For an orifice plate measuring incompressible liquids, flow rate is proportional to which expression?

• A. Cd*A*sqrt(2ΔP/ρ)
• B. ΔP*v
• C. ρ*A*ΔP
• D. Cd*A*ΔP/ρ

Answer: (A)

The main idea is that flow through an orifice is driven by the pressure drop and scales with area and the square root of the head created by that drop. For an incompressible liquid, energy conservation gives the velocity through the orifice as v ≈ sqrt(2ΔP/ρ). The actual volumetric flow rate is the velocity times the cross-sectional area, but real restrictors aren’t ideal, so a discharge coefficient Cd (dimensionless) is included to account for losses. Putting these together, the flow rate is proportional to Cd × A × sqrt(2ΔP/ρ). This captures how increasing area or pressure drop increases flow, while heavier fluids (larger ρ) reduce the velocity for a given ΔP. The other expressions don’t have the correct dependence on ΔP and ρ or don’t give the right units, so they don’t reflect the physics of orifice flow.