Full Answer Section

Activities:

1. Determine the Required Flow Rate:

   • You need to estimate the water demand for the intended use of the purified water stored in Overhead Tank 2. This will dictate the required flow rate through the treatment plant. Without this information, you’ll have to assume a flow rate for design purposes.
   • Consider peak demand and average demand. The pump and pipelines should be sized for the peak demand.

2. Calculate Pressure Drop in Each Section of the Pipeline:

   • Friction Losses (Major Losses): Use the Darcy-Weisbach equation:

     ΔP_f = f * (L/D) * (ρ * v^2 / 2)
     

     Where:

     • ΔP_f = Pressure drop due to friction
     • f = Darcy friction factor (depends on Reynolds number and pipe roughness)
     • L = Length of the pipe section (you’ll need to measure these from a scaled drawing or be given values)
     • D = Diameter of the pipe (this is what you need to size)
     • ρ = Density of water
     • v = Velocity of water in the pipe (v = Q/A, where Q is flow rate and A is cross-sectional area)
   • Minor Losses: Account for pressure drops due to fittings (bends, valves, entrances, exits). Use the minor loss coefficient (K) method:

     ΔP_m = K * (ρ * v^2 / 2)
     

     Where:

     • ΔP_m = Pressure drop due to minor losses
     • K = Minor loss coefficient (values depend on the type and number of fittings; you’ll need to look these up in fluid mechanics tables)
   • Total Pressure Drop: Sum the friction losses and minor losses for the entire pipeline from the pump intake to the inlet of Overhead Tank 2. You’ll need to do this iteratively as the velocity depends on the pipe diameter you are trying to determine.

3. Determine the Static Head:

   • This is the difference in elevation between the water level at the pump intake (assuming it’s drawing from a ground source, the lowest level) and the highest water level in Overhead Tank 2.

4. Calculate the Total Head Required by the Pump (H):

   • H = Static Head + (Total Pressure Drop / (ρ * g))
     • Where g is the acceleration due to gravity.

5. Select a Suitable Pump:

   • Based on the required flow rate (Q) and the total head (H), consult pump performance curves (provided by manufacturers).
   • Consider the pump’s efficiency at the operating point.
   • Select a pump type suitable for water treatment (e.g., centrifugal pump).
   • Determine the required power of the motor to drive the pump, considering the pump’s efficiency.

6. Size the Pipelines:

   • Choose a pipe diameter that results in an acceptable pressure drop and flow velocity. Higher velocities lead to higher friction losses but smaller pipe diameters (potentially lower cost). Lower velocities lead to lower friction losses but larger pipe diameters (potentially higher cost). There’s an economic optimum. Standard pipe sizes should be considered.

PowerPoint Presentation (Part A):

• Introduction: Briefly state the objective of sizing pipelines and selecting a pump for the water treatment plant.
• Assumptions: Clearly state any assumptions made regarding the required flow rate, water temperature, pipe material (which affects roughness), and the number and type of bends and valves.
• Flow Rate Calculation (if applicable): Explain how the required flow rate was determined or the assumed value used.
• Pipeline Layout: Show the schematic of the pipeline from the pump to Overhead Tank 2.
• Pressure Drop Calculations:
  • Explain the Darcy-Weisbach equation and the parameters involved.
  • Provide a table showing the calculated friction loss for each pipe section (based on assumed/calculated diameter).
  • Explain the minor loss coefficient method and provide a table showing the calculated minor losses for each type of fitting.
  • Present the total pressure drop calculation.
• Static Head Calculation: Show the elevation difference used.
• Total Head Calculation: Clearly state the total head the pump needs to overcome.
• Pump Selection:
  • Describe the type of pump selected and the reasons for this choice.
  • Present the operating point (flow rate and head) on a representative pump performance curve (you can use a generic curve for demonstration).
  • State the selected pump model (if you were able to choose one based on hypothetical data).
  • Calculate the required motor power.
• Pipe Sizing:
  • Justify the selected pipe diameter(s) based on the pressure drop and velocity considerations.
  • Mention the pipe material and its roughness factor.

