
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 9th, 2017, 02:51 AM  #1 
Newbie Joined: Dec 2016 From: Tr Posts: 2 Thanks: 0  Vector surface integral for triangle
I have question about vector surface integral and I am really stuck here could you please help me? 1 the triangle with vertices (1,0,0), (0,2,0) and (0,0,3) What is the amount of fluid passing through the triangle when the flow vector as given as F=(x,x,x) 2 How can I find this flow vector considering triangular box with vertices (0,0,0), (1,0,0), (0,2,0) and (0,0,3). I mean how can I evaluate flux for each faces of the triangle box for new vertices (0,0,0), (1,0,0), (0,2,0) and (0,0,3). 
January 9th, 2017, 11:09 AM  #2 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,329 Thanks: 94 
Flow across surface = $\displaystyle \int _{S}$ F.n dS dA=dxdy = k.dS = k.n dS $\displaystyle \int _{S}$F.n dS = $\displaystyle \int _{A}$ $\displaystyle \frac{F.n}{k.n}$dA A is projected area on x,y plane n is surface normal which is conatant 
January 10th, 2017, 05:38 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,104 Thanks: 850  Quote:
Quote:
 
January 11th, 2017, 08:43 AM  #4  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,329 Thanks: 94  Quote:
Equation of the triangular plane is given by n.p=d where n is unit normal to plane and d is distance from origin to plane and n=aXb/aXb where a and b are any two vectors in the plane, such as (0,2,1) and (0,3,1), and d=n.p where p is any vector from the origin to a point on the plane, such as (0,0,1). To do the flow integral you need z as a function of x,y on the surface to get F(x,y,z)=F(x,y,z(x,y)) on the surface: Solve n.p=d for z=z(x,y). 2) Repeat 1) to get flow across the other surfaces of the triangular box. On the x,y plane, for example, n=k, and z=0. F(x,y,z) = f$\displaystyle _{x}$(x,y,z)i + f$\displaystyle _{y}$(x,y,z)$\displaystyle j$+ f$\displaystyle _{z}$(x,y,z)$\displaystyle k$  

Tags 
integral, surface, triangle, vector 
Search tags for this page 
how we determine surface integral if sueface is triangular with given vertices,How to find surface integral of a tringle given three vertices
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Volume induced by a vector field across a moving surface  coderodde  Calculus  0  April 18th, 2015 08:46 AM 
What is a surface integral?  henrymerrild  Calculus  2  May 1st, 2014 10:33 AM 
Triangle plane surface 2m base and 3 height  rsoy  Physics  4  April 23rd, 2012 08:27 AM 
surface integral  kriko  Calculus  1  August 21st, 2010 10:55 AM 
Surface Integral  sansar  Calculus  1  May 10th, 2009 04:21 AM 