Duct Entrance Head Loss

Duct Entrance Head Loss

Calculates the head-loss coefficient and pressure drop at a smooth bellmouth duct (pipe) entrance as a function of the normalised rounding radius.

Rounding Ratio

$$x=\frac{r}{D_h}$$

where r is the radius of curvature of the bellmouth and $D_h$ is the hydraulic diameter of the duct.

• $x=0$: sharp (re-entrant) entrance, $K=0.50$.
• $x\approx 0.20$: well-rounded bellmouth, $K\approx 0.03$.

Loss Coefficient

A polynomial fitted to Idel'chik / ASHRAE tabulated data (accurate to ±10%):

$$K=235.03x^4-194.09x^3+56.739x^2-7.8163x+0.50$$

Pressure Drop

$$\Delta p=K\cdot \frac{1}{2}\rho V^2$$

where $\rho$ is the air density and $V$ is the mean flow velocity in the duct.

Validity

• $0\le x\le 0.20$.
• The correlation is ±10% (curve-fit accuracy).
• The formula is for a single entrance; not applicable to re-entrant projecting entries.

Tabulated Reference Data

References

• Roberson, J.A. and Crowe, C.T., Engineering Fluid Mechanics, 2nd Ed., Rudolf Steiner Press, London, 1976, pp. 360–384.
• Idel'chik, I.E. and Fried, E., Flow Resistance, Taylor & Francis, 1989, p. 52.
• ASHRAE, Handbook Fundamentals, 1977, p. 32.31.