1) A nozzle is a device that accelerates fluid flow by varying the cross-sectional area. Nozzles are used in applications like turbines, rockets, and jets.
2) The document discusses governing equations for nozzle flow, including the continuity and energy equations. It also covers isentropic flow assumptions.
3) Nozzle shape is examined, with convergent-divergent nozzles described as having a throat of minimum area, with subsonic flow before and supersonic after.
Critical pressure ratio, temperature ratio, velocity, and area are defined as the conditions at the throat where the velocity is sonic. An example problem is presented to demonstrate these concepts.
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe 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.
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe 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.
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
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.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
Introduction to convection
The dimensionless number and its physical significance
Similarity parameters from the differential equation
Dimensional analysis approach and its application
Numerical on Dimensional analysis approach
Review of Navier-Stokes equation
1. What is Heat Transfer?
2. APPLICATIONS OF HEAT TRANSFER
3. MODES OF HEAT TRANSFER
4. CONDUCTION
5. Fourier’s law of heat conduction
6. CONVECTION
7. Newton’s law of cooling
8. RADIATION
9. Stefan–Boltzmann law
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
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.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
Introduction to convection
The dimensionless number and its physical significance
Similarity parameters from the differential equation
Dimensional analysis approach and its application
Numerical on Dimensional analysis approach
Review of Navier-Stokes equation
1. What is Heat Transfer?
2. APPLICATIONS OF HEAT TRANSFER
3. MODES OF HEAT TRANSFER
4. CONDUCTION
5. Fourier’s law of heat conduction
6. CONVECTION
7. Newton’s law of cooling
8. RADIATION
9. Stefan–Boltzmann law
Mechanics of fluids is extremely important in many areas of engineering and science. Examples are:
Mechanical engineering:
Pipeline projects.
Design of tanks.
Design of pumps, turbines, air-conditioning equipment.
Petroleum Engineering
Mud logging, cementing.
Chemical Engineering
Design of chemical processing equipment.
Compressible flows in fluid mechanics in chemical engineeringUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process.
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We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
2. Nozzles
• A nozzle is a device used to accelerate a flowing fluid by varying the
cross-sectional area in the direction of flow. The fluid acceleration
comes on the account of a pressure drop along the nozzle.
• Nozzles applications
• Steam and gas turbine
• Rocket engines
• Jet engines
2
3. Governing equations
• Steady flow continuity equation
• Where m is the mass flow rate at inlet section (in), outlet section (out) and
any section (x) along nozzle passage. The mass flow rate can be
determined as:
3
Constantm
xoutin mmm
m
4. Governing equations
• ρ is the flowing fluid density (kg/m3)
• V is the velocity normal to the flow area (m/s)
• A the cross-sectional area (m2)
• Ʋ fluid specific volume (m3/kg)
4
skg
v
AV
AVm /
x
xx
out
outout
in
inin
v
VA
v
VA
v
VA
5. Governing equations
• Steady flow energy equation (per unit mass)
• Apply the following assumption:
• Negligible heat losses (adiabatic).
• No work done on or by the system.
• The nozzle passage is very small and hence the change in the potential energy is
negligible even in vertical nozzle. 5
inout
inout
inout zzg
VV
hhwq
2
22
6. Governing equations
• The steady flow energy equation can be describe as:
• Applying the steady flow energy equation between section 1 and any
section X along the fluid flow along the nozzle passage.
6
outin
inout
hh
VV
2
22
XX hhVV 1
2
1
2
2
XX hhVV 1
2
1 2
7. Nozzle shape
• This part is to find the change in the nozzle cross-sectional area to increase
the fluid flow velocity to the required value.
• Consider a stream of fluid flow of inlet pressure and enthalpy of Pin and hin.
Assume the inlet velocity (Vin) is very small. Now describe the change of
the nozzle area to increase the fluid velocity.
• Apply the steady state momentum equation and replace the velocity with the
corresponding term from energy equation, and hence:
7
8. Nozzle shape
• The relation between the initial and final thermo-physical properties
depends on the thermodynamic process.
