(b)

S_o, S_c, 0, +∞, -∞

S_o is the bottom slope.

S_c is the critical slope, equivalent to the f friction coefficient.

0 means that the gradually varied flow is asymptotic to the uniform flow.

+∞ and -∞ come from the hydraulic jump (rapidly varied flow).

(c)

In steady gradually varied flow, depth and velocity vary with distance along the channel.

In uniform flow, depth and velocity DO NOT vary with distance along the channel.

Application of steady gradually varied flow: The calculation of water-surface profiles, as in flow into a dam.

Application of uniform flow: The calculation of flow depth in a prismatic channel, for which we use the Manning equation.

(d)

In steady gradually varied flow, depth and velocity vary GRADUALLY with distance along the channel.

In steady rapidly varied flow, depth and velocity vary RAPIDLY with distance along the channel.

Application of steady gradually varied flow: The calculation of water-surface profiles, as in flow into a dam.

Application of steady rapidly varied flow: The calculation of flow over a spillway, for which we use the standard WES profiles.

(e)

In steady gradually varied flow, depth and velocity vary gradually with distance along the channel. DISCHARGE remains constant along the channel.

In unsteady flow, depth, velocity, AND DISCHARGE vary with distance along the channel.

Application of steady gradually varied flow: The calculation of water-surface profiles, as in flow into a dam.

Application of unsteady flow: Flood routing.

(f)

1. i. Direct-step method is DIRECT.

   ii. Standard-step method is ITERATIVE.

2. i. Direct-step method assumes flow depth and calculates distance.

   ii. Standard-step method assumes distance and calculates flow depth.

3. i. Direct-step method is restricted to prismatic (usually artificial) channels.

   ii. Standard-step method is used for natural channels (or any channel).

4. i. Direct-step method is EASY.

   ii. Standard-step method is DIFFICULT.

5. i. Answer in the direct-step method is always possible.

   ii. Answer in the standard-step method is not always possible.

(g)

3.0

(h)

• When a channel is dredged partially without a change in discharge, there is a small lowering of the water surface for some distance upstream of the dredge location (in subcritical flow).

• When a channel is dredged throughout its length without a change in discharge, there is a lowering of the water surface throughout. The lowering is approximately equal to the dredged depth.

• Dredging can increase the discharge (change the hydrology), particularly where the prevailing discharge is controlled by both surface and subsurface runoff. Dredging lowers the base level and increases the quantity of subsurface runoff (baseflow) into the channel, therefore, the total discharge.