# Forces on submerged surface

## Homework Statement

i dont 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

## The Attempt at a Solution

#### Attachments

• IMG_20160225_173918.jpg
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haruspex
Homework Helper
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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 FV 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, FH is the force acting on an imaginary vertical surface, as shown. (The pressure in that case varies with depth. FH is the integral of that pressure.)
The force acting on the curved surface is F, and this has horizontal and vertical conponents Fx and Fy respectively.
The text shows:
FH=Fx
FV=Fy+W
Which seems perfectly reasonable.

• werson tan
256bits
Gold Member

## Homework Statement

i dont 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.

• werson tan