Final answer:
Using the continuity equation, where the product of cross-sectional area and speed is constant, we can calculate the speed of water when it exits a pipe that has changed in diameter.
Step-by-step explanation:
The question concerns the continuity equation and Bernoulli's principle in fluid dynamics, a topic in physics. When a pipe changes diameter, the speed of the fluid changes to maintain a constant flow rate (continuity equation). According to this principle, the product of the cross-sectional area of the pipe and the speed of the fluid at any point along the pipe is constant. Therefore, if the diameter of the pipe decreases, the speed of the fluid must increase, and vice versa.
To solve the problem, we can use the continuity equation: A1 * v1 = A2 * v2, where A is the cross-sectional area and v is the speed of the fluid. We can calculate the cross-sectional areas of the two different diameters of the pipe using the formula A = π * d^2 / 4. Substituting the values for the diameters and the given speed into the continuity equation and solving for the unknown speed will provide us with the speed of the water exiting the pipe.