This gives you application of numerical analysis in real life situations developing detail view in it

1. Application of Numerical Analysis In
Real Life
(Reverse Osmosis, Accident reconstruction)
Ashwini Madhav Sangale
Charanpreet Narendrasingh Gehdoo
Pooja Dagadu Suryawanshi
Archana Tukaram Redekar
Mithun Kumar
Kunal Krishna Palkar
Dipika Sudhakar Bane
Ashwin Singh

2. Numerical Analysis
1. Numerical analysis is concerned with the mathematical derivation,
description and analysis of methods of obtaining numerical solution
of mathematical problems,
2. In simple words Numerical analysis is the study of algorithms that
use numerical approximation (as opposed to symbolic
manipulations) for the problems of mathematical analysis Numerical
analysis is one of part of mathematics.
3. To deal with a physical problem one often tries to construct a
mathematical model.

3. Reverse osmosis
Reverse osmosis is one of the most well-known and widely used separation techniques for water treatment.
The reverse osmosis (RO) process is used in industry for wastewater and ultra-water purification.
Reverse osmosis is a water purification process that uses a semi-permeable membrane to filter out unwanted
molecules and large particles such as contaminants and sediments like chlorine, salt, and dirt from drinking
water.
The reverse osmosis mechanism has been mathematically modelled.
To solving the model, numerical integration methods are used. We look at three different forms of numerical
integration rules: Riemann sums, trapezoidal rules, and Simpson's rule.

7. OBJECTIVES
• to produce safe and fresh potable water
• also satisfying the quality requirements of industrial
water usage using the most developed and
implemented membrane processes
• It is highly used in desalinating seawater.
• It has crucial applications in the medical field.
• It is used to purify water to prevent any diseases.
• It has a wide application in water treatment and
water purification.
• It is used in food industries, and it is applied for the
concentration of juices, milk, and other beverages.
• It is used to provide clean water for the community
water supply.
LIMITATIONS
 It requires routine filter changes and
maintenance.
 The installation cost of a reverse osmosis system
is high.
 Hard water can damage the system.
• The damaged membrane will allow any small
microorganism to pass through it.
• The RO system is not self-sustaining.
• Sometimes reverse osmosis leads to clogging of
the whole system.

8. ACCIDENTAL RECONSTRUCTION
• Accident data collection: The accident data collection is the first step in the accident study. The data collection of the
accidents is primarily done by the police. The data to be collected should comprise all of these parameters: General - Date,
time, person involved in accidentETC, Location, Road and traffic condition ,Nature of accident - Details of collision,
damages, injury and casualt etc.
• Accident investigation: It is the effort made to determine why the accident occurred from the data available and the
analysis of accident reconstruction studies.
• .Accident data analysis:.
1. Accident Rate per kilometer : R = A/L
R = total accident rate per km for one year
A = total number of accidents occurring in one year
L = length of control section in kms

9. 2.Accident Involvement Rate:
𝑅 = (N X 100000000) /V
R = accident involvement per 100 million vehicle-
kms of travel
N = total number of drivers of vehicles involved in
accidents during the period of investigation
N = total number of drivers of vehicles involved in
accidents during the period of investigation
3.Death Rate Based on Population: 𝑅
= (B X 100000) 𝑃
R = death rate per 100,000 population
B = total number of traffic death in one year
P = population of area
4. .Death Rate Based on Registration:
𝑅 = (B X 10000) /M
R = death rate per 10,000 vehicles registered
B = total number of traffic death in one year
M = number of motor vehicles registered in the
area
5. Accident Rate Based on Vehicle-kms of
Travel
𝑅 = 𝐶 × 100000000 /V
R = accident rate per 100 million vehicle kms of
travel
C = number of total accidents in one year
C = number of total accidents in one year

10. Application of Numerical Analysis on Accidental Reconstruction:
• Road reconstruction safety audit:
Example: Before reconstruction of an at-grade intersection, there were 20 accidents during 5 years. After
reconstruction there were 4 accidents during 2 years. Determine the effectiveness ofreconstruction.
 Road sign: Road signs are integral part of safety as they ensure safety of the driver himself (warning signs) and safety of
the other vehicles and pedestrians on road (regulatory signs). Driver should be able to read the sign from a distance so
that he has enough time to understand and respond
N = No. of words on the sign
v = speed of vehicle (kmph)
L = distance from which inscription should be discernible (m)

11. Objective
• Accident analysis is carried out in order to determine the
cause or causes of an accident (that can result in single or
multiple outcomes) so as to prevent further accidents of
a similar kind.
• Crash data collection and reconstruction is used to
improve vehicle crashworthiness and improve safety of
road users.
• The objective of crash reconstruction is to estimate the
collision sequences / parameters that best fit the
damaged vehicles, data found at the scene as well as
witness statements and depositions.
• These analyses may be performed by a range of experts,
including forensic scientists, forensic engineers or health
and safety advisers
• The purpose of Accident data analysis is to find possible
causes of accidentrelated to driver, vehicle, and roadway.
• Accident analyses are made to develop information such
as drivers, pedestrians, vehicle, and roadway.
Limitations
• They are not as elegant as analytic solutions.
• They do not provide any insight into
generalizations.
• An exact value may not be clear.
• Analytical solution methods are limited to
circumstances where computing power is not
enough to solve the problem numerically

12. CONCLUSION
 The reverse osmosis model highly depends on numerical integration. The more precise the
integral value we obtain, the more precise the results of the mathematical model we get.
 In this research, the influences of vehicle dynamic control systems on the vehicle collision are
comprehensively investigated since VDCS plays important roles in vehicle safety, ride and
stability.
 A unique 3-D vehicle dynamics/crash mathematical model is developed. This model combines
vehicle crash structures and vehicle dynamics control systems.
 The results obtained from different applied cases show that the VDCS affect the crash
situation, by different ratios related to each case, positively. The deformation of the vehicle
front-end structure is reduced when the ASC is applied, and hence helps protecting the
occupant inside the vehicle compartment.
 The vehicle body deceleration is insignificantly changed within the applied cases. The vehicle
pitch angle and its acceleration and yaw angle and its acceleration are dramatically reduced
when the UPC system is applied.