Respuesta :
Answer:
The hydro-static force against one side of the plate is 617400 N
Step-by-step explanation:
Here we have the depth given by
Depth of immersion = Height of triangle
Height, h of equilateral triangle of side L is given by;
[tex]h = \sqrt{L^2 -(\frac{L}{2})^2 }[/tex]
Therefore height h = [tex]\sqrt{6^2 -(\frac{6}{2})^2 } = 3\cdot\sqrt{3}[/tex]
If we take the width of a small section w(x) at a location of x m belo the surface, we have by similar triangles
[tex]\frac{w(x)}{6} = \frac{3\cdot\sqrt{3}-x }{3\cdot\sqrt{3}}[/tex]
Therefore, w(x) = [tex]6 -\frac{2\cdot x}{3\cdot \sqrt{3} }[/tex]
The
[tex]F = 1000 \times 9.8\times \int\limits^{3\cdot\sqrt{3}} _0 {x}[6-\frac{2x}{3\cdot \sqrt{3} } ] \, dx[/tex]
[tex]F = 1000 \times 9.8\times [3\cdot x^{2} -\frac{x^{2} }{3\cdot\sqrt{3} } ]^{3\cdot \sqrt{3}}_0[/tex] = 63×9800 = 617400 N
