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Unformatted text preview: π 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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