Area Cross-section

Written by Jerry Ratzlaff on . Posted in Solid Geometry

area cross section cube 1area cross section pipe 1Area 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 SI
\(\large{ A_c }\) = 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

 

Tags: Equations for Area Equations for Surveying