Answer:
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space. At every point in the field, the curl of that point is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point. The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.
The alternative terminology rotation or rotational and alternative notations rot F and ∇ × F are often used (the former especially in many European countries, the latter, using the del (or nabla) operator and the cross product, is more used in other countries) for curl F.
Unlike the gradient and divergence, curl does not generalize as simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This is a phenomenon similar to the 3-dimensional cross product, and the connection is reflected in the notation ∇ × for the curl.
Explanation:
Answer:
The BOD5 for this sample is 5 mg/L
Explanation:
The BOD5 takes into consideration the difference between the initial DO and the final DO divided by the fraction of the sample tested in a 300 mL BOD flask. The problem states that the sample was directly placed in a BOD bottle so we assume that the volume used was 300 mL of the water sample. The fraction of water is 1 (300/300).
BOD5 = (10-5)/1
BOD 5 = 5 mg/L
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