Gradually Varied Flow

Gradually Varied Flow

Objectives: To be able to classify different types of water surface profiles

Classification of water surface profiles

The equation for non-uniform flow is as follows:

[pic] (1)

It can be seen from equation (1) that the gradient of the free surface dD/dl may be positive or negative, depending on the signs of the numerator and denominator, which in turn will depend on the relative values of the actual depth D, the critical depth Dc, and the normal depth Dn. Whether the normal depth is above or below the critical depth will depend on the classification of the bed slope. Surface profiles are classified by a letter and a number. The letter refers to the bed slope, which may be one of the following categories:

M Mild slope Dn > Dc;

C Critical slope Dn = Dc;

S Steep slope Dn < Dc;

H Horizontal s = 0

A Adverse bed slope s is negative. (Note positive is ‘downhill’.)

The number refers to the relation between the actual depth of flow D, the normal depth Dn and the critical depth Dc as follows:

1. free surface of stream lies above both normal and critical depth lines;

2. free surface of stream lies between normal and critical depth lines;

3. free surface of stream lies below both normal and critical depth lines.

Although there are five categories of slope and three categories of depth only 12 combinations are possible. For horizontal and adverse slopes, uniform flow is impossible, thus eliminating the H1 and A1 curves; while for critical slope, critical depth and normal depth coincide, the eliminating the C2 curve. The water profiles corresponding to the various categories are shown in Fig. 1 with an indication of how they may occur. Note that the vertical scale has been exaggerated and that even a steep slope, in this context, would amount to only a few degrees inclination to the horizontal. Water surface curves in which...