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Head loss in water treatment trash racks

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Input data

Flow (Q)

Channel width (b)

Bar width (w)

Distance between bars (d)

Downstream water depth (yj)

Bar slope (𝝓)

Kirschmer β

Output data

Upstream velocity (Um)

Upstream energy (Em)

Upstream water depth (ym)

Downstream velocity (Uj)

Between bars velocity (U)

Downstream energy (Ej)

Head loss (Hf)

Water level difference (ym - yj)

Upstream depth at 50% obstruction (ym50%)

Upstream velocity at 50% obstruction (Um50%)

Upstream energy at 50% obstruction (Em50%)

Head loss at 50% obstruction (hf50%)

Between bars velocity at 50% obstruction (U50%)

Water level difference at 50% obstruction (ym50% - yj)

Description

Head Loss in Water Treatment Trash Racks

This calculation determines the head loss across trash racks used in water treatment, evaluating upstream and downstream depths, velocities, specific energies, and head loss for both clean and 50% obstructed conditions.

Trash rack Trash rack

Calculation Methods

Given downstream depth
Calculates parameters based on provided downstream water depth.
Given upstream depth
Calculates parameters based on provided upstream water depth.

Inputs and Outputs

Inputs

Parameter	Units	Description
Flow ( $Q$ )	m³/s	Water volumetric flow rate
Channel width ( $b$ )	m	Width of the channel
Bar width ( $w$ )	m	Width of the trash rack bars
Distance between bars ( $d$ )	m	Spacing between bars
Downstream water depth ( $y_j$ )	m	Water depth at the downstream side
Upstream water depth ( $y_m$ )	m	Water depth at the upstream side
Bar slope (𝝓)	deg	Angle of the bars relative to the flow
Kirschmer $\beta$	-	Dimensionless Kirschmer coefficient

Outputs

Parameter	Units	Description
Flow ( $Q_{out}$ )	m³/s	Volumetric flow rate
Upstream velocity ( $U_m$ )	m/s	Velocity at the upstream
Upstream energy ( $E_m$ )	J	Specific energy at the upstream
Upstream water depth ( $y_m$ )	m	Water depth at the upstream
Downstream velocity ( $U_j$ )	m/s	Velocity at the downstream
Between bars velocity ( $U$ )	m/s	Average velocity between bars
Downstream energy ( $E_j$ )	J	Specific energy at the downstream
Head loss ( $H_f$ )	m	Total head loss
Water level difference ( $y_m - y_j$ )	m	Height difference between upstream and downstream
Upstream depth at 50% obstruction ( $y_{50\%}$ )	m	Upstream depth considering 50% obstruction
Upstream velocity at 50% obstruction ( $U_{m50\%}$ )	m/s	Upstream velocity considering 50% obstruction
Upstream energy at 50% obstruction ( $E_{m50\%}$ )	J	Upstream energy considering 50% obstruction
Head loss at 50% obstruction ( $H_{f50\%}$ )	m	Head loss considering 50% obstruction
Between bars velocity at 50% obstruction ( $U_{50\%}$ )	m/s	Velocity between bars at 50% obstruction
Water level difference at 50% obstruction ( $y_{50\%} - y_j$ )	m	Height difference at 50% obstruction

References

Vianna, Marcos R. Produção, reservação e distribuição de água. e-book. Belo Horizonte, Bloom, 2021.
American Water Works Association. (2012). Water treatment plant design. McGraw Hill Professional.