How can I find the distance and centroid of a hatch in fluid mechanics?

[Jason03]

Im working on the problem below...

http://img90.imageshack.us/img90/4939/dfadfgs5.jpg

Im having trouble finding the distance I have labled in the problem...H_c...which is the distance from the fluid surface to the center of the hatch...It appears to be found just using geometry but I am not getting it...

I found the area of the hatch to be .160 m...by adding the areas of the rectangle and two semi circles...and I have the specific weight found by multiplying (.90 x 9.81 Kn/m^3) = 8.83 Kn/m^3...

so the resultant force formula is

F_r = specific weight x area x H_c...

and the correct answer for the resultant force is 1213 N...but I can't get H_c...

Also later in the problem I have to find the centroid of the hatch...so how would I go about doing that...would I take the centroid for each shape and average them?

 

[nvn]

Jason03: Study some trigonometry. I.e., memorize the definition of sine, cosine, and tangent for a right triangle. Remember those? You must learn those.

The length of the slanted side would be (0.6 m)/cos(40 deg), right? See if you can figure out how to find H_c and F_r now.

 

[Jason03]

yea actually i figured it out shortly after i posted...but i did it slightly differently..

Cos40 = y/.450

Y= .450cos40

Y= .344 m

So ….(.6 +.6) - .344 = .855

h_c = .855 m


and the centroids were easily enough found by just adding the sum of the composites of a circle and square...

Thanks!

 

[nvn]

Nice work. That is a good approach you used.