Velocity V
V=0
V=V
Area A
d
Velocity Profile
y
V
dy
dv
24. 24
y
X
y
Force F
Velocity
V
V = 0
V = V
Area A
d
Velocity
Profile
y
V
dy
dv
)
t
tan
cons
R
(
R
g
cos
2
h
:
rise
Capillary
25. 25
The rate of deformation (velocity
gradient) of a Newtonian fluid is
proportional to shear stress, and the
constant of proportionality is the
viscosity.
Variation of shear stress with the
rate of deformation for Newtonian
and non-Newtonian fluids (the
slope of a curve at a point is the
apparent viscosity of the fluid at
that point).
26. 26
Kinematic viscosity,
m2/s or stoke (1 stoke = 1 cm2/s)
The viscosity of liquids decreases and the
viscosity of gases increases with
temperature.
/
27. 27
This equation can be used to calculate the viscosity of a fluid by
measuring torque at a specified angular velocity.
Therefore, two concentric cylinders can be used as a viscometer, a
device that measures viscosity.
L length of the cylinder
number of revolutions per unit time
29. 29
Attractive forces acting on a liquid
molecule at the surface and deep
inside the liquid.
Stretching a liquid film with a U-
shaped wire, and the forces acting
on the movable wire of length b.
Surface tension: The work done per unit increase in the surface area of the liquid.
30. 30
Some consequences of surface
tension.
Liquid droplets behave like small
balloons filled with the liquid on a
solid surface, and the surface of
the liquid acts like a stretched
elastic membrane under tension.
The pulling force that causes this
tension acts parallel to the surface
and is due to the attractive forces
between the molecules of the
liquid.
The magnitude of this force per unit
length is called surface tension
(or coefficient of surface tension)
and is usually expressed in the unit
N/m.
This effect is also called surface
energy [per unit area] and is
expressed in the equivalent unit of
N m/m2.
32. 32
Capillary Effect
Capillary effect: The rise or fall of a liquid in a small-diameter tube
inserted into the liquid.
Capillaries: Such narrow tubes or confined flow channels.
The capillary effect is partially responsible for the rise of water to the top
of tall trees.
Meniscus: The curved free surface of a liquid in a capillary tube.
The contact angle for wetting and
non-wetting fluids.
The meniscus of colored water in a
4-mm-inner-diameter glass tube.
Note that the edge of the meniscus
meets the wall of the capillary tube
at a very small contact angle.
The strength of the capillary effect is
quantified by the contact (or wetting)
angle, defined as the angle that the
tangent to the liquid surface makes with
the solid surface at the point of contact.
33. 33
The capillary rise of water and the
capillary fall of mercury in a small-
diameter glass tube.
The forces acting on a liquid column
that has risen in a tube due to the
capillary effect.
Capillarity rise is inversely proportional to the radius of the tube and
density of the liquid
)
t
tan
cons
R
(
R
g
cos
2
h
:
rise
Capillary
35. 35
s
a
ŷ
ycp
C.G
C.P
F
ĥ
Free Surface
