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In mathematics, the curl of a vector is the maximum rotation on a vector field, oriented perpendicularly to the certain plane. The curl of a vector is defined by this form:
∇ x F =
[i . . . . j . . . . . k]
[∂/∂x ∂/∂y ∂/∂z]
[P. . . Q. . . .R. . ]
...given that F = <P,Q,R> or Pi + Qj + Rk
Perform the cross-product of the terms to obtain:
∇ x F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k
What else can I help you with?
What is meant by null vector?
a vector with nothing in it
What is vorticity vector?
The vorticity vector is DelxV = v/r sin(RV)H1, the Curl of the vector V. The unit vector H1, is perpendicular to the plane formed by the radius vector R and and the vector V.
How does vector calculus apply in fluid mechanics?
The velocity at each point in the fluid is a vector. If the fluid is compressible, the divergence of the velocity vector is nonzero in general. In a vortex the curl is nonzero.
What is curl in mathematical terms?
Curl represents the force of rotation in a 3-D vector field. Generally, the curl vector at a given point is the answer to the question, "What would happen if I stuck something there that could spin but couldn't move?" Unless the curl is zero, it would spin perpendicularly to the curl vector (according to the right-hand rule), and the longer the vector is, the faster. Curl is mathematically defined in a given direction as the limit of "circulation over area", i.e. the line integral of a circle around the point, divided by the area of the circle, with the circle shrinking towards the point. More practically, the actual vector can found by taking the cross product of the gradient operator with the function that defines the field: curl_x = ∂F/∂y - ∂F/∂z curl_y = ∂F/∂z - ∂F/∂x curl_z = ∂F/∂x - ∂F/∂y
What is meant by ratio?
Well .. A ration is soemthing we use in Maths.
Is curl of vector function F must perpendicular to every vector function f?
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
Under what condition is a vector field considered conservative if the curl of the field is zero?
A vector field is considered conservative when its curl is zero.
What is the relationship between the curl of a vector field and its representation in polar coordinates?
In polar coordinates, the curl of a vector field represents how much the field is rotating around a point. The relationship between the curl and the representation in polar coordinates is that the curl can be calculated using the polar coordinate system to determine the rotational behavior of the vector field.
What is the difference between curl and divergence?
Divergence: rate of spread of vector in free space for non closed path. and Curl: rate of spread of vector in free space for closed path.
What is meant by null vector?
a vector with nothing in it
What is vorticity vector?
The vorticity vector is DelxV = v/r sin(RV)H1, the Curl of the vector V. The unit vector H1, is perpendicular to the plane formed by the radius vector R and and the vector V.
What is the relationship between vorticity and velocity in cylindrical coordinates?
In cylindrical coordinates, vorticity is related to the velocity by the curl of the velocity field. The vorticity vector is the curl of the velocity vector, which represents the local rotation of the fluid at a point in the flow.
How does vector calculus apply in fluid mechanics?
The velocity at each point in the fluid is a vector. If the fluid is compressible, the divergence of the velocity vector is nonzero in general. In a vortex the curl is nonzero.
What is the curl of polar coordinates?
The curl of polar coordinates is a mathematical operation that measures the rotation or circulation of a vector field around a point in the polar coordinate system. It helps to understand the flow and behavior of the vector field in a two-dimensional space.
What is curl in mathematical terms?
Curl represents the force of rotation in a 3-D vector field. Generally, the curl vector at a given point is the answer to the question, "What would happen if I stuck something there that could spin but couldn't move?" Unless the curl is zero, it would spin perpendicularly to the curl vector (according to the right-hand rule), and the longer the vector is, the faster. Curl is mathematically defined in a given direction as the limit of "circulation over area", i.e. the line integral of a circle around the point, divided by the area of the circle, with the circle shrinking towards the point. More practically, the actual vector can found by taking the cross product of the gradient operator with the function that defines the field: curl_x = ∂F/∂y - ∂F/∂z curl_y = ∂F/∂z - ∂F/∂x curl_z = ∂F/∂x - ∂F/∂y
What is meant by resultant of a vector?
A resultant vector is one vector which can replace all the other vectors and produce the same effect.
How do you use the right hand rule for the cross product in vector mathematics?
To use the right hand rule for the cross product in vector mathematics, align your right hand fingers in the direction of the first vector, then curl them towards the second vector. Your thumb will point in the direction of the resulting cross product vector.
