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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 curl of a vector in maths?
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
Is a vector necessarily changed if it is rotated through an angle?
Yes. A vector is defined as having magnitude and direction (in reference to a fixed frame). Changing either of these properties redefines the vector.
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.
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 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.
Why curl of electrical field is zero?
Because Electric field can be expressed as the gradient of a scalar. Curl of a gradient is always zero by rules of vector calculus.
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 vector product and explain its properties?
cereal
What is meant by curl of a vector in maths?
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 is physical interpretation of vector space?
A vector has two properties: magnitude and direction. The representation of a vector is an arrow. The tip of the arrow points to the direction the vector is acting. The length of the arrow represents the magnitude.
Is a vector necessarily changed if it is rotated through an angle?
Yes. A vector is defined as having magnitude and direction (in reference to a fixed frame). Changing either of these properties redefines the vector.
What are properties of a vector quantity?
A vector quantity not only has a size, it also has a direction. Velocity is a vector quantity. "30 mph north" and "30 mph east" are different velocities. "Speed" is a part of velocity ... its size alone, without its direction, so speed is not a vector quantity.
Can you name the legacy classes and interface for collections?
Dictionary, Hashtable ,Properties ,Stack and vector are the legacy classes in java
