Force on Curved areas

Not Reviewed
Equation / Last modified by mike on 2015/07/29 07:18
`f = `
Force on Curved areas
Variable Instructions Datatype
Radius of Hemisphere Enter radius of hemisphere Decimal
Density of Water Enter density of water Decimal
Type
Equation
Category
vCommons
Contents
2 variables
Rating
ID
DavidC.Force on Curved areas
UUID
b3d86153-4469-11e3-a47b-bc764e049c3d

A Hemispherical bowl, radius `r`, just full of water,  will exert a total force down equal to the sum of all forces acting on the surface.

Total force down = area x pressure intensity at centroid

     =`2pir^2 *"density of water"*"depth of centroid"*g`

     = `2pir^2*rho*(r/2)g`

     =`pir^3rhog`

 

But the forces acting around the hemispherical centroid balance out on opposite sides of the vertical axis and:

Resultant Force Down = volume of hemisphere * density of water * `g`

                                           = `2/3pir^3rhog`