Flow Coefficients

Overview

Engineering reference data for Flow Coefficients in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Flow Coefficient Formulas by Fluid Type

Liquids

For incompressible liquids like water, the flow coefficient ($C_v$) can be calculated using either volumetric or mass flow rates.

Volume Flow Rate (Imperial): $C_v = q \sqrt{\frac{SG}{dp}}$

Volume Flow Rate (Metric): $C_v = 11.6 \cdot q \sqrt{\frac{SG}{dp}}$

Mass Flow Rate (Imperial): $C_v = \frac{w}{500 \sqrt{dp \cdot SG}}$

Mass Flow Rate (Metric): $C_v = \frac{5.8 \cdot w}{500 \sqrt{dp \cdot SG}}$

Example: A valve passing 25 GPM of water ($SG=1$) with a 1 psi pressure drop has $C_v = 25$.

Saturated Steam

Due to compressibility, steam formulas account for pressure drop behavior relative to critical (choked) flow.

Critical (Choked) Pressure Drop ($p_o \approx 0.58 \cdot p_i$): $C_v = \frac{m}{1.61 \cdot p_i}$

Non-Critical Pressure Drop ($p_o > 0.58 \cdot p_i$): $C_v = \frac{m}{2.1 \sqrt{(p_i + p_o) \cdot dp}}$

Superheated Steam

The flow coefficient for superheated steam requires a temperature correction factor. $C_v = C_{v_{\text{saturated}}} \left(1 + 0.00065 \cdot dt\right)$ Where $dt$ is the steam temperature above saturation (°F).

Wet Saturated Steam

Moisture content reduces the effective flow capacity. $C_v = C_{v_{\text{saturated}}} \sqrt{\zeta}$ Where $\zeta$ is the steam dryness fraction.

Example: For steam with 5% moisture, $\zeta = 0.95$, so $C_v = 0.97 \cdot C_{v_{\text{saturated}}}$.

Air and Other Gases

Critical Pressure Drop ($p_o \approx 0.53 \cdot p_i$): $C_v = \frac{q \sqrt{SG \cdot (T + 460)}}{834 \cdot F_L \cdot p_i}$ Where $T$ is temperature (°F) and $F_L$ is the liquid recovery factor.

References

• Original Source