A Completely Submerged Tilted Rectangular Plate
sin
)
2
/
a
s
(
h
b
a
sin
2
a
S
g
A
h
g
F
)
b
a
(
)
2
/
a
s
(
12
/
a
b
2
a
s
y
3
cp
36. 36
a
ŷ
ycp
C.G
C.P
F
ĥ
Free Surface
When the Upper Edge of the Submerged Tilted Rectangular Plate is at
the Free Surface and thus (S = 0)
sin
)
2
/
a
(
h
b
a
sin
2
a
g
A
h
g
F
a
3
2
)
b
a
(
)
2
/
a
(
12
/
a
b
2
a
y
3
cp
37. 37
= 90o
a
s
ŷ = ĥ
ycp = hcp
C.G
C.P
F
Free Surface
A Completely Submerged Vertical Rectangular Plate = 90o
b
a
2
a
S
g
A
h
g
F
)
b
a
(
)
2
/
a
s
(
12
/
a
b
2
a
s
h
3
cp
0
90
sin
:
where
)
2
/
a
s
(
h
o
38. 38
= 90o
a
ŷ = ĥ
ycp = hcp
C.G
C.P
F
Free Surface
When the Upper Edge of the Submerged Tilted Rectangular Plate is at
the Free Surface and thus ( = 0 & S = 0)
b
a
2
a
g
A
h
g
F
a
3
2
)
b
a
(
)
2
/
a
(
12
/
a
b
2
a
h
3
cp
0
s
,
0
90
sin
:
where
)
2
/
a
(
h
o
41. 41
El. 50
El. 40
El. 150 ft
1000 ft &
D1=8 in
P
A
B
HP
hL(2)
hL(1)
p
)
2
(
L
)
1
(
L H
)
B
A
(
h
h
2
5
2
2
L Q
D
g
L
f
8
g
2
V
D
L
f
h
c
/
H
Q
g
power p
Neglecting all losses except
main losses (friction losses)
EGL
Rise in EGL and HGL due to Pump
HGL
42. 42
El. 50
El. 40
El. 150 ft
1000 ft &
D1=8 in
T
A
B
HT
hL(1)
hL(2)
)
B
A
(
H
h
h T
)
2
(
L
)
1
(
L
2
5
2
2
L Q
D
g
L
f
8
g
2
V
D
L
f
h
c
/
H
Q
g
power p
Neglecting all losses except
main losses (friction losses)
EGL
Drop in EGL and HGL due to Pump
HGL
44. 44
A
B
junction
1
1
1 D
&
f
&
L
2
2
2 D
&
f
&
L
3
3
3 D
&
f
&
L
B
A
h
h )
2
(
L
)
1
(
L
)
3
(
L
)
2
(
L h
h
3
2
1 Q
Q
Q
.
)
1
(
L
h
)
3
(
L
)
2
(
L h
h
2
Q
c
2
5
2
L Q
D
g
L
f
8
h
c
/
h
Q L
where
Pipe and pipe
are connected in Series
Pipe and pipe
are connected in Series
and 5
2
D
g
/
L
f
8
c
45. 45
A
B
C
junction
1
1
1 D
&
f
&
L
2
2
2 D
&
f
&
L
3
3
3 D
&
f
&
L
B
A
h
h )
B
J
(
L
)
J
A
(
L
C
A
h
h )
C
J
(
L
)
J
A
(
L
3
2
1 Q
Q
Q
)
J
A
(
L
h
)
B
J
(
L
h
)
C
J
(
L
h
2
Q
c
2
5
2
L Q
D
g
L
f
8
h
c
/
h
Q L
where
46. 46
A
B
C
junction
1
1
1 D
&
f
&
L
2
2
2 D
&
f
&
L
3
3
3 D
&
f
&
L
B
A
h
h )
B
J
(
L
)
J
A
(
L
C
A
h
h )
C
J
(
L
)
J
A
(
L
3
1 Q
with
Q
Compare
)
J
A
(
L
h
0
h )
B
J
(
L
)
C
J
(
L
h
2
Q
c
2
5
2
L Q
D
g
L
f
8
h
c
/
h
Q L
where
= 0
47. 47
A
B
C
junction
1
1
1 D
&
f
&
L
2
2
2 D
&
f
&
L
3
3
3 D
&
f
&
L
C
A
h
h )
C
J
(
L
)
J
A
(
L
C
B
h
h )
C
J
(
L
)
J
B
(
L
3
2
1 Q
with
Q
Q
Compare
)
J
A
(
L
h
0
h )
J
B
(
L
)
C
J
(
L
h
2
Q
c
2
5
2
L Q
D
g
L
f
8
h
c
/
h
Q L
where
49. 49
Q1&D1= 6 in
Q2&D2=3 in
Q3&D3=4 in
Q2=Q3= ½ Q
=30o
= 45o
x
y
If the “T” in a horizontal position, Z1 = Z2 + Z3
2
2
1
2
g
2
V
g
p
Z
g
2
V
g
p
Z
The energy (Bernoulli’s) Eq. is
The continuity Eq. gives
3
2
1 Q
Q
Q
50. 50
Summary
• The No-Slip Condition
• Classification of Fluid Flows
Viscous versus Inviscid Regions of Flow
Internal versus External Flow
Compressible versus Incompressible Flow
Laminar versus Turbulent Flow
Natural (or Unforced) versus Forced Flow
Steady versus Unsteady Flow
One-, Two-, and Three-Dimensional Flows
• A Brief History of Fluid Mechanics
• Vapor Pressure and Cavitation
• Compressibility and Speed of Sound
• Viscosity
• Surface Tension and Capillary Effect