Laminar Flow

Examples of Laminar Flow in the following topics:

• Poiseuille's Equation and Viscosity

  • This is generally split into two categories, laminar and turbulent flow.
  • 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.
  • In practice, Poiseuille's equation holds for most systems involving laminar flow of a fluid, except at regions where features disrupting laminar flow, such as at the ends of a pipe, are present.
  • Laminar fluid flow in a circular pipe at the same direction.

• Motionof an Object in a Viscous Field

  • If N′R is less than about 1, flow around the object can be laminar, particularly if the object has a smooth shape.
  • Depending on the surface, there can be a turbulent wake behind the object with some laminar flow over its surface.
  • For an N′R between 10 and 10^6, the flow may be either laminar or turbulent and may oscillate between the two.
  • (See . ) Laminar flow occurs mostly when the objects in the fluid are small, such as raindrops, pollen, and blood cells in plasma.
  • Here the flow is laminar with N′R less than 1.

• Turbulence Explained

  • It is possible to predict if flow will be laminar or turbulent.
  • At low velocity, flow in a very smooth tube or around a smooth, streamlined object will be laminar.
  • In fact, at intermediate velocities, flow may oscillate back and forth indefinitely between laminar and turbulent.
  • In the spring, when the flow is faster, the flow may start off laminar but it is quickly separated from the leg and becomes turbulent.
  • In the transition region, the flow can oscillate chaotically between laminar and turbulent flow.

• 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 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.
  • Assess the significance of studying volumetric flow in addition to flow velocity

• 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.

• The Junction Rule

  • Kirchhoff's junction rule states that at any circuit junction, the sum of the currents flowing into and out of that junction are equal.
  • Kirchhoff's junction rule states that at any junction (node) in an electrical circuit, the sum of the currents flowing into that junction is equal to the sum of the currents flowing out of that junction.
  • Because charge is conserved, the only way this is possible is if there is a flow of charge across the boundary of the region.
  • This flow would be a current, thus violating Kirchhoff's junction law.
  • Kirchhoff's Junction Law illustrated as currents flowing into and out of a junction.

• Application of Bernoulli's Equation: Pressure and Speed

  • For "ideal" flow along a streamline with no change in height, an increase in velocity results from a decrease in static pressure.
  • The Bernoulli equation can be adapted to flows that are both unsteady and compressible.
  • Compressibility effects depend on the speed of the flow relative to the speed of sound in the fluid.
  • The flow rate out can be determined by drawing a streamline from point ( A ) to point ( C ).
  • Adapt Bernoulli's equation for flows that are either unsteady or compressible

• Overview of Electric Current

  • Electric current is the flow of electric charge and resistance is the opposition to that flow.
  • The flow of electricity requires a medium in which charge can flow .
  • Note that the direction of current flow in the figure is from positive to negative.
  • The rate of flow of charge is current.
  • An ampere is the flow of one coulomb through an area in one second.

• Flow through a Channel

  • We can see many of the features of the supersonic flow through a de Laval nozzle in the flow through a channel.
  • Notice that we have neglected the vertical velocity of the flow.
  • One is a small deviation in the level of the surface that corresponds to a subcritical flow.
  • The second has a large deviation (supercritical flow).
  • When the flow is critical these two solutions coincide.