Question Bank • QB_DFE_ADV_004 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Unit Operations in Dairy and Food Engineering

Subtopic: Pasteurization

Question Statement:

In a continuous High-Temperature Short-Time (HTST) milk pasteurizer operating at a milk flow rate of $3600\text{ L/h}$, the holding tube has an internal diameter of $50\text{ mm}$. To ensure a minimum holding time of $15\text{ seconds}$ for the fastest flowing particle (with velocity profile laminar ratio of $0.83$ for turbulent flow), the required length of the holding tube is ________ $\text{m}$ (round off to two decimal places).

Answer Key:

9.20

Step-by-Step Solution & Explanation

1. Milk volumetric flow rate ($Q$): $Q = \frac{3600\text{ L/h}}{3600} = 1.0\text{ L/s} = 0.001\text{ m}^3/\text{s}$ 2. Cross-sectional area of tube ($A$) with $D = 0.05\text{ m}$: $A = \frac{\pi}{4} D^2 = \frac{\pi}{4} (0.05)^2 = 1.9635 \times 10^{-3}\text{ m}^2$ 3. Average velocity ($v_{\text{avg}}$): $v_{\text{avg}} = \frac{Q}{A} = \frac{0.001}{1.9635 \times 10^{-3}} = 0.5093\text{ m/s}$ 4. Maximum (fastest) flow velocity ($v_{\text{max}}$): $v_{\text{max}} = \frac{v_{\text{avg}}}{0.83} = \frac{0.5093}{0.83} = 0.6136\text{ m/s}$ 5. Required holding tube length ($L$): $L = v_{\text{max}} \times t_{\text{holding}} = 0.6136\text{ m/s} \times 15\text{ s} = 9.204\text{ m} \approx 9.19\text{ to } 9.20\text{ m}$
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