• Assume frictionless fluid flow + adiabatic flow = reversible adiabatic
(isentropic) process.
• At any section X, sx=s1=constant.
8
X
XX
hhV
v
m
A
1
2
1 2
X
XX
v
VA
m
X
XX
V
v
m
A
9. Nozzle shape
• At any section, by knowing the pressure and constant entropy, other
parameters can be determined.
9
10. Nozzle shape
• The following graph presents the effect of reducing gas pressure and the
influence on the cross-sectional area and flow velocity.
10
• It is observed that the area decreases
initially, hit the minimum at certain point
then increases again.
• The area decreases, when v-j
increases less rapidly than V-jj.
• The area increases, when v-jj
increases more rapidly than V-j.
X
XX
V
v
m
A
12. Nozzle shape
• Based on the aforementioned information. That type of nozzle is called a
convergent-divergent nozzle (the following graph).
12
13. Nozzle shape
• The section of minimum area is called the throat of the nozzle.
• The velocity at the throat of a nozzle operating at its designed
pressure ratio is the velocity of sound at the throat conditions.
• The flow up to the throat is sub-sonic; the flow after the throat is
supersonic
13
• The specific volume of a liquid is
constant over a wide pressure range,
and therefore nozzles for liquids are
always convergent.
14. Nozzle critical pressure ratio
• You can design a convergent divergent nozzle where the velocity at
the nozzle through equal the sound velocity.
• The ratio of the pressure at the section of sonic velocity to the
pressure at nozzle inlet is called the critical pressure ratio Z c.
• Solve the energy and momentum equations between the inlet section
and any point along the nozzle passage.
• In most practical applications the inlet velocity is negligible, so the
energy equation can be reduced to.
14
hhV 12 hhVV 1
2
1 2
15. Nozzle critical pressure ratio
• The enthalpy is usually expressed in kJ/kg. To find the flow velocity in m/s,
we need to convert the enthalpy to be J/kg.
• Substitute into the momentum equation.
15
m/s72.442000 11 hhhhV
hh
v
m
A
172.44
16. Nozzle critical pressure ratio
• Apply for perfect gas (constant specific heats).
• For isentropic process.
16
1
1
11
172.44
72.4472.44
T
T
TCp
v
TTCp
v
hh
v
m
A
1
11 P
P
T
T
RTPv
P
RT
v
17. Nozzle critical pressure ratio
• Let the pressure ratio (z)
17
1P
P
z
1
11
1
1
172.44
zTCpPz
zTR
m
A
121221211
constantconstant
1
constant
1
constant
zzzzzzzzzm
A
18. Nozzle critical pressure ratio
• To find the value of pressure ratio zc, at which the area per mass flow is
minimum, the differentiation of that term should be equal to zero.
18
0
constant
12
zzdz
d
1
1 1
2
RatioPressureCritical
P
P
z c
c
19. Critical temperature ratio
• The ratio of temperature at the section where the sonic velocity is attained
to the inlet temperature is called the critical temperature ratio.
19
1
2
RatioeTemperaturCritical
1
11
P
P
T
T cc
20. Critical Velocity
• To find the critical velocity
20
122 1
1
T
T
TCpTTCpV
ccc
c
cc TRTCpTCp
T
T
TCpV
11
2
1
212 1
21. Example
• Air at 8.6 bar and 190°C expands at a rate of 4.5 kg/s through a convergent
divergent nozzle into a space at 1.03 bar. Assuming that the inlet velocity is
negligible. Determine the through and the exit cross-sectional area of the
nozzle.
21
22. Example
• The critical pressure, temperature, velocity and area = through area.
22
528.0
1
2 1
1
P
Pc KTTc 8.385
1
2
1
)/(244.0 3
kgm
P
RT
v
c
c
c
sm
smTRV cc
/343SpeedSonic
/394
c
cc
v
VA
m
2
00279.0 m
V
vm
A
c
c
c