Filtration of Liquids - Chapter 4 solution (Particle Technology by Holdich)Bobby Canja
This is the my own solution to chapter 4 problems from Fundamentals of Particle Technology by Holdich. I hope it helped you. :) Just e-mail me if ever there are corrections at vic_zhou14@yahoo.com.ph.
-Detective Freddie
Kalman filter is a algorithm of predicting the future state of a system based on the previous ones.
In the presentation, I introduce to basic Kalman filtering step by step, with providing examples for better understanding.
Classification of signals
Deterministic and Random signals
Continuous time and discrete time signal
Even (symmetric) and Odd (Anti-symmetric) signal
Periodic and Aperiodic signal
Energy and Power signal
Causal and Non-causal signal
Filtration of Liquids - Chapter 4 solution (Particle Technology by Holdich)Bobby Canja
This is the my own solution to chapter 4 problems from Fundamentals of Particle Technology by Holdich. I hope it helped you. :) Just e-mail me if ever there are corrections at vic_zhou14@yahoo.com.ph.
-Detective Freddie
Kalman filter is a algorithm of predicting the future state of a system based on the previous ones.
In the presentation, I introduce to basic Kalman filtering step by step, with providing examples for better understanding.
Classification of signals
Deterministic and Random signals
Continuous time and discrete time signal
Even (symmetric) and Odd (Anti-symmetric) signal
Periodic and Aperiodic signal
Energy and Power signal
Causal and Non-causal signal
Top 13 Famous Civil Engineering Scientistgettygaming1
List of Best Scientist Who Gives Big Contribution in Civil Engineering Filed, in this we provide how they Contribute in Civil Engineering filed, For Data Collection civilthings.com helps us a lot.
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Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
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The family offers a choice of engines
Calpeda pumps are renowned for their reliability and efficiency in fluid management solutions. With a legacy spanning over 70 years, Calpeda specializes in producing a wide range of pumps, including centrifugal, submersible, and booster pumps, catering to various industrial, commercial, and residential applications. Their commitment to innovation and quality engineering ensures optimal performance and longevity in fluid handling systems.
Online blood donation management system project.pdfKamal Acharya
Blood Donation Management System is a web database application that enables the public to make online session reservation, to view nationwide blood donation events online and at the same time provides centralized donor and blood stock database. This application is developed
by using ASP.NET technology from Visual Studio with the MySQL 5.0 as the database management system. The methodology used to develop this system as a whole is Object Oriented Analysis and Design; whilst, the database for BDMS is developed by following the steps in Database Life Cycle. The targeted users for this application are the public who is eligible to donate blood ,'system moderator, administrator from National Blood Center and the staffs who are working in the blood banks of the participating hospitals. The main objective of the development of this application is to overcome the problems that exist in the current system, which are the lack of facilities for online session reservation and online advertising on the nationwide blood donation events, and also decentralized donor and blood stock database. Besides, extra features in the system such as security protection by using password, generating reports, reminders of blood stock shortage and workflow tracking can even enhance the efficiency of the management in the blood banks. The final result of this project is the development of web database application, which is the BDMS.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
2. Lecture 12
• Lecture topics
1. Numerical problem solution
2. Dynamic error in first order system
2
3. Numerical problem related to
second order system
1. Step Response
A force sensor has a mass of 0.5 kg, stiffness of 2 × 102 Nm−1 and a damping
constant of 6.0 N s m−1.
A. Calculate the steady-state sensitivity, natural frequency and damping ratio
for the sensor.
