 Solid blue lines and broken grey lines represent the streamlines. The red arrows show the direction and magnitude of the flow velocity. These arrows are tangential to the streamline. The group of streamlines enclose the green curves ( C1 and C2) to form a streamtube.
 Particles on the same streakline can take different paths to reach there. The image shows the streaklines originating from the same point at two different time instances and the pathlines for four different particles on those streaklines. Fluid flow is described in general by a vector field in three (for steady flows) or four (for non-steady flows including time) dimensions. Pathlines, streamlines, and streaklines are field lines of different vector field descriptions of the flow. Image File history File links Download high-resolution version (815x518, 17 KB) I, the creator of this work, hereby release it into the public domain. ...
Image File history File links Download high-resolution version (815x518, 17 KB) I, the creator of this work, hereby release it into the public domain. ...
Image File history File links Pathlines_and_streakline. ...
Image File history File links Pathlines_and_streakline. ...
Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ...
Equipotential surfaces are surfaces of constant scalar potential. ...
- Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow. This means that if a point is picked then at that point the flow moves in a certain direction. Moving a small distance along this direction and then finding out where the flow now points would draw out a streamline.
- A streakline is the locus of points of all the fluid particles that have passed continuously though a particular spatial point in the past. This can be found experimentally by releasing dye into the fluid in a time period at a fixed point and then at a later time finding out where the dye was.
- Pathlines are the trajectory that a fluid particle would make as it moves around with the flow.
By definition, streamlines defined at a single instant in a flow do not intersect. This is so because a fluid particle cannot have two different velocities at the same point. Similarly streaklines cannot intersect themselves or other streaklines, because two particles cannot be present at the same location at the same instance of time. However, pathlines are allowed to intersect themselves or other pathlines (except the starting and end points of the different pathlines, which need to be distinct). In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...
In mathematics, the word tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry. ...
The velocity of an object is its total speed in a particular direction. ...
. The initial letter is shown capitalized due to technical restrictions. ...
In mathematics, a locus (Latin for place, plural loci) is a collection of points which share a common property. ...
In simple terms, streamlines and streaklines are like a snapshot of the flowfield whereas pathlines are time-history of the flow.
A region bounded by streamlines is called a streamtube. Because the streamlines are tangent to the flow velocity, fluid that is inside a stream tube must remain forever within that same stream tube. A scalar function whose contours define the streamlines is known as the stream function. The Comet Nucleus Tour (CONTOUR) was a Discovery-class space mission. ...
In fluid dynamics, the stream function is defined for two-dimensional flows. ...
Mathematical description
Streamlines Streamlines are defined as If the components of the velocity are written , we deduce , which shows that the curves are parallel to the velocity vector. Here s is a variable which parametrizes the curve . For streamlines there is no t (time) dependence. This is because they are calculated instantaneously, meaning that at one instance of time they are calculate throughout the fluid. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ...
In computer science and mathematics, a variable (IPA pronunciation: ) (sometimes called a pronumeral) is a symbolic representation denoting a quantity or expression. ...
Pathlines Pathlines are defined by The suffix P indicates that we a following the motion of a fluid particle. Note that at point the curve is parallel to the flow velocity vector , where the velocity vector is evaluated at the position of the particle at that time t.
Streaklines Streaklines can be expressed as, where, is the velocity of a particle P at location and time t. The parameter τP, parametrizes the streakline and , where t0 is a time of interest.
Steady flows In steady flow (which flows that remain the same for all time), the streamlines, pathlines, and streaklines coincide. This is because when a particle on a streamline reaches a point, a0, further on that streamline the equations governing the flow will send it in a certain direction . As the equations that govern the flow remain the same when another particle reaches a0 it will also go in the direction . If the flow is not steady then when the next particle reaches position a0 the flow would have changed and the particle will go in a different direction. Steady flow is a type of liquid flow in which The liquid flow is smooth and uniform. ...
This is useful, because it is usually very difficult to look at streamlines in an experiment. However, if the flow is steady, one can use streaklines to describe the streamline pattern.
