If a 3-inch hose is flowing 150 gpm and a 2-inch hose is flowing 150 gpm, what can be concluded?

• A. The 3-inch hose has a higher velocity
• B. The flow rate is the same for both hoses
• C. The 2-inch hose is flowing at a higher velocity
• D. The 2-inch hose has a lower flow rate

Answer: (C)

To understand why the conclusion states that the 2-inch hose is flowing at a higher velocity, we need to analyze how flow rate, hose diameter, and velocity are related in fluid dynamics.

Velocity in a hose is determined by the flow rate and the cross-sectional area of the hose. The formula for calculating flow velocity (V) is:

[ V = \frac{Q}{A} ]

where ( Q ) is the flow rate (in gallons per minute, gpm) and ( A ) is the cross-sectional area of the hose (in square inches).

In this specific scenario, both hoses are flowing the same amount of water (150 gpm). However, the cross-sectional area of the hoses differs due to their diameters. The larger diameter of the 3-inch hose results in a larger cross-sectional area compared to the 2-inch hose.

Given that the flow rate is constant (150 gpm) for both hoses:

• The area of the 3-inch hose is greater than that of the 2-inch hose, which means that the velocity of the water flow through the 3-inch hose must be lower than through the 2-inch hose to maintain the same flow rate because there is more space for the