Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates
The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating
that the flow equations possess an infinite set of solutions.
Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flows
A New Velocity Expression for Open Channel and its Application to Lyari River
In this communication an expression for mean
velocity of waste flow via an open channel is proposed which
is an improvement over Manning formula. The discharges,
storages and depths are computed at all locations of the Lyari river
by utilizing proposed expression. The results attained through
proposed expression are in good agreement with the observed data
and better than those acquired using Manning formula.
Comparison, Depth, Flow, Open Channel, Proposed
Quantitative Study for Exchange of Gases from Open Sewer Channel to Atmosphere
In this communication a quantitative modeling
approach is applied to construct model for the exchange of gases
from open sewer channel to the atmosphere. The data for the
exchange of gases of the open sewer channel for the year January
1979 to December 2006 is utilized for the construction of the model.
The study reveals that stream flow of the open sewer channel
exchanges the toxic gases continuously with time varying scale. We
find that the quantitative modeling approach is more parsimonious
model for these exchanges. The usual diagnostic tests are applied for
the model adequacy. This model is beneficial for planner and
managerial bodies for the improvement of implemented policies to
overcome future environmental problems.
Open sewer channel, Industrial waste, Municipalwaste, Gases exchange, Atmosphere, Stochastic models, Diagnosticschecks.
Quantitative Estimation of Periodicities in Lyari River Flow Routing
The hydrologic time series data display periodic
structure and periodic autoregressive process receives considerable
attention in modeling of such series. In this communication long
term record of monthly waste flow of Lyari river is utilized to
quantify by using PAR modeling technique. The parameters of
model are estimated by using Frances & Paap methodology. This
study shows that periodic autoregressive model of order 2 is the most
parsimonious model for assessing periodicity in waste flow of the
river. A careful statistical analysis of residuals of PAR (2) model is
used for establishing goodness of fit. The forecast by using proposed
model confirms significance and effectiveness of the model.
Diagnostic checks, Lyari river, Model selection,Monthly waste flow, Periodicity, Periodic autoregressive model.
Some Rotational Flows of an Incompressible Fluid of Variable Viscosity
The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.
Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system
Quantification of Periodicities in Fugitive Emission of Gases from Lyari Waterway
Periodicities in the environmetric time series can be
idyllically assessed by utilizing periodic models. In this
communication fugitive emission of gases from open sewer channel
Lyari which follows periodic behaviour are approximated by
employing periodic autoregressive model of order p. The orders of
periodic model for each season are selected through the examination
of periodic partial autocorrelation or information criteria. The
parameters for the selected order of season are estimated individually
for each emitted air toxin. Subsequently, adequacies of fitted models
are established by examining the properties of the residual for each
season. These models are beneficial for schemer and administrative
bodies for the improvement of implemented policies to surmount
future environmental problems.
Exchange of Gases, Goodness of Fit, Open Sewer
Channel, PAR(p) Models, Periodicities, Season Wise Models.
Looking for a Favorable Central Place for the Establishment of Educational and Health Care Centre to Equally Facilitate Both Genders in Taluka Kunri of District Umerkot, Sindh, Pakistan
Population in rural areas are scattered in the form of different villages or settlements. The proper selection of land to launch any educational or health activities to equally facilitate both the genders is the sticky situation, both for Govt. and Private organizations. Govt. spends substantial funds for the establishment of education institution/health centre at the place which is feasible and accessible to general public. However for specific gender, the gender population is also considered so that both the gender may be benefited equally. In this research, efforts have been made to illustrate how one can choose or locate the best central place/ area in Taluka Kunri of district Umerkot Sindh Pakistan where the Educational or Health activity is to be initiated. For the purpose the concept of centre of mass theorem is used as a tool to develop mathematical model, subsequently utilize in achieving the objectives.
Centre of mass theorem, Establishment of technical/ vocational/ health care centre, Gender population of taluka Kunri of District Umerkot, Graphical interpretation of town committee/villages.
Vaccinated Susceptible Infected and Recovered (VSIR) Mathematical Model to Study the Effect of Bacillus Calmette-Guerin (BCG) Vaccine and the Disease Stability Analysis
Tuberculosis (TB) remains a leading cause of
infectious mortality. It is primarily transmitted by the respiratory
route, individuals with active disease may infect others through
airborne particles which releases when they cough, talk, or sing and
subsequently inhale by others. In order to study the effect of the
Bacilli Calmette-Guerin (BCG) vaccine after vaccination of TB
patient, a Vaccinated Susceptible Infected and Recovered (VSIR)
mathematical model is being developed to achieve the desired
objectives. The mathematical model, so developed, shall be used to
quantify the effect of BCG Vaccine to protect the immigrant young
adult person. Moreover, equations are to be established for the
disease endemic and free equilibrium states and subsequently utilized
in disease stability analysis. The stability analysis will give a
complete picture of disease annihilation from the total population if
the total removal rate from the infectious group should be greater
than total number of dormant infections produced throughout
Bacillus Calmette-Guerin vaccine, disease-free
equilibrium state, VSIR Quantification, disease stability analysis.