Given a system with A1 = 50 cm² and A2 = 800 cm², what is the value of s2 if s1 = 16 cm?

To find the value of s2 based on the given areas A1 and A2, we can use the principle of the continuity equation in fluid dynamics, which states that for incompressible fluids, the product of the area and the velocity must remain constant along a streamline.

The relationship can be expressed as:

A1 * s1 = A2 * s2

Given:

A1 = 50 cm²

A2 = 800 cm²

s1 = 16 cm

We can rearrange the equation to solve for s2:

s2 = (A1 * s1) / A2

Now substituting the known values into the equation:

s2 = (50 cm² * 16 cm) / 800 cm²

Calculating the above expression:

s2 = (800 cm³) / 800 cm² = 1 cm

Therefore, the correct answer is 1 cm. This demonstrates the principle of conservation of mass in fluid flows, where an increase in cross-sectional area corresponds to a decrease in fluid velocity, maintaining the flow continuity in the system.