Final answer:
The shape of the cross section of a duct described as having a square cross section is a square. The cross-sectional area of a square with side length 's' is A = s², which is important in determining fluid flow rates. The correct option is 1.
Step-by-step explanation:
The question asks about the shape of the cross section of a duct through which water flows. If a duct is described as having a square cross section, then the shape of the cross section is indeed a square. This means that all four sides of the cross section are of equal length and that the angles between the sides are right angles (90 degrees).
In fluid dynamics, the cross-sectional area of a pipe or duct is critical in determining the flow rate and velocity of the fluid passing through it. As per the equation of continuity and conservation of mass, if an incompressible fluid flows through two points in a steady flow system, the mass flow rate at both points must be equal. This implies that where the cross-sectional area is smaller, the fluid must travel faster; conversely, if the area is larger, the fluid travels slower.
For a duct of square cross section, this means that the flow rate (denoted as Q) is calculated by the product of the cross-sectional area (A) of the square and the average velocity (v) of the fluid. The relationship is represented by the equation Q = Av. A square cross section with sides of length 's' would have an area of A = s².
Hence, Option 1 is correct.