Balancing Canal depth

Balancing Canal depth:

Balancing canal depth comes when the canal is in partially embankment and partially in cutting.It is the depth of the canal(H) which gives equal amount of filling(i.e earth required for formation of Banks) and cutting(i.e earth from digging). For a given cross-section of a canal, it has only one balancing depth. For this depth the canal sectional will be economical.
B= Bed width.

b1,b2= width of embankment of left and right side respectively.

d= excavation depth.

h= embankment height.
H=height of embankment from the bed of the canal.

    X- sectional area in cutting =Bd+sd²

     ^{X- sectional area in embankment =} (b1+b2)h+2s1 h²

^{For balancing depth,}

^{Area in cutting= Area in embankment.}

^or,  Bd+sd^{2  =} (b1+b2)h+2s1 h²

or, Bd+sd^2=(b1+b2)(H-d)+2s1(H-d)^2.

From this equation 'd' can be calculated.