A triangular plate with height 3 ft and a base of 5 ft is submerged vertically in water so that the top is 1 ft below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Give your answer correct to the nearest whole number.)

49KN

Explanation:

F = \int_0^5 \rho g xw dx =

\frac{3}{5}\rho g \int_0^5 x^2 dx =

\frac{3}{5}\rho g \frac{x^3}{3} \Big|_0^5 =

 \frac{1}{5}\rho g (25 - 0) =

5\rho g \approx

49 kN

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