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ITS » Master Theses » Statistika -- Matematika Industri
Posted by anis at 02/01/2007 10:19:00  •  29026 Views


MODEL MATEMATIKA DARI ALIRAN AIR DI PERMUKAAN BEBAS DIATAS GUNDUKAN BERBENTUK SEBARANG DALAM SUATU KANAL

MATHEMATIKAL MODELING OF WATER FLOWS IN THE FREE SURFACE OVER ABRITRERY SHAPE STEP IN A CHANNEL

Author :
SAMSUDIN 




ABSTRAK

Secara teori matematika perhitungan aliran air di permukaan bebas dimensi dua tak berputar tak mampu mampat meliputi tidak hanya dalam hal penentuan dari fungsi potensial atau fungsi aliran dalam kanal tetapi juga batas dari daerah penyelesaian yang merupakan variabel yang tak diketahui. Dalam penelitian ini akan dibuat model matematika dan bentuk profil dari aliran air di permukaan bebas di atas gundukan yang dipengaruhi oleh gravitasi bumi dengan tinggi gundukan non- dimensi dan lebar gundukan non-dimansi. Penyelesaian masalah aliran air di permukaan bebas di atas gundukan yang dipengaruhi oleh gravitasi bumi digunakan teknik perhitungan secara numerik dengan metode integral batas. Untuk memperoleh persamaan integral batas dari aliran air di permukaan bebas didasarkan pada masalah Riemann-Hilbert. Pertama-tama dari bentuk fisis aliran air di permukaan bebas di atas gundukan yang dipengaruhi oleh gravitasi bumi diubah ke dalam bentuk potensial dengan menggunakan transformasi Schwartz-Christoffel sehingga masalahnya menjadi masalah nilai batas campuran Riemann-Hilbert. Dengan teori rata-rata Muskhelisvhilli akan diperoleh persamaan integral non-linier. Selanjutnya dengan menggunakan metode substitusi akan diperoleh persamaan integral batas bidang fisis. Model matematika dari aliran fluida di permukaan bebas tersebut diselesaikan dengan menggunakan perhitungan numerik.


ABSTRACT

The computation of free surface fluid flows in two-dimensional irrotational and incompressible mathematically are not only in either potential function or stream function but also in solution domains boundary which make up unknown variables. In this research will be formed mathematical modelling and profile of water flow in the free surface over a step under the gravity effects with non-dimensioan step high and non-dimension step wide. To solve the free surface water flows over steps under gravity problems are used numerical computational techniques with boundary integral method. To obtain boundary integral equations of free surface water flows over steps based on Riemann-Hilbert problem. Firstly the physical shapes of the free surface water flows over steps under the gravity effects could be changed into potential form by using Schwartz- Christoffel transformation. By using Muskhelisvhilli average theory non-linear integral equations will be obtained. Further by using substitution methods will be obtained physical plane boundary integral equations. The mathematical method of free surface fluid flows can be solved by using numerical computation.



KeywordsAliran air di permukaan bebas;fungsi aliran dalam kanal;gravitasi bumi;free surface fluid flows
 
Subject:  Model matematika
Contributor
  1. DR. Basuki Widodo, M.Sc
    Drs. Sentot Didik Surjanto, M.Si.
Date Create: 02/01/2007
Type: Text
Format: pdf ; 65 pages
Language: Indonesian
Identifier: ITS-Master-3100002014680
Collection ID: 3100002014680
Call Number: 511.8 Sam m


Source
Theses Industry Mathematic RT 511.8 Sam m, 2001

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