fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...

, pipe flow is a type of

liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, ...

flow within a closed conduit, such as a

pipe Pipe(s), PIPE(S) or piping may refer to: Objects * Pipe (fluid conveyance), a hollow cylinder following certain dimension rules ** Piping, the use of pipes in industry * Smoking pipe ** Tobacco pipe * Half-pipe and quarter pipe, semi-circular ...

or tube. The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important aspect. Pipe flow does not have a free surface which is found in open-channel flow. Pipe flow, being confined within closed conduit, does not exert direct

atmospheric pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, ...

, but does exert

hydraulic pressure Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counte ...

on the conduit. Not all flow within a closed conduit is considered pipe flow.

Storm sewer A storm drain, storm sewer ( United Kingdom, U.S. and Canada), surface water drain/sewer ( United Kingdom), or stormwater drain ( Australia and New Zealand) is infrastructure designed to drain excess rain and ground water from impervious su ...

s are closed conduits but usually maintain a free surface and therefore are considered open-channel flow. The exception to this is when a storm sewer operates at full capacity, and then can become pipe flow. Energy in pipe flow is expressed as

head A head is the part of an organism which usually includes the ears, brain, forehead, cheeks, chin, eyes, nose, and mouth, each of which aid in various sensory functions such as sight, hearing, smell, and taste. Some very simple animals ...

and is defined by the Bernoulli equation. In order to conceptualize head along the course of flow within a pipe, diagrams often contain a hydraulic grade line (HGL). Pipe flow is subject to frictional losses as defined by the Darcy-Weisbach formula.

Laminar-turbulence transition

The behaviour of pipe flow is governed mainly by the effects of

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...

and gravity relative to the

inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...

l forces of the flow. Depending on the effect of viscosity relative to inertia, as represented by the

Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dom ...

, the flow can be either laminar or

turbulent In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...

. For circular pipes of different surface roughness, at a

below the critical value of approximately 2000 pipe flow will ultimately be laminar, whereas above the critical value turbulent flow can persist, as shown in

Moody chart In engineering, the Moody chart or Moody diagram (also Stanton diagram) is a graph in non-dimensional form that relates the Darcy–Weisbach friction factor ''f'D'', Reynolds number Re, and surface roughness for fully developed flow in a circul ...

. For non-circular pipes, such as rectangular ducts, the critical Reynolds number is shifted, but still

\sim \mathcal(10^3)

depending on the aspect ratio. Earlier transition to turbulence, happening at Reynolds number one order of magnitude smaller, i.e.

\sim \mathcal(10^2)

, can happen in channels with special geometrical shapes, such as the

Tesla valve A Tesla valve, called a valvular conduit by its inventor, is a fixed-geometry passive check valve. It allows a fluid to flow preferentially in one direction, without moving parts. The device is named after Nikola Tesla, who was awarded in 1920 ...

. Flow through pipes can roughly be divided into two: *

Laminar flow In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mi ...

- see Hagen-Poiseuille flow *

Turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...

- see Moody diagram

Laminar-turbulence transition

See also

References

Further reading