Area Cross-section
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
