Abstract: 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.
Abstract: 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.
Abstract: 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.
Abstract: 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.
Abstract: 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.