Short note: Design of lined canals

Design of a lined canal follows the principle of a rigid-boundary channel: the section need not be silt-regime, so Manning's formula is used with the limiting velocity of the lining.

Data needed

Discharge $Q$, available bed slope $S$, side slope $z$ (1:1 to 1.5:1 for concrete), roughness $n$ (0.014-0.016 for concrete) and limiting velocity (about 2.0-2.5 m/s for concrete; lower for brick and soil cement).

Procedure

1. Choose the economical (best hydraulic) section: $R = D/2$, $B = 2D(\sqrt{1+z^2} - z)$ and $A = D^2(2\sqrt{1+z^2} - z)$.
2. Insert into Manning's formula, $Q = \frac{1}{n}AR^{2/3}S^{1/2}$, and solve for $D$, then $B$.
3. Compute $V$. If $V \le V_{lim}$, the section is accepted.
4. If $V > V_{lim}$: fix $V = V_{lim}$, find $R = (Vn/\sqrt S)^{3/2}$, $A = Q/V$, $P = A/R$ and solve for $B$ and $D$ from $A = (B + zD)D$ and $P = B + 2D\sqrt{1+z^2}$ (a wider and shallower section results, using the permitted slope).
5. Provide freeboard (0.5-0.75 m for medium canals) and lining thickness (5-10 cm for concrete), expansion joints and drains behind the lining to relieve back pressure.
6. Check the economic justification of the lining (saving in seepage water, maintenance and land against the cost of lining).