If a 3-inch hose is flowing 150 GPM, and a 2-inch hose is also flowing at 150 GPM, which one is flowing at a higher velocity?

To determine which hose is flowing at a higher velocity, it is important to understand the relationship between flow rate, hose diameter, and velocity. Flow rate is essentially the volume of fluid passing through a cross-section of the hose over time, expressed in gallons per minute (GPM). Velocity, on the other hand, is how fast the fluid is moving through that hose, typically measured in feet per second.

The velocity of the fluid can be calculated using the formula:

Velocity (V) = Flow rate (Q) / Cross-sectional area (A)

For a circular hose, the cross-sectional area can be calculated using the formula:

A = π * (d/2)²

where d is the diameter of the hose.

In this scenario, although both hoses are flowing at the same flow rate of 150 GPM, the cross-sectional area of the two hoses differs significantly. The 2-inch hose has a smaller diameter, which leads to a smaller cross-sectional area. Therefore, when the same volume of water (150 GPM) passes through a narrower area, the fluid must move faster, resulting in a higher velocity.

Therefore, the 2-inch hose, with its smaller diameter and less cross-sectional area, indeed flows at a