B. Calculate the displacement of the sensor for a steady input force of 2 N.
C. If the input force is suddenly increased from 2 to 3 N, derive an expression
for the resulting displacement of the sensor
3
4. • Solution
A.
i. Steady state sensitivity of a second order system can be given by,
ii. Natural frequency of a second order system is,
iii. And, damping ratio is
4
𝑲 =
𝟏
𝒌
…(7.20)
𝝎𝒏 = 𝒌
𝒎 …(7.8)
𝝃 =
𝝀
𝟐 𝒌 ∙ 𝒎
…(7.9)
5. • Solution
Given data,
• Spring stiffness, k = 2 × 102 Nm−1
• Sensor mass, m = 0.5 kg
• Damping constant, λ = 6.0 N s m−1
• Putting the values in respective equations
• Steady state sensitivity
• Natural frequency
• Damping ratio
5
𝑲 =
𝟏
𝟐 × 𝟏𝟎𝟐
= 𝟓 × 𝟏𝟎−𝟑 mN−1
𝝎𝒏 = 𝟐 × 𝟏𝟎𝟐
𝟎. 𝟓 = 𝟐𝟎 rad/s
𝝃 =
𝟔. 𝟎
𝟐 𝟐 × 𝟏𝟎𝟐 ∙ 𝟎. 𝟓
= 𝟎. 𝟑
6. • Solution
B.
i. Steady state response of second order system can be given by,
• Previously calculated,
• Steady state sensitivity, K = 5 ×10-3 mN-1
• Given data,
• Steady state input, Is = 2 N
Therefore, the sensor output will be,
6
𝑶𝒔 = 𝑲 ∙ 𝑰𝒔
𝑶𝒔 = 𝟓 × 𝟏𝟎−𝟑
∙ 𝟐 = 𝟎. 𝟎𝟏 m
7. • Solution
C.
i. The system is underdamped as damping ratio = 0.3. Therefore Step
response of the system can be given by,
• Previously calculated,
• Damping ratio, ξ = 0.3
• Natural frequency, ωn= 20 rad s-1
• Given data
• Initial output, O(t-) = 0.01 m (This is steady state output)
• Initial input, I(t-) = 2 N
• Final input, I(t) = 3 N
• Therefore, step height, H = I(0) - I(0-) = 3 – 2 = 1 N
7
Or, 𝒇𝟎 𝒕 = 𝟏 − 𝒆−𝝃𝝎𝒏𝒕 cos 𝝎𝒅𝑡 +
𝝃
𝟏 − 𝝃𝟐
sin 𝝎𝒅𝑡
…(10.25)
8. • Solution
C.
• Therefore, the expression for sensor output will be,
• Putting the values,
8
𝑶 𝒕 = 𝑶 𝒕 − + 𝑲 ∙ 𝑯 ∙ 𝟏 − 𝒆−𝝃𝝎𝒏𝒕
cos 𝝎𝒏 𝟏 − 𝝃𝟐𝑡 +
𝝃
𝟏 − 𝝃𝟐
sin 𝝎𝒏 𝟏 − 𝝃𝟐𝒕
𝑶 𝒕 = 𝟏 × 𝟏𝟎−𝟐
+ 𝟓 × 𝟏𝟎−𝟑
∙ 𝟏 ∙ 𝟏 − 𝒆−𝟎.𝟑∙𝟐𝟎𝒕
cos 𝟐𝟎 𝟏 − 𝟎. 𝟑𝟐𝑡 +
𝟎. 𝟑
𝟏 − 𝟎. 𝟑𝟐
sin 𝟐𝟎 𝟏 − 𝟎. 𝟑𝟐𝒕
𝑶 𝒕 = 𝟏 × 𝟏𝟎−𝟐 + 𝟓 × 𝟏𝟎−𝟑 𝟏 − 𝒆−𝟔𝒕 cos 𝟏𝟗. 𝟎8𝑡 + 𝟎. 𝟑𝟑 sin 𝟏𝟗. 𝟎𝟖𝒕
9. Dynamic errors in first order
system
If there are n number of elements in the system, each of which is having steady
