# Laminar Water Flow Explained: An Easy Guide to Understand

### Key Takeaways

• Water exhibits laminar flow conditions at a low Reynolds number.

• Constant velocity and pressure differences are desired to maintain a laminar water flow velocity profile.

• CFD simulation can help systems designers characterize laminar flow regimes to ensure all requirements are met during system design.

Analyzing the flow regime is an important part of hydrodynamical analysis and design. In nature, water mostly exhibits turbulent flow, which is also reflected in most industrial applications. However, laminar flow behaviors can also be observed in the form of water flow in pipes or ducts or airflow over airfoils. Laminar water flow explained with computational fluid dynamics (CFD) models provide engineers with a clear analysis of the flow problems encountered during the development of an engineering solution for water flow in such pipes, ducts, or distribution systems.

The analysis of fluid friction and boundary conditions applied to laminar flow conditions in a CFD model through appropriate simulation and numerical analysis can help system designers achieve an ideal laminar flow for water in a fluid system.

## Laminar Water Flow Explained: Reynolds Number and Flow Law

If you visualize the flow of blood in the veins or water coming out of the nozzle at a low velocity, you may realize that these fluids appear to flow in an almost static manner. This is laminar flow. A flow is considered to exhibit laminar or streamlined behavior when the fluid particles travel in a smooth, parallel path without any intermixing or disruption between the adjacent layers. Laminar flow is mostly observed in viscous or low-velocity fluids. At any given point, the velocity, pressure, and other flow attributes in a laminar flow remain constant.

In a closed system, a laminar flow can be identified numerically with the help of Reynolds number. Reynolds number is simply a dimensionless parameter that helps system designers distinguish between flow regimes. The value of Reynolds number (Re) can be indicated as:

Note:

ρ is the fluid density

V is the fluid velocity

D is the hydraulic diameter (of pipe, tube, or duct)

μ is the fluid viscosity

As we can observe, the Reynolds number is dependent on the value of viscosity and velocity of the fluid; the value for laminar flow is bound to be lower in comparison to turbulent flow due to high viscosity or low velocity. Generally, for Reynolds numbers up to 2300, the flow is considered to be laminar. When the Reynolds number starts exceeding 2300, the flow starts the transition phase from laminar to turbulent.

### Laminar Water Flow Law

For laminar flow in water flowing through a cylinder such as a tube or a pipe laid horizontally, the velocity profile of water is maximum at the centerline. The velocity decreases as it gets closer to the wall, with the velocity next to the wall being zero. To maintain a steady flow profile for laminar flow,  it is necessary to have a pressure difference between the two ends of the pipe. This is expressed by Poiseuille’s law as:

Note:

∆p is the pressure difference

l is the length of the pipe

R is the radius of the pipe

uavg is the average velocity of flow

µ is the  fluid viscosity

Q is the flow rate

Laminar water flow explained with the above equations establishes that the flow is proportional to the pressure gradient while inversely proportional to fluid viscosity and pipe length. Thus, to maintain a laminar regime for water flow, a constant velocity and pressure difference needs to be maintained.

## Achieving Laminar Water Flow With a CFD Solver

The efficient design of laminar water flow systems can be a challenge, especially in complex distribution networks. The proper verification of flow regimes can allow system designers to accurately infer the considerations to be made during the design. A proper laminar water flow can be achieved through the visualization and numerical analysis supported by a CFD solver.

With CFD solvers, the desired velocity and pressure drop can be established to develop an accurate laminar flow model. And, the governing flow equation can be analyzed for laminar conditions through CFD modeling. This is made possible through CFD platforms such as Omnis and Pointwise from Cadence, which can aid in laminar water flow analysis for complex networks at the desired speed and fidelity levels.