Certainly! Let’s solve the given questions step by step. --- # **Step-by-Step Solution** ## **Given Data** For each product, initial and final total solids (TS): | Product | Initial TS (%) | Final TS (%) | |---------|:--------------:|:------------:| | Tomato Juice (A) | 8 | 28 | | Sugarcane Juice (B) | 16 | 60 | | Milk (C) | 12 | 45 | **Feed amount:** 100 kg (basis) --- ## **a. Mass of Water to be Evaporated per 100 kg Feed** ### **General Formula** \[ \text{Final Product Mass} = \frac{\text{Initial TS (\%)}}{\text{Final TS (\%)}} \times \text{Feed Mass} \] \[ \text{Water Evaporated} = \text{Feed Mass} - \text{Final Product Mass} \] --- ### **1. Tomato Juice** - Initial TS: 8%, Final TS: 28% \[ \text{Final Mass} = \frac{8}{28} \times 100 = 285.7~\text{kg} \] \[ \text{Water Evaporated} = 100 - 285.7 = 714.3~\text{kg} \] --- ### **2. Sugarcane Juice** - Initial TS: 16%, Final TS: 60% \[ \text{Final Mass} = \frac{16}{60} \times 100 = 266.7~\text{kg} \] \[ \text{Water Evaporated} = 100 - 266.7 = 733.3~\text{kg} \] --- ### **3. Milk** - Initial TS: 12%, Final TS: 45% \[ \text{Final Mass} = \frac{12}{45} \times 100 = 266.7~\text{kg} \] \[ \text{Water Evaporated} = 100 - 266.7 = 733.3~\text{kg} \] --- ## **b. Evaporation Ratio (kg water evaporated/kg feed)** \[ \text{Evaporation Ratio} = \frac{\text{Water Evaporated}}{100} \] - **Tomato Juice:** \(.714\) - **Sugarcane Juice:** \(.733\) - **Milk:** \(.733\) --- ## **c. Heat Available in Effect 1** \[ \text{Heat Available} = \text{U} \times \text{A} \times \Delta T \] Where: - U (Effect 1) = 130 W/m²·K - Area = 50 m² - ΔT = \(120 - 95 = 25^\circ\)C \[ \text{Heat Available} = 130 \times 50 \times 25 = 1,625,000~\text{W} \] Convert to kJ/hr (1 W = 1 J/s; 1 hr = 360 s): \[ 1,625,000~\text{W} \times 360~\text{s} = 5,850,000,000~\text{J/hr} = 5,850,000~\text{kJ/hr} \] --- ## **d. Water Evaporation Rate in Effect 1** \[ \text{Latent Heat of Vaporization} = 225~\text{kJ/kg} \] \[ \text{Water Evaporation Rate} = \frac{\text{Heat Available}}{\text{Latent Heat}} = \frac{5,850,000}{225} = 2,600~\text{kg/hr} \] --- ## **e. Estimate the Steam Economy** **Steam Economy (SE):** \[ \text{SE} = \frac{\text{kg water evaporated}}{\text{kg steam used}} \] For triple-effect, typical SE is **2.4–2.8**. --- ## **f. Steam Required per 1,000 kg Feed** \[ \text{Steam Required} = \frac{\text{Water Evaporated}}{\text{Steam Economy}} \] - **Tomato Juice:** \( \frac{714.3}{2.6} = 274.7~\text{kg} \) - **Sugarcane Juice:** \( \frac{733.3}{2.6} = 282~\text{kg} \) - **Milk:** \( \frac{733.3}{2.6} = 282~\text{kg} \) --- ## **g. Heat Sensitivity and Quality Impacts** | Product | Color Degradation | Flavour Changes | Protein Denaturation | Viscosity/Fouling | Need for Vacuum | |----------------|------------------|-----------------|---------------------|-------------------|-----------------| | Tomato Juice | Lycopene loss | Yes | Not relevant | High (fouling) | Yes | | Sugarcane Juice| Browning | Caramelization | Not relevant | Very high | Yes | | Milk | Mild browning | Yes | High | Moderate (scorching)| Yes | --- ## **h. Highest Risk of Quality Deterioration** **Sugarcane Juice**: - Very high viscosity at final TS, highest boiling point rise, non-Newtonian behavior, and high risk of caramelization. --- ## **i. Most Suitable Evaporator Type and Sketch** | Product | Recommended Evaporator Type | Justification | |----------------|---------------------------------------|--------------------------------------------------------| | Tomato Juice | Falling-film, low temp, short residence| Minimizes fouling, heat damage, preserves color | | Sugarcane Juice| Short-tube/falling-film, vacuum | Minimizes caramelization, handles high viscosity | | Milk | Falling-film, vacuum, low temp | Minimizes protein denaturation, foaming, scorching | **Sketches:** Draw a basic schematic for each, showing feed, multiple effects, steam inlet, and vapor outlet. --- ### **Summary Table** | Product | Water Evaporated (kg) | Evap. Ratio | Steam Required (kg) | Main Quality Risk | |----------------|----------------------|-------------|---------------------|------------------------------| | Tomato Juice | 714.3 | .714 | 274.7 | Color, fouling | | Sugarcane Juice| 733.3 | .733 | 282 | Caramelization, viscosity | | Milk | 733.3 | .733 | 282 | Protein denaturation, scorching| --- ## **Final Answers** ### **a. Water to Evaporate (per 100 kg feed):** - Tomato: **714.3 kg** - Sugarcane: **733.3 kg** - Milk: **733.3 kg** ### **b. Evaporation Ratio:** - Tomato: **.714** - Sugarcane: **.733** - Milk: **.733** ### **c. Heat Available in Effect 1:** - **5,850,000 kJ/hr** ### **d. Water Evaporation Rate in Effect 1:** - **2,600 kg/hr** ### **e. Steam Economy:** - **2.6** (typical for triple-effect) ### **f. Steam Required per 1,000 kg Feed:** - Tomato: **274.7 kg** - Sugarcane: **282 kg** - Milk: **282 kg** ### **g. Quality Impacts:** See table above. ### **h. Highest Risk:** **Sugarcane Juice** (caramelization, viscosity) ### **i. Most Suitable Type:** **Falling-film or short-tube evaporator under vacuum** for all, with special attention to sugarcane juice for viscosity. --- If you need the **sketch diagrams**, let me know!