Frame dependence Streamlines are frame-dependent. That is, the streamlines observed in one inertial reference frame are different from those observed in another inertial reference frame. For instance, the streamlines in the air around an aircraft wing are defined differently for the passengers in the aircraft than for an observer on the ground. When possible, fluid dynamicists try to find a reference frame in which the flow is steady, so that they can use experimental methods of creating streaklines to identify the streamlines. In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines. An inertial reference frame is one in which Newtons first and second laws of motion are valid. ...
Layers of Atmosphere (NOAA) Air redirects here. ...
An Airbus A380, currently the worlds largest passenger airliner An aircraft is any vehicle or craft capable of atmospheric flight. ...
A Laughing Gull on the beach in Atlantic City, USA. Wing shapes: a swept wing KC-10 Extender from Travis Air Force Base, California, refuels a delta wing F/A-22 Raptor. ...
Observation is an activity of a sapient or sentient living being, which senses and assimiliates the knowledge of a phenomenon in its framework of previous knowledge and ideas. ...
Applications Knowledge of the streamlines can be useful in fluid dynamics. For example, Bernoulli's principle, which expresses conservation of mechanical energy, is only valid along a streamline. Also, the curvature of a streamline is an indication of the pressure change perpendicular to the streamline. The instantaneous centre of curvature of a streamline is in the direction of increasing pressure, and the magnitude of the pressure gradient can be calculated from the curvature of the streamline. Bernoullis Principle states that in an ideal fluid (low speed air is a good approximation), with no work being performed on the fluid, an increase in velocity occurs simultaneously with decrease in pressure or gravitational energy. ...
In physics, mechanical energy is one of several forms of energy. ...
The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ...
Engineers often use dyes in water or smoke in air in order to see streaklines, and then use the patterns to guide their design modifications, aiming to reduce the drag. This task is known as streamlining, and the resulting design is referred to as being streamlined. Streamlined objects and organisms, like steam locomotives, streamliners, cars and dolphins are often aesthetically pleasing to the eye. The Streamline Moderne style, an 1930s and 1940s offshoot of Art Deco, brought flowing lines to architecture and design of the era. The canonical example of a streamlined shape is a chicken egg with the blunt end facing forwards. This shows clearly that the curvature of the front surface can be much steeper than the back of the object. Most drag is caused by eddies in the fluid behind the moving object, and the objective should be to allow the fluid to slow down after passing around the object, and regain pressure, without forming eddies. Engineering is the design, analysis, and/or construction of works for practical purposes. ...
Yarn drying after being dyed in the early American tradition, at Conner Prairie living history museum. ...
Smoke from a wildfire Smoke is a suspension in air (aerosol) of small particles resulting from incomplete combustion of a fuel. ...
Great Western Railway No. ...
A streamliner is any vehicle that incorporates streamlining to produce a shape that provides less resistance to air, and is more pleasing to the eye. ...
For the magazine called automobile, see Automobile Magazine. ...
Genera See article below. ...
Bathers building, now a Maritime Museum at San Franciscos Aquatic Park, 1937 Marine Air Terminal, LaGuardia Airport, 1939 Streamline Moderne, sometimes referred to by either name alone, was a late branch of the Art Deco style. ...
The 1930s (years from 1930–1939) were described as an abrupt shift to more radical and conservative lifestyles, as countries were struggling to find a solution to the Great Depression, also known in Europe as the World Depression. ...
The 1940s decade ran from 1940 to 1949. ...
Asheville City Hall. ...
In geometry, an oval or ovoid (from Latin ovum, egg) is any curve resembling an egg or an ellipse. ...
The same terms have since become common vernacular to describe any process that smooths an operation. For instance, it is common to hear references to streamlining a business practice, or operation.
See also In fluid dynamics, the stream function is defined for two-dimensional flows. ...
In fluid dynamics it is critically important to see the patterns produced by flowing fluids, in order to understand them. ...
The drag coefficient (Cd or Cx) is a number that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation. ...
In fluid mechanics, equipotentials are lines or surfaces of equal head that are in direct relation to pressure. ...
References - T. E. Faber (1995). Fluid Dynamics for Physicists. Cambridge University Press. ISBN 0-521-42969-2.
External links - Streamline illustration
- Flow Description at University of Sydney
- Flow Visualization at the College of Engineering at Purdue University
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