Turbulent Flow

Examples of Turbulent Flow in the following topics:

• Turbulence Explained

  • It is possible to predict if flow will be laminar or turbulent.
  • The phenomenon of turbulent air flow must be accounted for in many applications.
  • When flow is turbulent, particles exhibit additional transverse motion.
  • In the transition region, the flow can oscillate chaotically between laminar and turbulent flow.
  • Turbulent flow is visible around the bridge supports of the Longtown bridge.

• Poiseuille's Equation and Viscosity

  • This is generally split into two categories, laminar and turbulent flow.
  • Turbulent flow is characterized by irregular flow of a fluid in which there are both inconsistent flow patterns and velocity variations throughout the volume of the fluid in motion.
  • Analysis of turbulent flow can be very complex and often requires advanced mathematical analysis to simulate flow in systems on a near case-by-case basis.
  • At the lower limit of this mixed turbulent–laminar flow Reynolds number region there is another critical threshold value, below which only laminar flow is possible.
  • Laminar flow consists of a regular-flow pattern with constant-flow velocity throughout the fluid volume and is much easier to analyze than turbulent flow.

• Motionof an Object in a Viscous Field

  • Just as with flow in tubes, it is possible to predict when a moving object creates turbulence.
  • The transition to turbulent flow occurs for N′R between 1 and about 10, depending on surface roughness and so on.
  • For an N′R between 10 and 10^6, the flow may be either laminar or turbulent and may oscillate between the two.
  • For N′R greater than about 10^6, the flow is entirely turbulent, even at the surface of the object.
  • (b) At a higher speed, the flow becomes partially turbulent, creating a wake starting where the flow lines separate from the surface.

• Flow Rate and Velocity

  • These factors affect fluid velocity depending on the nature of the fluid flow—particularly whether the flow is turbulent or laminar in nature.
  • In the case of turbulent flow, the flow velocity is complex in nature and thus hard to predict; it must be analyzed on a system per system basis.
  • In the case of Laminar flow, however, fluid flow is much simpler and flow velocity can be accurately calculated using Poiseuille's Law.
  • The magnitude of the fluid flow velocity is the fluid flow speed.
  • This figure shows the relation between flow velocity and volumetric flow rate.

• Accretion Disks

  • Around this radius, the accretion flow must make a transition between a spherical inflow and a disk.
  • It is likely that accretion disks are turbulent magnifying the effects of small-scale viscosity to larger scales.
  • However, without simulating the turbulence directly, it is difficult to estimate the effective viscosity.

• Heat as Energy Transfer

  • The misconception arises because we are sensitive to the flow of heat, rather than the temperature.
  • Gravitational potential energy (PE) (work done by the gravitational force) is converted into kinetic energy (KE), and then randomized by viscosity and turbulence into increased average kinetic energy of atoms and molecules in the system, producing a temperature increase.

• Modelling the Stress

  • Shakura and Sunyaev argued that the viscosity is produced by turbulent eddies so its natural value is
  • where the inequality holds because the turbulent velocity is limited by the sound speed, and the size of the eddies is limited by the thickness of the disk.

• Flow Rate and the Equation of Continuity

  • The flow rate of a liquid is how much liquid passes through an area in a given time.
  • Volumetric flow rate can also be found with
  • where Q is the flow rate, V is the Volume of fluid, and t is elapsed time.
  • The equation of continuity works under the assumption that the flow in will equal the flow out.
  • Since the fluid cannot be compressed, the amount of fluid which flows into a surface must equal the amount flowing out of the surface.

• Steady Supersonic Flow

  • A flow can become supersonic abruptly as in a shock or continuously.
  • Let's imagine that a fluid is flowing through a pipe of variable cross section $A(x)$ and that the flow is steady so that all partial time derivatives vanish.
  • where we have assumed that the fluid flows in the $x$-direction.
  • On the other hand if the flow is supersonic ($v>c_s$) we have
  • If we have a tube in which the flow is initially subsonic and the area of the tube decreases, the flow will accelerate.

• Carnot Cycles

  • Irreversible processes involve dissipative factors, such as friction and turbulence.