7.7
6.95
6.9
7.63
6.645
7.219
7.168
5.275
Flow velocity GudangMovies21 Rebahinxxi LK21
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is scalar, the flow speed.
It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall).
Definition
The flow velocity u of a fluid is a vector field
u
=
u
(
x
,
t
)
,
{\displaystyle \mathbf {u} =\mathbf {u} (\mathbf {x} ,t),}
which gives the velocity of an element of fluid at a position
x
{\displaystyle \mathbf {x} \,}
and time
t
.
{\displaystyle t.\,}
The flow speed q is the length of the flow velocity vector
q
=
‖
u
‖
{\displaystyle q=\|\mathbf {u} \|}
and is a scalar field.
Uses
The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow:
= Steady flow
=
The flow of a fluid is said to be steady if
u
{\displaystyle \mathbf {u} }
does not vary with time. That is if
∂
u
∂
t
=
0.
{\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}=0.}
= Incompressible flow
=
If a fluid is incompressible the divergence of
u
{\displaystyle \mathbf {u} }
is zero:
∇
⋅
u
=
0.
{\displaystyle \nabla \cdot \mathbf {u} =0.}
That is, if
u
{\displaystyle \mathbf {u} }
is a solenoidal vector field.
= Irrotational flow
=
A flow is irrotational if the curl of
u
{\displaystyle \mathbf {u} }
is zero:
∇
×
u
=
0.
{\displaystyle \nabla \times \mathbf {u} =0.}
That is, if
u
{\displaystyle \mathbf {u} }
is an irrotational vector field.
A flow in a simply-connected domain which is irrotational can be described as a potential flow, through the use of a velocity potential
Φ
,
{\displaystyle \Phi ,}
with
u
=
∇
Φ
.
{\displaystyle \mathbf {u} =\nabla \Phi .}
If the flow is both irrotational and incompressible, the Laplacian of the velocity potential must be zero:
Δ
Φ
=
0.
{\displaystyle \Delta \Phi =0.}
= Vorticity
=
The vorticity,
ω
{\displaystyle \omega }
, of a flow can be defined in terms of its flow velocity by
ω
=
∇
×
u
.
{\displaystyle \omega =\nabla \times \mathbf {u} .}
If the vorticity is zero, the flow is irrotational.
If an irrotational flow occupies a simply-connected fluid region then there exists a scalar field
ϕ
{\displaystyle \phi }
such that
u
=
∇
ϕ
.
{\displaystyle \mathbf {u} =\nabla \mathbf {\phi } .}
The scalar field
ϕ
{\displaystyle \phi }
is called the velocity potential for the flow. (See Irrotational vector field.)
In many engineering applications the local flow velocity
u
{\displaystyle \mathbf {u} }
vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity
u
¯
{\displaystyle {\bar {u}}}
(with the usual dimension of length per time), defined as the quotient between the volume flow rate
V
˙
{\displaystyle {\dot {V}}}
(with dimension of cubed length per time) and the cross sectional area
A
{\displaystyle A}
(with dimension of square length):
u
¯
=
V
˙
A
{\displaystyle {\bar {u}}={\frac {\dot {V}}{A}}}
.
See also
References
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Flow velocity - Wikipedia
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity[1][2] in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is …
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Flow rate and velocity are related, but quite different, physical quantities. To make the distinction clear, think about the flow rate of a river. The greater the velocity of the water, the greater the flow rate of the river.
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Oct 31, 2018 · What Does Flow Velocity Mean? Flow velocity is the distance traveled by a fluid per time i.e. meter/second or feet/minute. Friction along the pipe walls can affect the flow velocity of a fluid.
Flow Rate and Its Relation to Velocity | Physics - Lumen Learning
Flow rate and velocity are related, but quite different, physical quantities. To make the distinction clear, think about the flow rate of a river. The greater the velocity of the water, the greater the flow rate of the river. But flow rate also depends on the size of the river.
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The fluid velocity in a pipe is a fundamental data to calculate to be able to characterize the flow in a pipe, thanks to the Reynolds number, and size a pipe circuit calculating the pressure drop expected for a certain flow.
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Flow rate and velocity are related, but quite different, physical quantities. To make the distinction clear, consider the flow rate of a river. The greater the velocity of the water, the greater the flow rate of the river. But flow rate also depends on the size and shape of the river.
