In a differential pressure flow meter, how is flow rate related to differential pressure and fluid density?

• A. Flow is proportional to ΔP/ρ.
• B. Flow is proportional to sqrt(ΔP/ρ).
• C. Flow is proportional to ΔP × ρ.
• D. Flow is proportional to ΔP^2/ρ.

Answer: (B)

Flow through a differential pressure meter is governed by how the restriction converts pressure drop into fluid velocity. The differential pressure created by speeding up the fluid is proportional to ρ times the velocity squared (ΔP ∝ ρ v^2). Since the volumetric flow rate is the cross-sectional area times velocity, the flow rate scales with velocity (Q ∝ v). Putting these together gives v ∝ sqrt(ΔP/ρ), so Q ∝ sqrt(ΔP/ρ). That’s why the flow rate is proportional to the square root of the differential pressure divided by density.

The other forms aren’t consistent with how pressure drop relates to velocity in a restriction. A linear ΔP relationship would ignore the quadratic nature of kinetic energy, and multiplying by density or squaring ΔP changes the fundamental units and the physics, leading to incorrect scaling.