14.3.2. Pressure Conditions

In open channel flow, the pressure at the free surface is equal to atmospheric pressure. This is because the flow is open to the atmosphere.

Open channel flow refers to any flow where the liquid is within a channel that is not completely enclosed. In such cases, the pressure at the top of the fluid is the same as the atmospheric pressure. This means that if you were to measure the fluid pressure just below the surface, it would be equal to the atmospheric pressure at that location. Thus, the only forces affecting the flow are gravity and friction against the channel's boundaries.

Imagine standing by a river. The water flows freely, and if you looked at the surface, it is open to the air. The pressure you would feel at the water's surface is equal to the air pressure around you. This is different from a water pipe, where pressure can build up due to being enclosed.

In open channel flow, since the pressure is atmospheric, we mainly consider two forces: gravity force and friction force. Pressure force is negligible.

In open channel flow, because the pressure at the free surface equates to atmospheric pressure, there is no additional pressure pushing down on the fluid. Therefore, the forces acting on the water in the channel primarily consist of the downward force due to gravity and the opposing force due to friction along the channel bed and sides. This significant distinction contrasts with pressure flow in pipes, where internal pressure can contribute to the flow dynamics.

Think of a slide at a playground. As you slide down, gravity pulls you downwards, but the roughness of the slide's surface can slow you down (the friction). In river flow, gravity pulls the water downstream, while the riverbed's roughness affects how quickly the water flows.

The friction force in open channel flow depends on the roughness of the channel's bed and sides, similar to how pipe flow is influenced by wall roughness.

Just as in pipes where the inner surface texture affects how water moves, the roughness of the channel's bottom and sides affects water flow in open channels. This 'roughness' introduces resistance, which slows down the flow of water. The greater the roughness, the more friction force you encounter, resulting in slower and less uniform flow.

Consider walking through a thick carpet versus a smooth floor. On the carpet (acting like a rough channel), you find it harder to walk quickly due to increasing friction, while on the smooth floor, you can glide easily. Similarly, water flows faster in smooth channels compared to those that are rough.

The velocity distribution in open channel flow is influenced by the no-slip condition, where the velocity at the boundary of the channel is zero.

The no-slip condition states that the velocity of the fluid at the point where it contacts the channel surfaces is zero, meaning there is no movement at that point. As you move away from the channel boundary into the center, the velocity increases due to the influence of gravity pulling the fluid downward. The result is a gradient in fluid speed, with slower speeds near the edges and faster speeds toward the center of the channel.

Imagine a crowd of people moving down a hallway. If some people are standing still along the walls (mimicking the no-slip condition), those in the middle of the hallway can move much faster. This leads to a higher speed in the center while the edges move slower.

Open channel flows can be categorized into three types: sub-critical, critical, and super-critical flow, based on the flow's velocity and the influence of gravity on the water's motion.

These classifications define how fluid behaves under certain conditions. Sub-critical flow occurs when the flow velocity is less than the wave speed, leading to slow and tranquil water movement. Critical flow happens at a specific velocity that creates minimal energy loss. Super-critical flow occurs when the flow velocity exceeds wave speed, resulting in rapid and sometimes chaotic water movement.

Think of flowing water going down a hill. If it meanders slowly (sub-critical), you can see the gentle flow and motion. At just the right slope (critical), the water moves beautifully — not too fast, not too slow. If the slope becomes steep (super-critical), the water rushes down, making splashes and creating turbulence!

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