Answer:



In this problem, we need to calculate the force of water acting on one side of a triangular area. The sides of the triangle measure 2 m, 3 m, and 3 m, respectively. The 2-m side is horizontal and 10 m below the surface. We need to calculate the force of water on the side of the triangle if it is vertical and horizontal.



The force of water on a surface is given by the formula:

F = γ × A × h

where

F = force of water on the surface
γ = specific weight of water
A = area of the surface
h = depth of the center of gravity of the surface below the water surface

The specific weight of water is 9810 N/m³.





To calculate the force of water on the vertical side of the triangle, we need to find the area and depth of the center of gravity of the triangle.

The area of the triangle can be calculated using Heron's formula:

s = (2 + 3 + 3)/2 = 4

A = √(s(s-2)(s-3)(s-3)) = 2.9047 m²

The depth of the center of gravity of the triangle can be calculated as follows:

h = 10 + (2/3)(3) = 12 m

Now we can calculate the force of water on the vertical side of the triangle:

F = γ × A × h = 9810 × 2.9047 × 12 = 339,991.4 N

Therefore, the force of water on the vertical side of the triangle is 339,991.4 N.



To calculate the force of water on the horizontal side of the triangle, we need to find the area and depth of the center of gravity of the triangle.

The area of the triangle can be calculated using the formula for the area of a triangle:

A = (1/2)bh = (1/2)(2)(3) = 3 m²

The depth of the center of gravity of the triangle can be calculated as follows:

h = 10 + (2/3)(2) = 11.3333 m

Now we can calculate the force of water on the horizontal side of the triangle:

F = γ × A × h = 9810 × 3 × 11.3333 = 333,996.9 N

Therefore, the force of water on the horizontal side of the triangle is 333,996.9 N.



In this problem, we calculated the force of water on one side of a triangular area. The sides of the triangle measured 2 m, 3 m, and 3 m, respectively, and the 2-m side was horizontal and 10 m below the surface. We calculated the force of water on the side of the triangle if it was vertical and horizontal. The force of water on the vertical side of the triangle was 339,991.4 N, and the force of water on the horizontal side of the triangle was 333,996.9 N.