# 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

$$\large{ A_c = \frac{ Q }{ k \; i } }$$

$$\large{ A_c = r_h \; P_w }$$

$$\large{ A_c = z \; h^2 }$$

$$\large{ A_c = h_m \; T }$$

$$\large{ A_c = \frac{ Q }{ v } }$$

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

$$\large{ A_c = \frac{ r^2 \;\left( \theta \;-\; sin \; \theta \right) }{ 2 } }$$

$$\large{ A_c = \pi \; r^2 - \frac{ r^2 \left( \theta \;-\; sin \; \theta \right) }{ 2 } }$$

$$\large{ A_c = \frac{ v_s \; A_v}{ v} }$$

Symbol English Metric
$$\large{ A_c }$$ = area cross-section $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ A_v }$$ = area cross-section of voids $$\large{ft^2}$$ $$\large{m^2}$$
$$\large{ \theta }$$   (Greek symbol theta) = degree $$\large{deg}$$

$$\large{rad}$$

$$\large{ Q }$$ = flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$
$$\large{ h }$$ = fluid depth $$\large{ft}$$ $$\large{m}$$
$$\large{ w }$$ = fluid top width $$\large{ft}$$ $$\large{m}$$
$$\large{ k }$$ = hydraulic conductivity $$\large{\frac{ft}{day}}$$ $$\large{\frac{m}{day}}$$
$$\large{ d_h }$$ = hydraulic depth $$\large{ft}$$ $$\large{m}$$
$$\large{ i }$$ = hydraulic gradient $$\large{dimensionless}$$
$$\large{ r_h }$$ = hydraulic radius $$\large{ft}$$ $$\large{m}$$
$$\large{ h_m }$$ = mean depth $$\large{ft}$$ $$\large{m}$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ft}$$ $$\large{m}$$
$$\large{ v_s }$$ = seepage velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ v }$$ = 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 $$\large{ft}$$ $$\large{m}$$