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Sludge Age given Concentration of Solids Formula

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Sludge Age given Concentration of Solids is the average length of time that solids (or sludge) remain in the treatment system before being removed. Check FAQs

θ c' = \frac{V \cdot X sa}{(Q w \cdot X R) + (Q max - Q w) \cdot X E}

θ_c' - Sludge Age given Concentration of Solids?V - Volume of Tank?X_sa - MLSS given Sludge Age?Q_w - Volume of Wasted Sludge per day?X^R - Concentration of Solids in Returned Sludge?Q_max - Peak Sewage Flow?X^E - Concentration of Solids in Effluent?

Sludge Age given Concentration of Solids Example

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Here is how the Sludge Age given Concentration of Solids equation looks like with Values.

Here is how the Sludge Age given Concentration of Solids equation looks like with Units.

Here is how the Sludge Age given Concentration of Solids equation looks like.

0.4378 = \frac{9 \cdot 91200}{(9.5 \cdot 0.526) + (11.17 - 9.5) \cdot 10}

0.4378d = \frac{9m³ \cdot 91200mg/L}{(9.5m³/s \cdot 0.526mg/L) + (11.17m³/s - 9.5m³/s) \cdot 10mg/L}

0.4378 = \frac{9 \cdot 91200}{(9.5 \cdot 0.526) + (11.17 - 9.5) \cdot 10}

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Sludge Age given Concentration of Solids Solution

Follow our step by step solution on how to calculate Sludge Age given Concentration of Solids?

FIRST Step Consider the formula

θ c' = \frac{V \cdot X sa}{(Q w \cdot X R) + (Q max - Q w) \cdot X E}

Next Step Substitute values of Variables

∴

θ c' = \frac{9m³ \cdot 91200mg/L}{(9.5m³/s \cdot 0.526mg/L) + (11.17m³/s - 9.5m³/s) \cdot 10mg/L}

Next Step Convert Units

∴

θ c' = \frac{9m³ \cdot 91.2kg/m³}{(9.5m³/s \cdot 0.0005kg/m³) + (11.17m³/s - 9.5m³/s) \cdot 0.01kg/m³}

Next Step Prepare to Evaluate

∴

θ c' = \frac{9 \cdot 91.2}{(9.5 \cdot 0.0005) + (11.17 - 9.5) \cdot 0.01}

Next Step Evaluate

∴

θ c' = 37830.1147624096s

Next Step Convert to Output's Unit

∴

θ c' = 0.437848550490851d

LAST Step Rounding Answer

∴

θ c' = 0.4378d

Sludge Age given Concentration of Solids Formula Elements

Variables

Sludge Age given Concentration of Solids

Sludge Age given Concentration of Solids is the average length of time that solids (or sludge) remain in the treatment system before being removed.

Symbol: θ_c'

Measurement: TimeUnit: d

Note: Value should be greater than 0.

Volume of Tank

Volume of Tank is defined as the capacity of flocculation and mixing tank.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

MLSS given Sludge Age

MLSS given Sludge Age is the concentration of suspended solids in the mixed liquor of an activated sludge system.

Symbol: X_sa

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Volume of Wasted Sludge per day

Volume of Wasted Sludge per day is the amount of sludge that is removed from a wastewater treatment process within a 24-hour period.

Symbol: Q_w

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Concentration of Solids in Returned Sludge

Concentration of Solids in Returned Sludge is the density of solid particles present in the sludge that is returned from the secondary settling tanks to the aeration tank.

Symbol: X^R

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Peak Sewage Flow

Peak Sewage Flow refers to the maximum rate at which sewage is discharged from a community or a facility over a short period.

Symbol: Q_max

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Concentration of Solids in Effluent

Concentration of Solids in Effluent is the amount of solid particles, both suspended and dissolved, present in a liquid effluent (wastewater or other discharged liquid).

Symbol: X^E

Measurement: DensityUnit: mg/L

Note: Value should be greater than 0.

Credits

Creator Image

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verifier Image

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other formulas in Sludge Age category

Go Mass of Wasted Activated Sludge

M ws = (Y \cdot Q s \cdot (Q i - Q o)) - (K e \cdot V \cdot X')

Go Concentration of Solids in Returned Sludge given MLSS

X Em = \frac{X' \cdot V}{Q w \cdot θ c}

See More

How to Evaluate Sludge Age given Concentration of Solids?

Sludge Age given Concentration of Solids evaluator uses Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent) to evaluate the Sludge Age given Concentration of Solids, The Sludge Age given Concentration of Solids formula is defined as the calculation of the sludge age when we have prior information of concentration of solids. Sludge Age given Concentration of Solids is denoted by θ_c' symbol.

How to evaluate Sludge Age given Concentration of Solids using this online evaluator? To use this online evaluator for Sludge Age given Concentration of Solids, enter Volume of Tank (V), MLSS given Sludge Age (X_sa), Volume of Wasted Sludge per day (Q_w), Concentration of Solids in Returned Sludge (X^R), Peak Sewage Flow (Q_max) & Concentration of Solids in Effluent (X^E) and hit the calculate button.

FAQs on Sludge Age given Concentration of Solids

What is the formula to find Sludge Age given Concentration of Solids?

The formula of Sludge Age given Concentration of Solids is expressed as Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent). Here is an example- 5.1E-6 = (9*91.2)/((9.5*0.000526)+(11.17-9.5)*0.01).

How to calculate Sludge Age given Concentration of Solids?

With Volume of Tank (V), MLSS given Sludge Age (X_sa), Volume of Wasted Sludge per day (Q_w), Concentration of Solids in Returned Sludge (X^R), Peak Sewage Flow (Q_max) & Concentration of Solids in Effluent (X^E) we can find Sludge Age given Concentration of Solids using the formula - Sludge Age given Concentration of Solids = (Volume of Tank*MLSS given Sludge Age)/((Volume of Wasted Sludge per day*Concentration of Solids in Returned Sludge)+(Peak Sewage Flow-Volume of Wasted Sludge per day)*Concentration of Solids in Effluent).

Can the Sludge Age given Concentration of Solids be negative?

No, the Sludge Age given Concentration of Solids, measured in Time cannot be negative.

Which unit is used to measure Sludge Age given Concentration of Solids?

Sludge Age given Concentration of Solids is usually measured using the Day[d] for Time. Second[d], Millisecond[d], Microsecond[d] are the few other units in which Sludge Age given Concentration of Solids can be measured.

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