### Open and Closed Water Systems: Applications and Design Equations

There are two main water systems types that are used for most engineering design and calculations: pressurized (or closed) pipes for water distribution and non-pressurized (or open) pipes for water collection.

Pressurized pipes are typically used for water supply, and they get their name from the fact that the pressure for any cross-section along the pipe, the pressure difference between the top and bottom of the pipe does not vary (except for the elevation head). In these types of systems, pressure is lost as water travels along the pipes due to friction. The pressure is typically supplied by a pump or simply by gravity itself, depending on the elevations of the start and end of the pipe.

In contrast, non-pressurized pipes are typically used for wastewater and they get their name from the fact that at least one pipe end is open to the atmosphere and therefore under atmospheric pressure. In these type of pipes, pressure changes both vertically across a cross section and horizontally (also due to friction) as the water travels along the pipes. Under non-pressurized conditions, water will flow from the highest to the lowest elevation as a function of the pipe size, slope, diameter and material.

Three common equations that are used for design of open and closed systems are: Hazen-Williams Equation, Mass Conservation or Continuity Equation and Manning’s Equation. The Hazen-Williams Equation is mostly applied in closed systems and it establishes a relationship between the volumetric flow rate against the head loss, pipe diameter, and the Hazen-Williams Coefficient, which varies depending on the pipe material. The equation gets the name after its developers, and it is commonly used for design of water supply, fire sprinklers and irrigation systems.

The Mass Conservation or Continuity Equation is a simple yet useful relationship that can be used both in open or closed systems. The formula is based on the fact that water is incompressible and the volumetric flow rate going through any point in time must be directly proportional to its velocity and the cross sectional area. Mass is always conserved in fluid systems regardless of their complexity and flow direction. What is also useful about this equation is that it can be used to compare the areas and velocities of two different pipes. When continuity exists, the mean velocities at all cross sections having equal areas are then equal, and if the areas are not equal, the velocities are inversely proportional to the areas of the respective cross sections. This is further shown in Figure 3 below.

Last but not least is the Manning’s Equation, which is the most popular for open water systems. It is used to calculate the velocity of a fluid flowing through a partially full pipe. Once the velocity is known, the flow can be calculated using the Continuity Equation. The equation is based on the fact that the flow through an open conduit is directly proportional to the flow area and slope (or energy loss), but indirectly proportional to the Manning’s coefficient and the wetted perimeter. The Manning’s coefficient is based on the pipe material roughness and is dimensionless

There are plenty of online resources out there that can further complement your reading when understanding how these equations are applied.  You may also reach out to me via LinkedIn to learn more or simply get in touch!

By: Salvador Bentolila, PE, ENV SP
Disclaimer: I do not hold any relationships or affiliations with the companies listed above other than my own LinkedIn profile.

Salvador Bentolila, PE, ENV SP is a Civil Engineer, specialized in Water Resources. He currently works as a Water/Wastewater engineer at AECOM and has experience with design and development of water supply, irrigation and wastewater systems.

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