Understanding Gradually Varied Flow | Civil Engineering Optional Notes for UPSC PDF Download

Gradually varied flow refers to the flow of water in open channels where the depth of the water changes gradually over the length of the channel. This type of flow occurs when there is a gradual change in the slope of the channel bed or when the channel geometry varies gradually. Gradually varied flow is an important concept in hydraulic engineering and is commonly encountered in natural streams, rivers, and engineered channels. 

There are two main types of gradually varied flow: 

• Mild slope or mild gradient flow: In this type of flow, the channel slope is relatively gentle, and the change in water depth is gradual over a long distance. Mild slope flow typically occurs in natural rivers and streams where the channel bed has a relatively uniform slope. 
• Steep slope or steep gradient flow: In steep slope flow, the channel slope is steep, leading to more rapid changes in water depth over a shorter distance. Steep slope flow is often encountered in steep mountain streams or in engineered channels with high gradients. 

Question: Gradually varied flow is
(a) steady uniform
(b) non-steady non-uniform
(c) non-steady uniform
(d) steady non-uniform
Ans: (d)
Gradually varied flow is steady non-uniform because the velocity of water remains constant at a specified point, but it changes from one point to another point.
The terms steady and uniform are used frequently in engineering, and thus it is important to have a clear understanding of their meanings.

• The term steady implies no change with time. The opposite of steady is unsteady, or transient.
• The term uniform, however, implies no change with location over a specified region.

Any devices such as turbines, compressors, boilers, condensers, and heat exchangers operate for long periods of time under the same conditions, and they are classified as steady-flow devices. During steady flow, the fluid properties can change from point to point within a device, but at any fixed point, they remain constant.

Note:

In the case of a nozzle, the velocity of water remains constant at a specified point, but it changes from the inlet to the exit (water accelerates along with the nozzle which represents the case of steady and non-uniform flow).
Above figure shows gradually varied flow in a nozzle. You may be tempted to think that acceleration is zero in steady flow since acceleration is the rate of change of velocity with time, and in a steady flow, there is no change with time. Well, a garden hose nozzle will tell us that this understanding is not correct. Even in a steady flow and thus constant mass flow rate, water will accelerate through the nozzle. Steady simply means no change with time at a specified location, but the value of a quantity may change from one location to another.