B. Designing a Venturi Flow Meter:

A venturi meter works based on Bernoulli’s principle and the principle of continuity. When the fluid flows through the converging section of the venturi, its velocity increases, and its pressure decreases. The pressure difference between the upstream section (throat) and the constricted section (throat) is measured and can be used to determine the flow rate.

Activities:

1. Determine the Design Parameters:

   • Upstream Pipe Diameter (D1): This will be the diameter of the pipeline where the venturi will be installed (determined in Part A).
   • Throat Diameter (D2): This is the constricted section of the venturi. You need to design this. A typical ratio of D2/D1 is between 0.3 and 0.7. A smaller D2 will result in a larger pressure difference, making it easier to measure but also causing a larger permanent head loss.
   • Converging and Diverging Angles: Standard angles are typically used for efficient flow and minimal head loss (e.g., converging angle of 15-20 degrees, diverging angle of 5-7 degrees).
   • Length of the Throat: A relatively short throat ensures the pressure measurement is taken at the point of maximum velocity.

2. Apply Bernoulli’s Equation and Continuity Equation:

   • Continuity Equation: A1 * v1 = A2 * v2 (where A is cross-sectional area and v is velocity at sections 1 and 2)
   • Bernoulli’s Equation (simplified for horizontal flow): P1 + (ρ * v1^2 / 2) = P2 + (ρ * v2^2 / 2)
   • Where P1 is the upstream pressure and P2 is the throat pressure.

3. Derive the Flow Rate Equation:

   • By combining the continuity and Bernoulli’s equations, you can derive the equation for the theoretical flow rate (Qt):

     Qt = A2 * sqrt(2 * (P1 - P2) / (ρ * (1 - (A2/A1)^2)))
     

4. Introduce the Discharge Coefficient (Cd):

   • The actual flow rate (Qa) is less than the theoretical flow rate due to frictional losses and non-ideal flow. A discharge coefficient (Cd), typically between 0.95 and 0.98 for well-designed venturi meters, is introduced:

     Qa = Cd * A2 * sqrt(2 * (P1 - P2) / (ρ * (1 - (A2/A1)^2)))
     

5. Design the Venturi Meter:

   • Choose a suitable throat diameter (D2) based on the desired pressure difference for the expected flow rate and the acceptable permanent head loss. You might need to iterate on this.
   • Specify the dimensions of the converging and diverging sections.
   • Indicate the locations for pressure taps.

PowerPoint Presentation (Part B):

• Introduction: Explain the purpose of a venturi flow meter and its working principle based on Bernoulli’s and continuity equations.
• Schematic of the Venturi Meter: Show a diagram of a venturi meter with its main components (converging section, throat, diverging section, pressure taps).
• Working Principle: Explain how the change in area leads to changes in velocity and pressure.
• Equations: Present the continuity equation, Bernoulli’s equation, and the derived flow rate equation (both theoretical and with the discharge coefficient).
• Design Parameters: Specify the chosen upstream diameter (D1), designed throat diameter (D2), converging and diverging angles, and throat length. Justify your choice of D2.
• Pressure Difference Measurement: Briefly explain how the pressure difference (P1 – P2) would be measured (e.g., using a differential pressure transducer or manometer).
• Flow Rate Calculation: Show how the flow rate can be calculated from the measured pressure difference using the derived equation and the discharge coefficient.
• Advantages of Venturi Meter: Briefly mention the advantages (low head loss compared to orifice plates, relatively accurate).

C. Selecting Appropriate Check Valves:

Check valves are essential to prevent backflow in the pipeline, which can damage equipment (like the pump) and contaminate the purified water. They should be installed before each filtration unit on the supply lines (as per the schematic).