Final answer:
The velocity in a 4 inch pipe is 9 times faster than in a 12 inch pipe when both are flowing full at the same flow rate (Q), due to the smaller pipe's decreased cross-sectional area.
Step-by-step explanation:
Assuming both are flowing full at the same FLOW RATE (Q). The velocity in a 4 inch pipe relative to a 12 inch pipe is 9 times faster. The flow rate can be explained by the formula Q = Av, where A is the cross-sectional area and v is the average velocity. As the diameter of a pipe decreases, its cross-sectional area decreases, and according to the continuity principle for incompressible fluids, if the flow rate (Q) is constant, the velocity (v) must increase when the area decreases. In the scenario of the pipes with diameters of 4 inches and 12 inches, the area of the larger pipe is 9 times that of the smaller pipe because the diameter is three times larger (the area of a circle being proportional to the square of the diameter). Therefore, the velocity in the 4 inch pipe must be 9 times faster than in the 12 inch pipe to maintain the same flow rate.