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Unformatted text preview: MTHSC 360 - Numerical Integration March 10, 2008 The Potential Energy behind a Dam Assume that we have a small dam and that we are interested in the amount of energy stored in the water behind the dam. Call the part of the dam that contacts the water the face of the dam. For our dam the face is a fairly flat parabola, y d = ( x/ 4) 2 . It is computed with the MATLAB function, damface(x) . As the height of the water behind the dam increases the shoreline extends further and further out. We will assume that the shoreline is also given by a parabola which depends on h , the height of the water, y h = (10 + h ) 2- x 2 . These parabolas are computed with the MATLAB function, shoreline(x,h) . Figure 1 shows the levels of the water behind the dam for different values of h . ! 20 ! 10 10 20 50 100 150 200 250 300 350 400 450 To) +ie. ! /hore¡ines ¢i6en Hei¢ht Wi:th in meters <en¢th in meters h = 0 h = 2 h = 4 h = £ h = 8 h = 10 100 200 300 400 1 2 3 4 5 £ @ 8 A 10 11 /i:e +ie. ! /ection at D=0...
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- Spring '08