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**How to design the Head of Filter feed pump in Sewage Treatment Plant?**

**Filter feed pumps** are essential components of **sewage treatment plants**. They are responsible for transferring water from one stage of the treatment process to another. The head of the filter feed pump is one of the most critical design parameters for achieving efficient and effective operation.

Here now we will cover the design formula and technical calculations necessary for designing the head of a filter feed pump, with the help of a case study for better understanding.

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**Design Formula for Head of Filter Feed Pump:**

The head of the filter feed pump is the difference between the discharge pressure and the suction pressure. It is the amount of energy required to lift the water from the suction side to the discharge side of the pump. The formula for calculating the head of a filter feed pump is as follows:

**Head = (Discharge Pressure – Suction Pressure) / Specific Gravity**

Where,

Discharge Pressure: The pressure of the fluid at the discharge side of the pump.

Suction Pressure: The pressure of the fluid at the suction side of the pump.

Specific Gravity: The specific gravity of the fluid being pumped.

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**Technical Calculations Formula: **

The technical calculations formula for designing the head of a filter feed pump is as follows:

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** 1. ****Calculate the Total Dynamic Head (TDH): **

TDH = Hs + Hf + Hl

Where,

Hs: Static Head (m)

Hf: Friction Head (m)

Hl: Losses Head (m)

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**2. ****Calculate the Static Head (Hs):**

** **Hs = (Hwf + Hdt + Hbf + Ht + Hm) – Hwf

Where,

Hwf: Water level fluctuation (m)

Hdt: Design top of water level (m)

Hbf: Bottom of filter bed (m)

Ht: Thickness of filter bed (m)

Hm: Media depth (m)

###
**3. ****Calculate the Friction Head (Hf): **

** **Hf = (f x L x Q²) / (D x 2g)

Where,

f: Darcy-Weisbach friction factor

L: Length of the pipeline (m)

Q: Flow rate (m³/hr)

D: Diameter of the pipeline (m)

g: Acceleration due to gravity (m/s²)

###
**4. ****Calculate the Losses Head (Hl): **** **

Hl = Hs x l

Where,

l: Loss factor

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**Case Study: **

Let us consider the following case study to illustrate the design formula and technical calculations for the head of a filter feed pump.

Design a filter feed pump for a sewage treatment plant having the following specifications:

• Flow rate = 500 m³/hr

• Suction pressure = 0.5 bar** **

** **• Discharge pressure = 1.5 bar** **

** **• Specific gravity = 1.0** **

** **• Length of the pipeline = 50 m** **

** **• Diameter of the pipeline = 300 mm

** **• Water level fluctuation = 2.0 m** **

** **• Design top of water level = 5.0 m** **

** **• Bottom of filter bed = 3.5 m** **

** **• Thickness of filter bed = 1.5 m** **** **

** **• Media depth = 1.0 m

• Loss factor = 0.02

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**Solution:**

Calculate the Total Dynamic Head (TDH):

TDH = Hs + Hf + Hl

TDH = (Hwf + Hdt + Hbf + Ht + Hm) - Hwf + (f x L x Q²) / (D x 2g) + Hs x l

TDH = (2.0 + 5.0 + 3.5 + 1.5 + 1.0) - 2.0 + (0.02 x 50 x 500²) / (0.3 x 2 x 9.81) + (13.0 x 0.02)

TDH = 21.08 m

Calculate the Static Head (Hs):

Hs = (Hwf + Hdt + Hbf + Ht + Hm) – Hwf

Hs = (2.0 + 5.0 + 3.5 + 1.5 + 1.0) - 2.0

Hs = 11.0 m

Calculate the Friction Head (Hf):

To calculate the friction head, we need to determine the Darcy-Weisbach friction factor (f). The friction factor depends on the

Reynolds number (Re), which is calculated as follows:

**Re = (D x Q) / (A x v)**

Where,

A: Cross-sectional area of the pipe (m²)

v: Kinematic viscosity of the fluid (m²/s)

Assuming the kinematic viscosity of water to be 10?? m²/s, the Reynolds number is:

Re = (0.3 x 500) / (0.07 x 10??)

Re = 2,142,857.14

Using Moody's chart, we can find the friction factor corresponding to the Reynolds number and the roughness of the pipe. Assuming a pipe roughness of 0.03 mm, the friction factor is approximately 0.018.

Now, we can calculate the friction head as follows:

Hf = (f x L x Q²) / (D x 2g)

Hf = (0.018 x 50 x 500²) / (0.3 x 2 x 9.81)

Hf = 3.47 m

Calculate the Losses Head (Hl):

Hl = Hs x l

Hl = 11.0 x 0.02

Hl = 0.22 m

Finally, we can calculate the head of the filter feed pump as:

**Head = (Discharge Pressure – Suction Pressure) / Specific Gravity **** **

Head = (1.5 – 0.5) / 1.0

Head = 1.0 m

Therefore, the total head required for designing the filter feed pump is:

Total Head = TDH + Head

Total Head = 21.08 + 1.0

Total Head = 22.08 m

**Summary: **

Designing the head of a filter feed pump in a sewage treatment plant is critical for achieving efficient and effective operation. The design formula and technical calculations for the head of the filter feed pump depend on various parameters such as flow rate, suction pressure, discharge pressure, specific gravity, length and diameter of the pipeline, water level fluctuation, design top of water level, bottom of filter bed, thickness of filter bed, media depth, and loss factor. By using the design formula and technical calculations in a case study, we can determine the total head required for designing the filter feed pump.

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References:

TDH -Pumps and Pumping System" by S. Sivakumar and P. Sundararajan

Hs - "Fluid Mechanics" by Frank M. White

Hf - "Fluid Mechanics" by Frank M. White

Hl - "Fluid Mechanics" by Frank M. White