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| Finding the Tension and Inclination of an underwater cable |
Macky_Bwoy22 |
04/26/07 |
This is a problem i have trouble with please if there is someone who can help dont refrain from doing so u can email me at Macky_Bwoy22 at hotmail.com for any clarification thanks in advance
The equations below are in math ml forma and can be viewed noramlly by pasting them into
http://www1.chapman.edu/~jipsen/mathml/asciimathdemo.html
In order to Find approximations of the Tension, T, and angle of Inclination from the horizontal, 'Phi', at a point on a cable or pipeline run underwater a number of equations of the form
1) $Phi = tan^-1[(T_0 sin Phi_0 -F)/(T_0 cos Phi_0 - G)]'
2) $T =[(T_0sinPhi_0 - F)^2 + (T_0 cos Phi_0 - G)^2]^(1/2)'
must be solved for 'Phi' and T. The functions F and G in (1) and (2) both involve 'Phi' and have the form
$F = s/2[ - f(Phi_0) sin Phi_0 - f(Phi)sin(Phi) + (Phi_0)cos(Phi_0)+g(Phi)cos(Phi) - ws'
$G = - s/2[-f(Phi_0)cos Phi_0 + f(Phi)cos(Phi)+g(Phi_0)sin(Phi_0)+g(Phi)sin Phi]'
for the given tangental and Normal hydrodynamic loading functions f and g
Suppose that $Phi_0 = pi/2,s = 0.1, T_0 = 2, w = 1' and the loading functions f and g are given by
$f(Phi) = 0.002cosPhi and g(Phi) = 0.98sin^2 Phi + 0.02sin Phi'
Use Newtons method to find an approximation to 'Phi' starting with both initial approxiamtions close to 'pi/2' what accuracy for 'Phi' is suficient ? |
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