Understanding Forces on Submerged Surfaces

[werson tan]

Homework Statement

i don't understand the statement 1 and 2 , can someone help to explain ?

for 1 , does the author mean Fh= Fv ??

for 2 , does the author mean Fv = Fh + W ? but in statement 1 , Fh already = Fv

Homework Equations

The Attempt at a Solution

 

[haruspex]

I struggle to read the subscripts in the attachment, they're a bit fuzzy, so I could be wrong, but here's what I think it says.
First the "horizontal projection" of the curved surface here means an imaginary horizontal surface found by projecting the curved surface down onto a horizontal plane passing through the lower edge of the curved surface. The force F_V is the normal force that acts on that surface (so it is the pressure at that depth multiplied by the area of the horizontal surface).
Similarly, F_H is the force acting on an imaginary vertical surface, as shown. (The pressure in that case varies with depth. F_H is the integral of that pressure.)
The force acting on the curved surface is F, and this has horizontal and vertical conponents F_x and F_y respectively.
The text shows:
F_H=F_x
F_V=F_y+W
Which seems perfectly reasonable.

 

[256bits]

Homework Statement

i don't understand the statement 1 and 2 , can someone help to explain ?

for 1 , does the author mean Fh= Fv ??

for 2 , does the author mean Fv = Fh + W ? but in statement 1 , Fh already = Fv

Hi, werson tan.
For 1, No he does not mean that Fh=Fv.

It is confusing by what the author means by "vertical projection of the curved surface."
The author himself does not explain it very well , so I do attribute some of fault of understanding to his in not referencing what he does actually means with the terms a vertical projection and horizontal projection.
( He is using the orientation of the plane for describing the projection rather than the direction of projecting the surface onto a plane. If he would have said "a projection onto a vertical plane" or "a projection onto a horizontal plane" it might have been more clear. )

If you take a look at Fig. 3-33, the vertical line where Fx is acting is the "vertical projection of the curved surface."
For the author, a vertical projection to him is,
- looking at the curved surface in the horizontal direction, the curved surface can be projected onto a vertical plane. This is where Fx acts.
Similarly, for the author, a horizontal projection is,
- looking at the curved surface in the vertical direction, the curved surface can be projected onto a horizontal plane. This is where Fy acts.

Hope that helps.

For some reason the connection terminated to PF around 0300hrs before I could post, so haruspex beat me in answereing.