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### Sluice Gate Flow Formula and Calculator

Flow Through a Sluice Gate Formula and Calculator

In the case of flow generated when a sluice gate that retains water in a reservoir is partially raised (Figure 1) Figure 1, Flow through a sluice gate.

By combining Bernoulli's equation and the continuity equation we get:

Eq. 1
ho = Q2 / ( 2 g b2 h2 ) + h

Eq. 2

Q2 = ho ( 2 g b2 h2 ) - h

Eq. 3

Q = [ ho ( 2 g b2 h2 ) - h ]1/2

The maximum flow rate is given by:

Eq. 4
( Q / b )2max = 8 / 27 g h30

Here too, the Froude number is a measure of flow rate. Maximum flow rate is present when the Froude number is unity. By raising the gate from its closed position, the flow discharge is increased until a maximum discharge is obtained, and the depth downstream is two-thirds of the reservoir depth. If the gate is raised beyond this critical height, the flow rate actually drops.

The above analysis and observation is also true for flow over the crest of a dam, and the same equation for max flow rate is valid-where is the water level in the reservoir measured from the crest level, and ho is the water level above the crest.

Where:

Q = flow, ( ft3 / sec, m3 / sec)
g = Gravity (32.2 ft/sec2 , 9.81 m/sec2 )
b = sluice opening width, (ft, m)
h0 = height, (ft, m)
h = flow height, (ft, m)

Related:

Reference:

Rules of Thumb for Mechanical Engineers
J. Edward Pope, Editor