# water flow through canals

## empirical formulae used to calculate pressure drops caused by friction

Only the following formula are routinely being used to calculate pressure drops caused by friction; the Manning-Strickler formula tends to be widespread because of its simplicity and because it generally applies to all uniform forms of flow in canals or rivers.

#### Manning‑Strickler formula

I = canal gradient, metre by metre:

γ and KS = wall unevenness constants.

The wetted perimeter is the total contact length between the fluid and the canal walls along a given section.

The nature and consistency of the walls can restrict the maximum permissible velocity in the vicinity of these walls.

The critical regime is reached in a rectangular section canal that has a width L and a water depth Hc such that Q2 = gL2H3c for a flow rate Q, that is, a critical velocity :

At higher velocities, we have a torrential flow: this flow obeys complex laws and must be covered by special studies (mathematical models, mock-ups …). Within this limit, the flow is said to be fluvial with H > Hc and V < Vc. In water treatment structures, flow will most frequently be of the fluvial type; the two earlier inequalities will, therefore, have to be verified.

In uniform fluvial flow modes, wetted section and velocity will be constant in successive profiles, the gradient precisely compensating for pressure drops caused by friction.

The Bazin or Manning-Strickler formula linking velocity, the hydraulic radius and the gradient, is used to calculate one of these values if the other two are known, i.e. three of the following four parameters: flow rate, wetted section, wetted perimeter and gradient.

Starting from the normal equilibrium defined in this manner, local level rises or surges caused by flow being brought up to speed or by tailrace generated by irregularities, have to be calculated.

In water treatment structures where straight lengths tend to be short, level variations through irregularities have a high relative significance.

## using the universal calculation chart

This calculation chart (figure 39) providing the pressure drop coefficient l caused by friction, also applies to canals that have walls of irregular unevenness. In concrete canals, the unevenness coefficient k will be between 0.5 mm (smooth render) and 2 mm (unsurfaced exposed concrete under average conditions) on average. The calculation method is the same as the one for pipelines (water head losses through friction in the pipelines) using the hydraulic diameter :

Sm being the section of the canal occupied by water and Pm the wetted perimeter, expressed in m² and m respectively.

## calculating minor losses

Calculations are carried out in the same way as for pipes (minor losses in the pipelines, fittings, valves… for water), starting downstream and for the uniform fluvial flow velocity obtained. Local upstream upsurges reveal pressure drops in conduit irregularities.

## pressure drop through a screen

• values for K3 (section of gap between bars)( table 69).

## dragging velocity for some materials

• 1 m water depth, straight canals
• Corrections for other water depths