# Step-by-Step Solutions --- ## 2(a): **Critical Deposition Velocity** **Question:** In relation to settling slurries, what is meant by "critical deposition velocity"? **Solution & Explanation:** - **Definition:** Critical deposition velocity the minimum velocity which a slurry must be transported in a pipeline to ensure that the solid particles remain suspended and do not settle to the bottom. - **Significance:** If the velocity falls below this value, solids start to deposit, forming a stationary or sliding bed, which may cause blockages or increased wear in the pipeline. - **Final Answer:** > Critical deposition velocity is the minimum flow velocity required in a pipeline to prevent particles in a settling slurry from depositing and forming a stationary bed at the bottom of the pipe. --- ## 2(b)(i): **Importance of Size Reduction in Slurry Transportation** **Solution & Explanation:** - **Reduces Settling Rate:** Smaller particles settle more slowly, reducing the risk of deposition. - **Improves Flowability:** Fine particles create a more homogeneous mixture, improving pumpability and reducing wear. - **Prevents Blockages:** Smaller, uniform particles are less likely to bridge or clog pipes. - **Uniform Product Quality:** Necessary for downstream processing and quality control. - **Energy Efficiency:** Finer particles may require less energy for transport due to reduced frictional losses. - **Final Answer:** > Size reduction in slurry transportation minimizes particle settling rates, enhances flowability, prevents pipeline blockages, ensures uniform product quality, and can improve energy efficiency by producing a more homogenous and easily transportable slurry. --- ## 2(b)(ii): **Moisture Removal at End of Slurry Transportation** **Options and Order of Preference:** 1. **Thickening:** Uses gravity to concentrate solids; low cost, suitable for large volumes. 2. **Filtration:** Removes water by passing slurry through a filter medium; gives drier cake than thickening. 3. **Centrifugation:** Uses centrifugal force; suitable for fine particles or when filtration is difficult. 4. **Drying:** Removes remaining moisture by evaporation; high energy cost, used for final moisture removal. **Order of Preference:** 1. Thickening (first, due to low cost and high capacity) 2. Filtration (second, for further moisture reduction) 3. Centrifugation (alternative to filtration, especially for fine particles) 4. Drying (last, for final moisture removal) **Final Answer:** > Moisture can be removed using thickening (gravity concentration), filtration, centrifugation, and drying. The preferred order is usually thickening, then filtration or centrifugation, and finally drying, as each step progressively reduces moisture content and increases energy requirements. --- ## 2(b)(iii): **Considerations for Selecting a Pump for Slurry Transportation** **Key Factors:** - **Slurry Properties:** Particle size, concentration, abrasiveness, and corrosiveness. - **Flow Rate & Pressure Requirements:** Needed to maintain critical deposition velocity and overcome pipeline friction. - **Material of Construction:** Must resist wear and corrosion from slurry. - **Pump Type:** Centrifugal pumps are common, but positive displacement pumps may be used for high-viscosity slurries. - **Maintenance & Reliability:** Easy maintenance and high durability are important due to abrasive nature. **Final Answer:** > When selecting a pump for slurry transportation, consider slurry characteristics (particle size, concentration, abrasiveness), required flow rate and pressure, material compatibility, pump type (centrifugal vs. positive displacement), and ease of maintenance and reliability. --- ## 2(c): **Rheological Models for Non-Settling Suspensions at High Concentrations** **Three Models:** 1. **Bingham Plastic Model:** \[ \tau = \tau_y + \mu_p \dot{\gamma} \] where \(\tau\) = shear stress, \(\tau_y\) = yield stress, \(\mu_p\) = plastic viscosity, \(\dot{\gamma}\) = shear rate. 2. **Power Law (Ostwald-de Waele) Model:** \[ \tau = K \dot{\gamma}^n \] where \(K\) = consistency index, \(n\) = flow behavior index. 3. **Herschel-Bulkley Model:** \[ \tau = \tau_y + K \dot{\gamma}^n \] where \(\tau_y\) = yield stress, \(K\) = consistency index, \(n\) = flow behavior index. **Final Answer:** > Three models for the rheological behavior of non-settling suspensions at high concentrations are: > 1. **Bingham Plastic Model:** \(\tau = \tau_y + \mu_p \dot{\gamma}\) > 2. **Power Law Model:** \(\tau = K \dot{\gamma}^n\) > 3. **Herschel-Bulkley Model:** \(\tau = \tau_y + K \dot{\gamma}^n\) --- ### **Summary Table** | Part | Final Answer Summary | |---------------|------------------------------------------------------------------------------------------------------| | 2(a) | Minimum velocity to prevent solid deposition in slurry pipelines. | | 2(b)(i) | Size reduction minimizes settling, improves flow, prevents blockages, and ensures uniformity. | | 2(b)(ii) | Moisture removal by thickening, filtration, centrifugation, drying (in order of preference). | | 2(b)(iii) | Consider slurry properties, flow/pressure needs, material, pump type, and reliability. | | 2(c) | Bingham Plastic (\(\tau = \tau_y + \mu_p \dot{\gamma}\)), Power Law (\(\tau = K \dot{\gamma}^n\)), Herschel-Bulkley (\(\tau = \tau_y + K \dot{\gamma}^n\)). | If you need further detail or expanded explanations for any part, let me know!