WATER FILTRATION PLANT

Full Answer Section

Sizing Pipelines and Selecting a Suitable Pump (LOs: 1, 2, 3, 4)

To size the pipelines and select a pump, we need to consider the following:

1. Flow Rate (Q): This is the most crucial parameter. We need to know the desired flow rate of purified water to be stored in Overhead Tank 2 per unit time (e.g., liters per second, cubic meters per hour). This will depend on the intended usage and demand. Without this information, I will proceed with a conceptual approach. You will need to insert the actual required flow rate for your design.

2. Pipe Lengths (L): The problem statement mentions lengths of pipes to cooling coils, which seems irrelevant to the water treatment plant itself. We need the lengths of the pipes connecting the source, filtration units, and overhead tanks as per Figure 1. Let's denote these generically as L_{source-filter}, L_filter-OT1, L_OT1-filter (if applicable), and L_OT1-OT2.

3. Number of Bends and Fittings: Bends, elbows, valves (including the isolating valves), and other fittings introduce minor losses in the flow. We need to estimate the number and type of these fittings in each pipe section based on Figure 1. Each fitting can be converted to an equivalent length of straight pipe (L_eq) to account for these losses.

4. Fluid Properties: For water, we need its density (ρ ≈ 1000 kg/m³) and dynamic viscosity (μ ≈ 1.002 x 10⁻³ Pa·s at 20°C - this will vary with temperature).

5. Head Requirements (H): The total head the pump needs to overcome is the sum of:

   • Static Head (H_s): The vertical difference in elevation between the water level at the source (assuming a pump at the source) and the water level in Overhead Tank 2.
   • Friction Head Loss (H_f): The energy loss due to friction in the pipelines. This is calculated using the Darcy-Weisbach equation:

     H_f = f * (L + ΣL_eq) / D * (V^2 / (2g))
     

     where:
     • f is the Darcy friction factor (depends on the Reynolds number and pipe roughness).
     • L is the actual pipe length.
     • ΣL_eq is the sum of the equivalent lengths of all fittings.
     • D is the pipe diameter.
     • V is the average flow velocity in the pipe (V = Q / A, where A is the cross-sectional area of the pipe).
     • g is the acceleration due to gravity (9.81 m/s²).
   • Minor Losses (H_m): These are the head losses due to bends, valves, and other fittings, already accounted for using equivalent lengths in the Darcy-Weisbach equation in this approach.
   • Pressure Head Difference (ΔP/ρg): If Overhead Tank 2 operates at a different pressure than the source (unlikely for open tanks), this needs to be considered. Assuming atmospheric pressure for both open tanks, this component is zero.

Pipeline Sizing:

• We need to choose appropriate diameters (D) for each pipe section. This involves an iterative process:
  1. Assume a diameter for each pipe section based on the estimated flow rate. Higher flow rates generally require larger diameters to minimize velocity and friction losses. Standard pipe sizes should be considered.
  2. Calculate the flow velocity (V) in each pipe section using V = Q / A.
  3. Calculate the Reynolds number (Re) for each section: Re = (ρ * V * D) / μ.
  4. Determine the Darcy friction factor (f):
     • For laminar flow (Re < 2300): f = 64 / Re
     • For turbulent flow (Re > 4000): Use the Colebrook-White equation (iterative) or an approximation like the Haaland equation to find f, considering the pipe roughness (ε). Assume a reasonable roughness for commercial steel or PVC pipes.
  5. Calculate the friction head loss (H_f) for each pipe section using the Darcy-Weisbach equation with the assumed diameter.
  6. Check Velocity: Ensure the velocity is within an acceptable range (typically 1-3 m/s for water systems) to avoid excessive noise, erosion, and head loss.
  7. Adjust Diameter: If the head loss is too high or the velocity is outside the acceptable range, adjust the pipe diameter and repeat steps 2-6.

