Discharge Coefficient Calculator

Calibrate C_d from measured flow data, or predict flow rate and pressure drop from a known C_d. Supports the velocity-of-approach factor E when pipe diameter is provided.

Fluid Mechanics II

Common fluids — click to auto-fill density

Inputs

Solve for:

Orifice / throat diameter D₂ (mm)

Fluid density ρ (kg/m³)

Pressure drop ΔP (kPa)

Measured flow rate Q (L/s)

Include velocity-of-approach factor E = 1/√(1−β⁴) — enter pipe diameter D₁

Theory

Discharge coefficient definition:

C_d = Q_actual / Q_ideal

Q_ideal = E × A₂ × √(2ΔP / ρ)

C_d accounts for all real-fluid losses — it is determined experimentally by measuring Q, ΔP, and geometry.

Three rearrangements:

C_d = Q / (E × A₂ × √(2ΔP/ρ)) [calibration]

Q = C_d × E × A₂ × √(2ΔP/ρ) [predict Q]

ΔP = ρ/2 × (Q / (C_d × E × A₂))² [predict ΔP]

Velocity-of-approach factor E:

β = D₂ / D₁ (diameter ratio)

E = 1 / √(1 − β⁴) [> 1 always]

E corrects for the non-negligible upstream velocity. When D₁ ≫ D₂ (β → 0), E → 1 and can be omitted. For β = 0.5, E = 1.033; for β = 0.7, E = 1.099.

Typical C_d values:

Meter / geometry	C_d
Sharp-edged orifice (standard)	0.61
Square-edged orifice	0.63
Well-rounded nozzle / entrance	0.98
ISA 1932 nozzle	0.96
Long-radius nozzle	0.98
Short tube orifice	0.82
Borda re-entrant tube	0.52
Classical venturi (machined)	0.995

Where:

C_d = discharge coefficient (0–1, dimensionless)
Q = actual volumetric flow rate [m³/s]
A₂ = orifice/throat area = π(D₂/2)² [m²]
ΔP = pressure drop across the meter [Pa]
ρ = fluid density [kg/m³]
β = D₂/D₁ — diameter ratio
E = velocity-of-approach factor (1 if D₁ unknown)