The rate of overflow per unit volume at a point of fluid is measured byGroup of answer choicesgradientcurlDivergencenone of these

To determine the appropriate answer for the rate of overflow per unit volume at a point of fluid, we need to analyze the relevant concepts in fluid dynamics.

Concept Analysis

1. Gradient: This operation represents the rate of change of a field, generally associated with scalar fields, and it indicates the direction of the steepest ascent of the field.

2. Curl: This operation measures the rotation or the twisting of a field and is primarily applied for vector fields. It provides information about the local rotation at a point but not specifically about the overflow per unit volume.

3. Divergence: This operation measures the rate at which "stuff" is expanding or overflowing from a point in a vector field. In fluid dynamics, the divergence of a velocity field gives the net rate of flow out of a point in the fluid, which can be interpreted as overflow.

4. None of These: This option can be considered if none of the other concepts align with the definition of the rate of overflow.

Conclusion

Given that divergence quantitatively expresses how much a vector field (such as fluid velocity) is diverging from a point, the best representation of the rate of overflow per unit volume at a point of fluid is:

Final Answer

Divergence