Question

Could a sluice gate be used as a flow measuring device?

Comment on the performance of the gate as a flow measuring device under both conditions (drowned and free)

Answer 1

Yes, discharge can be measured with sluice gate by the use of barnauli equation

The sluice gate flow rate measurement is based on the Bernoulli Equation and can be expressed as:

1/2 ρ v₁² + ρ g h₁ = 1/2 ρ v₂² + ρ g h₂        (1)

where

h = elevation height (m)

ρ = density (kg/m³)

v = flow velocity (m/s)

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)

where

q = flow rate (m³/s)

A = flow area (m²)

(2) can be modified to:

q = v₁ h₁ b

    = v₂ h₂ b      (3)

where

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 = c_d h₂ b [2 g h₁]^1/2      (7)

where

c_d = 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.