Sluice Gate Flow Measurement

Overview

Engineering reference data for Sluice Gate Flow Measurement 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

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Example Calculation

Problem: Water flows under a sluice gate with an opening height ($h_0$) of 0.4 m. The width of the sluice ($b$) is 3 m and the upstream water depth ($h_1$) is 10 m. Calculate the flow rate ($q$).

Solution: Given the depth ratio $h_0/h_1 = 0.4/10 = 0.04 < 0.2$, the standard discharge coefficient for free flow can be applied: $C_d \approx 0.61$.

Using the modified ideal equation (7): $q = C_d \cdot h_0 \cdot b \cdot \sqrt{2 g h_1}$ $q = 0.61 \times 0.4\ \text{m} \times 3\ \text{m} \times \sqrt{2 \times 9.81\ \text{m/s}^2 \times 10\ \text{m}}$ $q = 0.61 \times 0.4 \times 3 \times \sqrt{196.2}\ \text{m}^3\text{/s}$ $q \approx 0.732 \times 14.007\ \text{m}^3\text{/s}$ $q \approx 10.25\ \text{m}^3\text{/s}$

Discharge Coefficient ($C_d$)

The discharge coefficient accounts for real-world deviations from the ideal theoretical flow. It depends on several factors:

• Upstream and downstream water depths ($h_1$ and $h_2$)
• Gate opening height ($h_0$)
• Contraction of the flow vena contracta
• Flow condition (free flow vs. submerged flow)

For free flow conditions where the downstream water level does not affect the gate's discharge and the depth ratio $h_0/h_1 < 0.2$, a typical value is $C_d \approx 0.61$.

Relevant Specification

The most commonly used standard for sluice gates in water and wastewater applications is *ANSI/AWWA C560-00. This specification provides guidance for the selection of gates, operating equipment, and associated hardware.

References

• Original Source