This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

This study investigates the role of identity as a critical factor in mediating the relationship between local and regional politics within the broader context of international relations (IR). While identity is frequently acknowledged as a catalyst for political instability and conflict, its function in fostering interdependence across political levels remains underexplored, particularly through empirical research. To address this gap, the study adopts a quantitative methodology, drawing on theories of identity politics and interdependence. A structured survey was administered to assess public perceptions of identity's influence on international engagement and its bridging role between domestic and regional political dynamics. The fi

        Positions related parties have become a regular feature and the general business and trade these days as it can enter the facilities in transactions with related parties on terms no enters them is with the parties relationship in normal circumstances, and that he found the funniest people relationship have an effect on the outcome of activity and financial position of the entity and its decisions financial and operational. In order to ensure "transparency" in the financial reports, most accounting around the world standards determines that disclosure of transactions with related parties, it is important to have a local accounting rules these relations as well as the unnecessary disclosure of the

Over the years, the issue of inclusion of students with special educational needs (SEN) in mainstream schools is controversial worldwide. Evidence from research argues that without a positive teachers’ attitude towards the inclusion of students with SEN in mainstream schools, the successful implementation of inclusion is most likely doubtable. The aim of this paper is to understand teachers’ attitudes towards the inclusion of students with SEN in mainstream schools from different perspectives and from different contexts. The conclusion drawn in this review can be that teachers’ attitude is the most important key towards the appropriate inclusion implementation in mainstream schools. The disparity of teachers’ attitudes towards th

Providing useful information in estimating the amount and timing and the degree of uncertainty concerning the future cash flows is one of the three main objectives of the financial reporting system, which is done through the main financial statements. The interest on standard-setting bodies in the forecasting of future cash flows, especially Financial Accounting Standards Board (FASB) explain under Accounting Standard (1) of the year 1978 "Objectives of Financial Reporting by Business Enterprises", paragraph (37) thereof that accounting profits better than cash flows when forecasting future cash flows, In contrast, IAS (7) as amended in 1992 aims to compel economic units to prepare statement of c

This paper presents a numerical simulation of the flow around elliptic groynes by using CFD ‎software. The flow was simulated in a flume with 4m long, 0.4m wide, ‎and 0.175m ‎high ‎‎with a constant bed slope. Moreover, the first Groyne placed at 1m from the flow ‎‎inlet with a ‎constant the Groyne height of 10cm and a 1cm thickness, and the ‎width of Groynes equals ‎7cm‎. A submergence ratio of the elliptic Groynes of 75% was assumed, corresponding to a discharge of ‎0.0057‎m³/sec. The CFD ‎model showed a good ability to simulate the flow ‎around ‎Groynes with ‎ good accuracy. The results of ‎CFD software showed that when using double elliptic Groy

Production logging is used to diagnose well production problems by evaluating the flow profile, entries of unwanted fluids and downhole flow regimes. Evaluating wells production performance can be easily induce from production logs through interpretation of production log data to provide velocity profile and contribution of each zone on total production. Production logging results supply information for reservoir modeling, provide data to optimize the productivity of existing wells and plan drilling and completion strategies for future wells. Production logging was carried out in a production oil well from Mishrif formation of West Qurna field, with the objective to determine the flow profile and fluid contributions from the perforations af

In the present work, a closed loop circulation system consist of three testing sections was designed and constructed. The testing sections made from (3m) of commercial carbon steel pipe of diameters(5.08, 2.54 and 1.91 cm) . Anionic surfactant  (SDBS )with  concentrations  of (50,  100,  150, 200 and 250 ppm)  was tested as a drag reducing  agent.  The additive(SDBS)studied using crude oil from south of Iraq. The flow rates of crude oil were used in 5.08 and 2.54 cm I.D. pipes are (1 - 12) m³/hr while (1-6) m3/hr were used in 1.91 cm J .D. pipe . Percentage drag reduction (%Dr) was found to increase by increasing solution velocity, pipe diameter and additives concentration (i.e. increasi