Question

Tomato juice containing 7% solids by mass is feed to an evaporator and water is removed at a rate of 500 kg /hr. What should be the necessary feed rate to obtain concentrate with 35% solids?

• A. 6250 kg/hr
• B. 62.5 kg/hr
• C. 6.25 kg/hr
• D. 625 kg/hr

Hint:

In evaporation problems, remember that the "Amount of Solids" in the input always equals the "Amount of Solids" in the output. Only water leaves as vapor!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This is a steady-state mass balance problem in food engineering. We need to find the input feed rate of tomato juice given the initial and final solids concentrations and the amount of water removed.
Key Formula or Approach: Total Mass Balance: $F = C + W$
Solids (Component) Balance: $F \times x_F = C \times x_C$
Where: $F$ = Feed rate (kg/hr) $C$ = Concentrate rate (kg/hr) $W$ = Water removal rate (kg/hr) = 500 $x_F$ = Fraction of solids in feed = 0.07 $x_C$ = Fraction of solids in concentrate = 0.35

Step 2: Detailed Explanation:

• From the total mass balance: $C = F - 500$.
• Substitute $C$ into the solids balance equation: \[ 0.07 \times F = 0.35 \times (F - 500) \]
• Expand the equation: \[ 0.07F = 0.35F - (0.35 \times 500) \] \[ 0.07F = 0.35F - 175 \]
• Rearrange to solve for $F$: \[ 175 = 0.35F - 0.07F \] \[ 175 = 0.28F \] \[ F = \frac{175}{0.28} \]
• Calculate the final value: \[ F = 625 \text{ kg/hr} \]

Step 3: Final Answer: The necessary feed rate is 625 kg/hr to achieve the desired concentration.