Page History

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First, the various parameters from the above picture were calculated.
The width of the floc hopper had to line up evenly with the width of the sedimentation sludge drain (this side of the floc hopper lies on the sludge drain):

{latex}
\large
$$
W_{FlocHopper} = W_{SedSludgeFlat}
$$
{latex}

The length of the floc hopper is required to cover the entire width of the sedimentation tank, so the two must be equal:

{latex}
\large
$$
L_{FlocHopper} = W_{SedBayActual}
$$
{latex}

The first lamella and the floc hopper must be lined up vertically - in order for this to happen, the horizontal distance from the bottom of the first lamella to the chimney wall must be equal to the horizontal distance from the top of the floc hopper to the chimney wall.
The horizontal length from the bottom of the first lamella to the chimney wall:

{latex}
\large
$$
L_{FlocHopperOffset} = L_{SedPlate} \cdot \cos \left( {AN_{SedPlate}} \right)
$$
{latex}

The vertical component of the floc hopper's height depended on the elevation of the sedimentation inlet slopes, as well as the height of the sedimentation sludge drain. The vertical height:

{latex}
\large
$$
Z_{FlocHopper}= Z_{SedSlopes} - H_{SedSludge}
$$
{latex}

 The actual height of the floc hopper was calculated using the Pythagoreas Theorem, with L.FlocHopperOffset and Z.FlocHopper serving as the two sides of a right triangle, and the height of the floc hopper as the hypotenuse:

{latex}
\large
$$
H_{FlocHopper} = ({L_{FlocHopperOffset}^2 + Z_{FlocHopper}^2})^{{1 \over 2}}
$$
{latex}

The thickness of the floc hopper was assumed to be equal to the thickness of the sedimentation slope plate:

{latex}
\large
$$
T_{FlocHopper}= T_{SedSlopePlate}
$$
{latex}

The angle that the floc hopper must be rotated was then calculated. With respect to the sedimentation sludge drain, the angle the floc hopper must be rotated:

{latex}
\large
$$
AN_{FlocHopper} = atan\left( {{{Z_{FlocHopper}} \over {L_{FlocHopperOffset}}}} \right)
$$
{latex}