# 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

 $$\large{ A_c = \frac{ Q }{ k \; i } }$$ $$\large{ A_c = r_h \; P_w }$$ $$\large{ A_c = z \; h^2 }$$ $$\large{ A_c = h_m \; T }$$ $$\large{ A_c = \frac{ Q }{ v } }$$

### Where:

 Units English Metric $$\large{ A_c }$$ = area cross-section $$\large{ft^2}$$ $$\large{m^2}$$ $$\large{ Q }$$ = flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$ $$\large{ h }$$ = fluid depth $$\large{ft}$$ $$\large{m}$$ $$\large{ k }$$ = hydraulic conductivity $$\large{\frac{ft}{day}}$$ $$\large{\frac{m}{day}}$$ $$\large{ i }$$ = hydraulic gradient $$\large{dimensionless}$$ $$\large{ r_h }$$ = hydraulic radius $$\large{ft}$$ $$\large{m}$$ $$\large{ h_m }$$ = mean depth $$\large{ft}$$ $$\large{m}$$ $$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ P_w }$$ = wetted perimeter $$\large{ft}$$ $$\large{m}$$ $$\large{ z }$$ = width of channel slope $$\large{ft}$$ $$\large{m}$$ $$\large{ T }$$ = width of water surface top $$\large{ft}$$ $$\large{m}$$

## Related Area Cross-section formulas

 $$\large{ A_c = d_h \; w }$$ (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

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

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

$$\large{ r }$$ = radius

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

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

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

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