What is the continuity equation relating flow rate, velocity, and cross-sectional area in a pipe?

What is the continuity equation relating flow rate, velocity, and cross-sectional area in a pipe?

• A. Q = ρ v A
• B. Q = v × A
• C. Q = P / (ρ g)
• D. Q = A / v

Answer: (B)

Volumetric flow rate through a pipe section is determined by how fast the fluid is moving and how much area the flow has to pass through. The amount of volume crossing per second is simply velocity times the cross-sectional area, so Q = v × A. This makes sense because the units line up: velocity (m/s) times area (m²) gives cubic meters per second (m³/s), the unit for flow rate. If the cross-sectional area changes in steady, incompressible flow, the velocity adjusts so that the same volume passes each section per second, keeping Q constant. The other expressions mix in density or invert the relationship, which would describe mass flow rate or an incorrect quantity, not the volumetric flow rate.

Volumetric flow rate through a pipe section is determined by how fast the fluid is moving and how much area the flow has to pass through. The amount of volume crossing per second is simply velocity times the cross-sectional area, so Q = v × A. This makes sense because the units line up: velocity (m/s) times area (m²) gives cubic meters per second (m³/s), the unit for flow rate.

If the cross-sectional area changes in steady, incompressible flow, the velocity adjusts so that the same volume passes each section per second, keeping Q constant. The other expressions mix in density or invert the relationship, which would describe mass flow rate or an incorrect quantity, not the volumetric flow rate.