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Unformatted text preview: d 2 /4 = 50.265 in 2 i 1 2 3 4 5 6 7 8 9 10 11 12 x i (in) 1 2 2.5 4 5 7 8 11 12 13 14 15 p(x i ) psi 110 130 140 170 185 210 215 185 135 100 90 70 40 Numerical Integration A look at the given data reveals uneven intervals of x Use Trapezoidal rule Integral = {0.5*(x i+1 x i )*[ p(x i ) + p(x i+1 )]} where the summation is from i = 0 to 11 Final Solution Using the above formula, the numerical solution of the integral of p(x) with respect to x for x varying from 0 to 15 inches yields an answer of 2248.75 lb per in. Multiplying by the area of the piston gives the work over the stroke as 113033.4 lb in Thus the work done over the stroke is 9419 lb ft (around 12800 J) The End...
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 Fall '08
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