Hydrostatics - submerged lamina

[cd19]

Homework Statement

Calculate the depth below the water surface of the centre of pressure of the water pressure acting on the submerged triangular lamina, height 3m, base 2m and located at a depth of 1m below the surface.

Homework Equations

not entirely sure

The Attempt at a Solution

I found the centroid location at 2.5m from the surface, c= (2)(3)^³/36.. now i have no clue what to do. any tips?, I now that the center of pressure must be below this point

 

[tjkubo]

Some vital information is missing from the problem statement.

 

[nlightner]

, but I am not sure how to calculate the exact depth.

I would approach this problem by first understanding the concept of hydrostatics. This branch of fluid mechanics deals with the behavior of fluids at rest. In this case, we are dealing with a submerged lamina, which is a flat object submerged in a fluid (in this case, water).

To calculate the depth of the center of pressure, we need to first understand what it is. The center of pressure is the point where the total force of the water acting on the lamina is considered to be acting. This point is located at a certain depth below the surface of the water.

To calculate the depth of the center of pressure, we can use the equation: D = I/c, where D is the depth of the center of pressure, I is the moment of inertia of the lamina, and c is the distance from the surface to the centroid of the lamina.

You have correctly calculated the centroid of the lamina at 2.5m from the surface. To calculate the moment of inertia, we need to use the equation: I = (1/12)bh^3, where b is the base of the lamina and h is the height.

Substituting the values given in the problem, we get: I = (1/12)(2)(3)^3 = 4.5m^4. Now, we can plug in these values in the equation D = I/c to get the depth of the center of pressure. This will give us: D = (4.5m^4)/(2.5m) = 1.8m.

Therefore, the center of pressure is located at a depth of 1.8m below the surface of the water. This means that the total force of the water acting on the lamina is considered to be acting at this point. I hope this helps in solving the problem.