Pump Selection:

• Once the pipeline diameters are tentatively sized and the total head (H = H_s + ΣH_f) required to move the desired flow rate (Q) from the source to Overhead Tank 2 is calculated, we can select a suitable pump.
• Pump Performance Curve: Pumps are characterized by their performance curves, which plot head (H) against flow rate (Q) for a given impeller size and speed.
• Operating Point: The operating point of the system is where the system head curve (total head required at different flow rates) intersects the pump performance curve. We need to select a pump whose performance curve provides the required head at the desired flow rate with reasonable efficiency.
• Pump Type: Consider centrifugal pumps, which are commonly used for water transfer applications. The specific type (e.g., end-suction, submersible) will depend on the source location and installation requirements.
• Net Positive Suction Head Required (NPSHr): Ensure that the Net Positive Suction Head Available (NPSHa) at the pump suction is greater than the NPSHr of the selected pump to prevent cavitation. NPSHa depends on the suction head, atmospheric pressure, vapor pressure of water, and suction losses.
• Pump Power (P): The hydraulic power required by the pump is P_hydraulic = ρ * g * Q * H. The actual motor power will be higher due to pump efficiency (η_pump): P_motor = P_hydraulic / η_pump.

B. Designing a Venturi Flow Meter (LOs: 2, 3)

A Venturi meter is a flow measurement device that works based on the Bernoulli's principle and the principle of continuity. It consists of three main sections:

1. Converging Section: A gradually reducing conical section that increases the flow velocity and decreases the pressure.
2. Throat: A short, straight section with a smaller diameter where the velocity is maximum and the pressure is minimum.
3. Diverging Section: A gradually expanding conical section that decreases the flow velocity and recovers most of the pressure loss.

How the Venturi Works:

1. Continuity Equation: As the water flows through the converging section into the narrower throat, the principle of continuity (A₁V₁ = A₂V₂) dictates that the velocity of the water increases because the cross-sectional area decreases (A₂ < A₁).

2. Bernoulli's Principle: According to Bernoulli's principle, for a steady flow of an incompressible fluid, an increase in velocity is accompanied by a decrease in pressure (assuming negligible change in elevation). Therefore, the pressure in the throat (P₂) will be lower than the pressure in the upstream section (P₁).

3. Pressure Difference Measurement: Pressure taps are installed at the upstream section (before the convergence) and at the throat to measure the pressure difference (ΔP = P₁ - P₂).

4. Flow Rate Calculation: The flow rate (Q) can be calculated using the following equation derived from Bernoulli's principle and the continuity equation:

   Q = C_d * A₂ * sqrt(2 * (P₁ - P₂) / (ρ * (1 - (A₂/A₁)²)))
   

   where:

   • Q is the volumetric flow rate.
   • C_d is the discharge coefficient (a dimensionless factor that accounts for friction and non-ideal flow conditions, typically between 0.95 and 0.99).
   • A₁ is the cross-sectional area of the upstream pipe.
   • A₂ is the cross-sectional area of the throat.
   • P₁ is the pressure at the upstream section.
   • P₂ is the pressure at the throat.
   • ρ is the density of the water.

Venturi Meter Design Considerations:

• Upstream and Throat Diameters (D₁ and D₂): The ratio of the throat diameter to the upstream diameter (β = D₂/D₁) is a key design parameter. Typical β values range from 0.25 to 0.75. A smaller β results in a larger pressure difference for a given flow rate, making it easier to measure, but also leads to a higher permanent head loss.
• Length of Converging and Diverging Sections: Gradual tapers (typically 15-20 degrees for the converging section and 5-7 degrees for the diverging section) are used to minimize energy losses due to flow separation

Sample Answer

Okay, let's break down the design considerations for the water treatment plant as described. Since I cannot directly interact with Figure 1, I will make some reasonable assumptions about the piping layout based on a typical water treatment plant schematic. You will need to adapt these assumptions to the actual layout in Figure 1.

Assumed Piping Layout (Based on typical water treatment):

• Source to Filtration: A pipe network drawing raw groundwater from the source to the inlet of Filtration Plant 1, Filtration Plant 2, and Filtration Plant 3.
• Filtration to Overhead Tank 1: Pipes connecting the outlet of each Filtration Plant to Overhead Tank 1.
• Overhead Tank 1 to Filtration (Recirculation/Backwash - Assumption): Assuming a potential recirculation or backwash loop, pipes might exist from Overhead Tank 1 back to the filtration plants. If this is not the case in Figure 1, this part of the design will be simplified.
• Overhead Tank 1 to Overhead Tank 2: A pipe(s) transferring treated water from Overhead Tank 1 to Overhead Tank 2 for final storage.