Fluid Mechanics Forces on Curved Surfaces

[teknodude]

Not really a homework problem, but I'm having a hard time with this section. It's mostly dealing with the horizontal component of the force.

This is from my book, Fluid Mechanics by frank m white 5 th ed,

"The horizontal component of force on a curved surafce equals the force on the plane area formed by the projection of the curved surafce onto a vertical plane normal to the component."

From the book and lecture, I come to the conclusion that I'm looking at the projected area from a top view or looking straight down from above? This idea has worked well with most of my homework problems until i saw this figure:

[img=http://img166.imageshack.us/img166/2269/fluidgs5.th.png]
For this one i thought the projected area was just a square that was 3m wide and 4m high. The way they did the solution shows that they projected the area to the right as if you are viewing the gate from the left.

 

[Cyrus]

it is looking down onto the 3/8 circle from above.

Edit: I looked too fast at the picture. What is this F_h?

 

[teknodude]

I'm still not seeing it...

If I look at it from above, I should see a rectangle that's (2 m + 1.414m) long and 3 m wide.

 

[Cyrus]

Ohhhhhhhhhhhhh, I see it now.

That is an F_h. God-dammit, I thought that was an F_b. :grumpy:
(Picture didnt scan very sharp, no biggie).

It is the force of the the water from the side. Look at the 3/8 from the side. They are giving you the forces. That's a very easy problem to solve.

 

[teknodude]

Why are we looking at it from the side? I'm just confused on how these projected areas should look like. I thought we always just look at it from the top view like a plan view, but in this case its the side?!


btw
The forces weren't given, just the figure on the top. I just cut and pasted part of the solutions from the manual.

 

[Cyrus]

Look at it from the top and the side.

There are two forces created by water. One in the x direction (from the side) and one in the y direction (from above).

 

[teknodude]

Look at it from the top and the side.

There are two forces created by water. One in the x direction (from the side) and one in the y direction (from above).

ok i get it now... i totally misinterpreted the books definition and example figure

Now i got to do the vertical forces which looks like it needs some integration.

Thanks for the help man

 

[Cyrus]

Yep, my friend actually had me point out this sameeeeeee exact thing to him in the library a few days ago.