# Area Cross-section

Written by Jerry Ratzlaff on . Posted in Solid Geometry  Area cross-section, abbreviated as $$A_c$$, is a two-dimension plane slice of a three-dimension plane.

## Area Cross-section formulas

 FORMULA: SOLVE FOR: $$\large{ A_c = \frac{ Q }{ k \; i } }$$ $$\large{ A_c = r_h \; P_w }$$ $$\large{ A_c = z \; h^2 }$$ $$\large{ A_c = h_m \; T }$$ $$\large{ A_c = d_h \; w }$$ (Hydraulic Depth) $$\large{ A_c = \frac { r^2 \;\left( \theta \;-\; sin \; \theta \right) } { 2 } }$$ (Hydraulic Radius of a Partially Full Pipe (Less than Half Full)) $$\large{ A_c = \pi \; r^2 - \frac { r^2 \left( \theta \;-\; sin \; \theta \right) } { 2 } }$$ (Hydraulic Radius of a Partially Full Pipe (More than Half Full)) $$\large{ A_c = \frac { v_s \; A_v} { v} }$$ (Seepage Velocity) $$\large{ A_v = \frac { v \; A_c} { v_s} }$$ (Seepage Velocity)

### Where:

$$\large{ A_c }$$ = area cross-section

$$\large{ A_v }$$ = area cross-section of voids

$$\large{ \theta }$$   (Greek symbol theta) = degree

$$\large{ h }$$ = depth of fluid

$$\large{ Q }$$ = flow rate

$$\large{ w }$$ = fluid top width

$$\large{ k }$$ = hydraulic conductivity

$$\large{ d_h }$$ = hydraulic depth

$$\large{ i }$$ = hydraulic gradient

$$\large{ r_h }$$ = hydraulic radius

$$\large{ h_m }$$ = mean depth

$$\large{ p }$$ = pressure

$$\large{ r }$$ = radius

$$\large{ v_s }$$ = seepage velocity

$$\large{ T }$$ = top of water surface width

$$\large{ v }$$ = darcy velocity or flux

$$\large{ P_w }$$ = wetted perimeter

$$\large{ z }$$ = width of channel slope