Fluid Dynamics: Free Surface and Pressure Flow Principles

Free Surface Flows

Free surface flows occur when a liquid circulates without filling the tube that carries it, or when water is driven by a canal. In these cases, the liquid is at atmospheric pressure. We say that the pipe is working as a channel flow. This is also referred to as sewer flow, flow without pressure, gravity flow, or free flow.

Surface Current Force and Pressure Flow

When the liquid completely fills a conduit of circular cross-section and exerts pressure on the walls of the pipe, it is said to be working as a conduit under pressure. This is known as pipe flow by pressure or forced flow. In this case, the movement of the fluid is due to the pressure present inside the duct.

Fluid Flow Regimes

Laminar Flow

In laminar flow, each element of the fluid moves in the same direction and at the same rate as all other elements, creating power lines. The trajectories of two particles are always parallel to each other and parallel to the fluid velocity.

Turbulent Flow

In a turbulent flow, not all elements move in the same direction and with the same speed. There is movement across the streamlines, which creates erratic circles known as eddies or secondary currents. These currents generate more internal friction than laminar flow.

Types of Open Channels

An open channel is a conduit in which water flows with a free surface. According to its origin, a channel can be natural or artificial:

• Natural Channels: These include all types of water currents that occur naturally on Earth, varying in size from small creeks to large rivers, estuaries, and tidal flows. Underground currents carrying water with a free surface are also considered natural open channels.
• Artificial Channels: These correspond to works made of different materials and sizes, manufactured by humans for specific purposes. Examples include navigation channels, canals for hydropower plants, irrigation canals, drainage ditches along roads, landfills, and overflow channels.

The hydraulic properties of these channels can be controlled to a desired level or designed to meet specific requirements. Sewer pipes are also considered channels since they have a free surface.

Flow Rate and Velocity Relationships

Flow (Q)

Flow (Q) is the ratio between the volume of liquid (V) passing through a section (S) and the time (t) used to pass.

Relationship Between Speed and Section

The relationship between speed and section shows that the smaller the section of the canal, the greater the velocity of the fluid, assuming the same flow through both sections.

If both flows are the same: S₁ * v₁ = S₂ * v₂

The height h can be calculated if we accept that it is the same height reached by a body thrown upward with velocity v: h = v² / 2g