In a piping system with incompressible flow, which statement about velocity and cross-sectional area for a fixed flow rate is true?

In a piping system with incompressible flow, which statement about velocity and cross-sectional area for a fixed flow rate is true?

• A. The velocity increases as area increases, for a fixed Q.
• B. The velocity remains constant when area changes, for a fixed Q.
• C. The velocity is proportional to area squared for a fixed Q.
• D. The velocity is inversely proportional to area for a fixed Q.

Answer: (D)

When the flow rate Q is fixed in an incompressible system, the fluid must pass through every cross-section at the same volumetric rate. The relationship Q = v × A holds at any section, so the velocity is v = Q / A. This means velocity is inversely proportional to the cross-sectional area: if the area grows, velocity drops; if the area shrinks, velocity increases. For example, doubling the area halves the velocity while keeping the same Q. This is why narrow sections speed the fluid up and wide sections slow it down. The other options don’t fit because they either imply velocity changes in the wrong direction with area, assume velocity stays constant, or suggest an incorrect proportionality like area squared.

When the flow rate Q is fixed in an incompressible system, the fluid must pass through every cross-section at the same volumetric rate. The relationship Q = v × A holds at any section, so the velocity is v = Q / A. This means velocity is inversely proportional to the cross-sectional area: if the area grows, velocity drops; if the area shrinks, velocity increases. For example, doubling the area halves the velocity while keeping the same Q. This is why narrow sections speed the fluid up and wide sections slow it down. The other options don’t fit because they either imply velocity changes in the wrong direction with area, assume velocity stays constant, or suggest an incorrect proportionality like area squared.