Solving Plane Pressure Problem: Finding the Line of Action

[Phys5]

Homework Statement

I am trying to study for an exam and a section in the book on pressure on a plane is shown in the attached picture. I am trying to understand how equation15.16 was derived. I know normally the line of action is found using moments so this seems to be a short cut but I can'tunderstand how the book got to this equation. Any help would be muchappreciated. Thanks![/B]

Homework Equations

The Attempt at a Solution

 

[kuruman]

Equation 15.16 is illegible. Please post it with a better picture. Also post the relevant equations and your bet attempt at solving or understanding what is going on.

 

[Cutter Ketch]

I don't believe the issue is that they took some clever shortcut as it is that they plain just didn't say anything about how they got there. I am sure they just found the centroid as the that is pretty easy and I can't imagine there being anything shorter.

Write the pressure as a function of depth h and integrate

∫ h P(h) / ∫ P(h)

from h1 to h2.

 

[kuruman]

∫ h P(h) / ∫ P(h)

This is not an equation. An equation has two sides. Which side is this, what is the other side and what is the equation supoosed to represent?

 

[haruspex]

I am sure they just found the centroid

Or even just looked it up... Centroid of a trapezoid.