GATE — Agricultural Engineering (AG), for dairy engineering aspirants · India · IITs and IISc on rotation
Original practice questions written to the published syllabus · not past papersFluid properties, pumping, thermodynamics and heat transfer worked as dairy plant problems.
In the exams: ICAR AICE subject 38 Units 1 and 4; ICAR AIEEA-PG group 17 Unit III (fluid mechanics, pumps, heat transfer, thermodynamics, dimensional analysis); GATE XL-U Section 4; GATE AG dairy and food engineering
How our questions for GATE spread across the units of Fluid Flow, Thermodynamics & Heat Transfer in Dairy Plants. Difficulty: 6 easy, 21 medium, 3 hard.
| Mass and energy balances in dairy processes | 5 | |
| Fluid properties and Bernoulli's equation | 4 | |
| Pipe flow, Reynolds number and friction losses | 4 | |
| Heat exchangers: LMTD and effectiveness-NTU | 4 | |
| Laws of thermodynamics; steam tables | 3 | |
| Conduction, convection and radiation | 3 | |
| Sanitary centrifugal and positive displacement pumps; pump selection | 2 | |
| Flow of non-Newtonian dairy fluids | 2 | |
| Fins and insulation | 2 | |
| Dimensionless numbers and dimensional analysis | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Milk flows at 10 m³/h through a pipe of 51 mm internal diameter. What is its mean velocity?
D. 1.36 m/s
A = π(0.051)²/4 = 2.04 × 10⁻³ m²; v = (10/3600)/A = 1.36 m/s. Forgetting the /4 in the area gives 0.34.
Further reading: Singh and Heldman, Introduction to Food Engineering
Six bends each with K = 0.9 are in a line carrying milk at 1.5 m/s. What is the total minor loss?
B. 0.62 m
h_m = ΣK v²/2g = 6 × 0.9 × 0.1147 = 0.62 m.
Further reading: Singh and Heldman, Introduction to Food Engineering
A centrifugal pump delivers 20 m³/h of milk against 25 m of head at 60% efficiency. What shaft power is needed?
A. 2.34 kW
P = ρgQH/η = 1,030 × 9.81 × 0.00556 × 25/0.6 = 2,339 W = 2.34 kW. 1.40 kW is the hydraulic power.
Further reading: Singh and Heldman, Introduction to Food Engineering
A yoghurt follows τ = Kγ̇ⁿ with K = 10 Pa·sⁿ and n = 0.3. What is its apparent viscosity at 10 s⁻¹?
D. 2.00 Pa·s
μ_app = Kγ̇^(n−1) = 10 × 10^(−0.7) = 2.00 Pa·s; at 100 s⁻¹ it falls to 0.40 Pa·s.
Further reading: Steffe, Rheological Methods in Food Process Engineering
How much heat is needed to warm 5,000 kg/h of milk (c_p = 3.9 kJ/kg K) from 60 °C to 90 °C?
D. 162.5 kW
Q = ṁc_pΔT = 5,000 × 3.9 × 30 = 585,000 kJ/h = 162.5 kW. Using water's c_p gives 174.2 kW.
Further reading: Singh and Heldman, Introduction to Food Engineering
How much heat is conducted through 1 m² of stainless steel 0.6 mm thick (k = 16 W/m K) with 1 K across it?
D. 26,667 W
Q = kAΔT/L = 16 × 1 × 1/0.0006 = 26,667 W. Using L in mm gives 26.7.
Further reading: Incropera et al., Fundamentals of Heat and Mass Transfer
In a counter-current exchanger, hot water enters at 90 °C and leaves at 80 °C; milk enters at 60 °C and leaves at 75 °C. The LMTD is:
C. 17.4 K
ΔT₁ = 90 − 75 = 15 K, ΔT₂ = 80 − 60 = 20 K; LMTD = 5/ln(20/15) = 17.4 K, slightly below the arithmetic mean of 17.5 K.
Further reading: Singh and Heldman, Introduction to Food Engineering
Raw milk enters a pasteuriser at 4 °C and leaves the regenerator at 66 °C; pasteurisation is at 72 °C. The regeneration efficiency is:
A. 91%
η_R = (66 − 4)/(72 − 4) = 62/68 = 91%. Dividing by 72 forgets the inlet temperature.
Further reading: Tetra Pak Dairy Processing Handbook
A plate section has U = 3,000 W/m² K and A = 20 m² with an LMTD of 17.4 K. Its duty is about:
D. 1043 kW
Q = UA·LMTD = 3,000 × 20 × 17.4 = 1043 kW.
Further reading: Singh and Heldman, Introduction to Food Engineering
10,000 kg/h of skim milk at 9% total solids is evaporated to 45% TS. How much water is removed?
C. 8,000 kg/h
Solids 900 kg/h; concentrate = 900/0.45 = 2,000 kg/h; water = 10,000 − 2,000 = 8,000 kg/h.
Further reading: Singh and Heldman, Introduction to Food Engineering
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