The pressure components in the equation are in general irrelevant since pressure upstream and downstream are the same (p1 - p2 = 0).
Assuming uniform upstream and downstream velocity profiles - the Continuity Equation gives:
q = v1 A1
= v2 A2 (2)
q = flow rate (m3/s)
A = flow area (m2)
(2) can be modified to:
q = v1 h1 b
= v2 h2 b (3)
b = width of the sluice (m)
h1 = upstream height (m)
h2 = downstream height (m)
Combining (1) and (3), gives the "ideal" equation:
q = h2 b [2 g (h1 - h2) /(1 -(h2 / h1))]1/2 (4)
Assuming h1 >> h2 (4) can be modified to:
q = h2 b [2 g h1]1/2 (5)
This is approximately true when the depth ratio h1 / h2 is large, the kinetic energy upstream is negligible (v1 is small) and the fluid velocity after it has fallen the distance (h2 - h1) ≈ h1 - is:
v2 = [2 g h1]1/2 (6)
The ideal equation (3) can be modified with a discharge coefficient:
q = cd h0 b [2 g h1]1/2 (7)
cd = discharge coefficient
The discharge coefficient depends on different parameters - such as upstream and tail-water depths, gate opening, contraction coefficient of the gate and the flow condition.
In practice the typical discharge coefficient is approximately 0.61 for free flow conditions and depth ratios ho / h1 < 0.2.
The most commonly used specification for sluice gates in water and wastewater treatment plants is ANSI/AWWA C560-00. This specification should be used as a guidance for gates selection and operating equipment and associated hardware.
Water flows under a sluice gate with an opening height of 0.4 m. The width of the sluice is 3 m and the height from the water surface to the bottom of the sluice is 10 m.
Since h1 >> h2 and the depth ratio 0.4/10 < 0,2 - the contraction coefficient can be set to 0.61 - and equation (7) can be used for flow calculation:
q = 0.61 (0.4 m) (3 m) [2 (9.81 m/s2) (10 m)]1/2
= 10.25 m3/s
Flow metering principles - Orifice, Venturi, Flow Nozzles, Pitot Tubes, Target, Variable Area, Positive Displacement, Turbine, Vortex, Electromagnetic, Ultrasonic Doppler, Ultrasonic Time-of-travel, Mass Coriolis, Mass Thermal, Weir V-notch, Flume Parshall and Sluice Gate flow meters and more.
Conservation of energy in a non-viscous, incompressible fluid at steady flow.
Calculate the discharge length from the open end of a partially filled horizontal pipe.
Introduction to accuracy in flow measurement devices.
Turndown ratio (Rangeability) can be used to compare flow measurement devices like orifices, venturi meters etc.
The Equation of Continuity is a statement of mass conservation.
An introduction to the different types of fluid flowmeters - Orifices, Venturies, Nozzles, Rotameters, Pitot Tubes, Calorimetrics, Turbine, Vortex, Electromagnetic, Doppler, Ultrasonic, Thermal, Coriolis.
Elevation and potential energy in hydropower.
Flow rate or discharge in an open conduit, channel or river can be calculated with the velocity-area principle.
Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!
We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.
Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.