Question Bank • QB_APE_DRY_001 NAT • 2 Marks

Section 6: Agricultural Process Engineering

Evaporation and Drying

Subtopic: Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers

Question Statement:

A forward-feed double-effect evaporator is used to concentrate $6000\text{ kg/h}$ of tomato juice from an initial total solids content of $8.0\%\text{ (w/w)}$ to a final concentration of $24.0\%\text{ (w/w)}$. The steam economy of the double-effect evaporator system is $1.75\text{ kg water evaporated / kg steam supplied}$. The required mass flow rate of fresh steam supplied to the first effect is ________ $\text{kg/h}$ (round off to two decimal places).

Answer Key:

2285.71

Step-by-Step Solution & Explanation

Multi-Approach Solution: **Method 1: Overall Solids and Water Balance** 1. Feed flow rate: $F = 6000\text{ kg/h}$, with solids fraction $x_F = 0.08$. Total solids: $S = 6000 \times 0.08 = 480\text{ kg/h}$. 2. Product flow rate ($P$): $P = 480 / 0.24 = 2000\text{ kg/h}$. 3. Total water evaporated ($V$): $V = 6000 - 2000 = 4000\text{ kg/h}$. 4. Steam consumption ($S_{\text{steam}}$): $S_{\text{steam}} = 4000 / 1.75 \approx 2285.71\text{ kg/h}$. **Method 2: Direct Evaporation Ratio Formula** $V = F \left(1 - \frac{x_F}{x_P}\right) = 6000 \left(1 - \frac{0.08}{0.24}\right) = 4000\text{ kg/h}$ $S_{\text{steam}} = \frac{4000}{1.75} = 2285.71\text{ kg/h}$
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