Numerical methods
Upcoming SlideShare
Loading in...5
×
 

Numerical methods

on

  • 508 views

 

Statistics

Views

Total Views
508
Views on SlideShare
506
Embed Views
2

Actions

Likes
0
Downloads
10
Comments
0

1 Embed 2

http://www.slideshare.net 2

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Numerical methods Numerical methods Presentation Transcript

  • MATHEMATICALMODELS
    Lizeth Paola Barrero Riaño
    PetroleumEnginnering
    Industrial University of Santander
    2010
  • Definition
    A mathematical model can be defined broadly, as a formulation or an equation that expresses the essential characteristics of a physical system or process in mathematical terms. Its variables are obtained by studying the physical laws that are involved in the process.
  • Characteristics
  • Components
    Overall, the model can be represented by the functional relationship of the form:
    Dependent = f (independent variables, parameters, forcefunctions )
    variables
  • Darcy’s law
    Darcy's Law is a generalized relationship for flow in porous media. It shows the volumetric flow rate is a function of the flow area, elevation, fluid pressure and a proportionality constant. It may be stated in several different forms depending on the flow conditions..
  • One-Dimensional Flow
    Where:
    Q = Volumetric flow rate (m3/s or ft3/s),
    A = Flow area perpendicular to L (m2 or ft2),
    K = Hydraulic conductivity (m/s or ft/s),
    l = Flow path length (m or ft),
    h = Hydraulic head (m or ft), and
    D = Denotes the change in h over the path L.
  • Thehydraulic head at a specificpoint, histhesum of thepressure head and theelevation, or
    h = (p/r g + z) Normal SI form of the equation__
    h = (p/g + z)Usual form used with English units
    Where:
    p = waterpressure (N/m2, lb/ft2),r = waterdensity (kg/m3),g = waterspecificweight (lb/ft3),g = acceleration of gravity (m/s2or ft/s2), andz = elevation (m or ft).
  • Bibliography
    CHAPRA, Steven. Métodos números para ingenieros. Thirdedition. McGraw-Hill Editorial. 2000
    Article: Conceptos básicos de modelación matemática y simulación computacional de sistemas biológicos una herramienta útil para la docencia y la investigación. Authors: Alejandro Pelaez and Sergio Mejia. CES Odontología Magazine Vol. 3 No 1.2000
    http://bioen.okstate.edu/Darcy/LaLoi/basics.htm