state sensitivity of Ki and transfer function of Gi(s), then overall transfer function of
system becomes,
9
∆𝑶(𝒔)
∆𝑰(𝒔)
= 𝑮 𝒔 = 𝑮𝟏(𝒔) ∙ 𝑮𝟐(𝒔) ∙ ⋯ ∙ 𝑮𝒊(𝒔) ∙ 𝑮𝒏(𝒔) …(12.1)
Or, ∆𝑶(𝒔) = ∆𝑰(𝒔) ∙ 𝑮 𝒔
Or, ∆𝑶(𝒕) = ℒ−𝟏
∆𝑰(𝒔) ∙ 𝑮 𝒔 …(12.2)
10. Dynamic errors in first order
system
Now error can be given by,
Using Eq. 12.2
Now if the input signal is sinusoidal i.e. 𝐼 𝑠𝑖𝑛 𝜔𝑡 , The output signal will be,
The error will be
10
𝑬 𝒕 = ∆𝑶 𝒕 − ∆𝑰 𝒕
𝑬 𝒕 = ℒ−𝟏 ∆𝑰(𝒔) ∙ 𝑮 𝒔 − ∆𝑰 𝒕 …(12.3)
∆𝑶(𝒕) = 𝑮 𝒋𝜔 ∙ 𝐼 sin 𝜔𝑡 + 𝝋 …(12.4)
𝑬 𝒕 = 𝑮 𝒋𝜔 ∙ 𝐼 sin 𝜔𝑡 + 𝝋 − 𝐼 sin 𝜔𝑡
Or, 𝑬 𝒕 = 𝑰 ∙ 𝑮 𝒋𝜔 sin 𝜔𝑡 + 𝝋 − sin 𝜔𝑡 …(12.5)
11. Dynamic errors in first order
system
Now if the input signal is periodic (combination of more than one sinusoid),
The output signal will become
11
∆𝑶(𝒕) =
𝒏=𝟏
∞
𝑰𝒏 𝑮 𝒋𝒏𝜔𝟏 sin 𝒏𝜔𝟏𝑡 + 𝝋𝒏 …(12.7)
𝑬 𝒕 =
𝒏=𝟏
∞
𝑰𝒏 𝑮 𝒋𝒏𝜔𝟏 sin 𝒏𝜔𝟏𝑡 + 𝝋𝒏 − sin 𝒏𝜔𝟏𝑡 …(12.8)
∆𝑰(𝒕) =
𝒏=𝟏
∞
𝑰𝒏 sin 𝒏𝜔𝟏𝑡 …(12.6)
12. Numerical problem related to first
order system dynamic error
1. Sinusoidal Response
A temperature measurement system for a gas reactor consists of linear
elements and has an overall steady-state sensitivity of unity. The temperature
sensor has a time constant of 5.0 s; an ideal low-pass filter with a cut-off
frequency of 0.05 Hz is also present. The input temperature signal is periodic
with period 63 s and can be approximated by the Fourier series:
Where ω0 is the angular frequency of the fundamental component.
Calculate expressions for the time response of:
(i) The system output signal
(ii) The system dynamic error.
12
𝑻 𝒕 = 𝟏𝟎 sin 𝜔0𝑡 +
1
2
sin 2𝜔0𝑡 +
𝟏
𝟑
sin 3𝜔0𝑡 +
𝟏
𝟒
sin 4𝜔0𝑡
13. • Solution
The expression for output signal for a first order system with periodic input
may be given by,
• Given data,
Time constant, τ = 5 sec
Angular frequency, ω0 = 2π/T = 0.1 rad/sec
Therefore, sensor transfer function will become,
And phase angle will be,
13
∆𝑶(𝒕) =
𝒏=𝟏
∞
𝑰𝒏 𝑮 𝒋𝒏𝜔𝟎 sin 𝒏𝜔𝟎𝑡 + 𝝋𝒏 …(12.7)
𝑮 jnω0 =
1
1 + 𝜏𝟐(𝒏ω0)𝟐
…(10.5)
𝝋 = tan−𝟏
−nω0𝜏 …(10.6)