What is the change in velocity when a 6 inch gravity pipe is increased to 12 inches, while maintaining constant flow?

To understand the change in velocity when the diameter of a gravity pipe is increased while maintaining constant flow, it is important to consider the relationship between flow rate, cross-sectional area, and velocity.

Flow rate (Q) is defined by the equation Q = A × v, where A is the cross-sectional area of the pipe and v is the velocity of the fluid. The area of the pipe is given by the formula A = π(d/2)², where d is the diameter of the pipe.

When the diameter of the pipe increases from 6 inches to 12 inches, the cross-sectional area changes significantly:

• The area for a 6-inch pipe is A₁ = π(6/2)² = π(3)² = 9π square inches.
• The area for a 12-inch pipe is A₂ = π(12/2)² = π(6)² = 36π square inches.

The new area (36π) is four times the original area (9π). Since the flow rate must remain constant, if the area increases, the velocity must decrease to keep the equation Q = A × v balanced.

With the area being four times larger, to maintain the same flow rate