8/19/2019 CE 321BXL Hydrostatic Forces on Curved Surfaces Report

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Hydrostatic Forces on Curved Surfaces

INTRODUCTION

 The principle of the resultant hydrostatic

force on curved surfaces is somewh

at the same of the resultant hydrostatic forceon plane surfaces The !oal of the en!ineer

is to model the force due to pressure with an

e"uivalent force vector actin! throu!h the

center of pressure

One approach is to inte!rate the pressure

force alon! the curved surface and #nd the

e"uivalent force The same thin! on how the

previous reporters delivered on the topic ofHydrostatic Forces on $lane Surfaces

%&"uations from $lane Surfaces'

Since we already (now how to !et the

resultant hydrostatic force) the vertical

location of line of action and the lateral

location of line of action) we can apply it on

how to !et the resultant hydrostatic force

considerin! curved surfaces with the

indicated pressure distri*ution

%Fi!ure +,-'

It is much easier to sum forces for a free

*ody de#ned in the #!ure

%Drawin! of "uarter of a circle'

So this free *ody dia!ram shows how the

force actin! on the curved surface relates to

the force F actin! on the free *ody

.e ta(e into account to *rea( the resultant

force F into components

%Drawin! of "uarter of a circle with the forces

already'

So from this picture) there are + o*vious

forces which are/

, .ei!ht of the 0uid- Hydrostatic forces that acts on the

side and top surfaces which are the

vertical and hori1ontal components+ Resultant force that we are solvin! for

Summin! of the forces in the hori1ontal

direction !ives us2 %write on *oard'

 F  X = F 

 AC 

 The line of action for the force F 

 AC   is

throu!h the center of pressure for side 3C

desi!nated asY cp  %which was also

discussed from the previous report'

Summin! the forces in the vertical

direction !ives us2 %write on *oard'

 F  y=W + F CB

where / . 4 wei!ht of the 0uid in the

free *ody that acts throu!h the center of

!ravity of the free *ody and F CB  is the

force on side C5 and acts throu!h the

centroid of surface C5

 The line of action for the vertical force

may *e found *y summin! the moments

a*out any convenient a6is

%$icture of resultant force with 7cp and

8cp'

From the picture shown) the resultant

force that acts on the curved surface can

*e determined usin! the vertical location

and lateral location of line of action Usin!

tri!onometry) we are a*le to arrive with

resultant force