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22-Agric-A1 Applied Plant, Animal or Human Physiology · May 2013

Question 5 of 6: Sensible Heat Production of a Barn of Pigs

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 04-Agric-A1 Animal or Human Physiology, National Exams May 2013 — a three-hour closed-book examination; one of two approved calculator models (Casio or Sharp) is permitted. The cover page states that five (5) questions constitute a complete exam paper and that only the first five as they appear in the answer book are marked, that each question is of equal value, and that full marks are not available for a bare correct answer — the reasoning must be communicated clearly. All six printed questions are worked here, because the set is a study resource rather than a timed attempt.

Reference texts. S.E. Curtis, Environmental Management in Animal Agriculture (thermoneutral zone, lower/upper critical temperature and the factors that shift them, group and flooring effects); D. McDonald et al., Animal Nutrition, 7th ed. (gross/digestible/metabolizable/net energy partition, heat increment of feeding); M.K. Yousef (ed.), Stress Physiology in Livestock (external stressors and energy partition, thermoregulatory heat-flow pathways); P.D. Lewis and T.R. Morris, Poultry Lighting: the Theory and Practice (photoperiod versus light-intensity reciprocity); ASABE Standards (American Society of Agricultural and Biological Engineers) (metabolic body-size scaling and sensible heat production of livestock).

Question 5: Sensible Heat Production of a Barn of Pigs (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. An ASABE reference table gives the sensible heat-production rate of a 60-kg reference pig at two ambient temperatures; a barn holds 1000 pigs of a different body mass (70 kg) at a third ambient temperature, and the metabolic body-size exponent 0.75 is to be used to scale between body masses.

Given data
QuantitySymbolValue
Reference pig mass$M_{\text{ref}}$60 kg
Sensible heat rate at 10°C$q_{10}$2.0 W/kg
Sensible heat rate at 20°C$q_{20}$1.3 W/kg
Barn ambient temperature$T$18°C
Actual pig mass$M$70 kg
Herd size$n$1000 pigs
Metabolic body-size exponent$b$0.75

Find. The total sensible heat production of the barn's 1000 pigs at 18°C.

Approach. Interpolate the tabulated rate to the barn temperature for the 60-kg reference pig, convert that rate to a total heat-production rate for one reference pig, rescale to the actual 70-kg pig using the metabolic body-size relation $q \propto M^{b}$, then multiply by the herd size.

  1. Interpolate the specific rate at 18°C for the 60-kg reference pig. The two tabulated points bracket the barn temperature, so linear interpolation between them gives $$q_{18} = q_{10} + (q_{20}-q_{10})\frac{T-10}{20-10} = 2.0 + (1.3-2.0)\frac{18-10}{20-10} = \boxed{1.44\ \text{W/kg}}$$
  2. Convert to a total rate for one 60-kg reference pig. The tabulated value is heat production per kg of the reference animal's own mass, so the reference pig's total sensible heat production at 18°C is $$Q_{\text{ref}} = q_{18}\,M_{\text{ref}} = (1.44)(60) = \boxed{86.4\ \text{W}}$$
  3. Rescale to the actual 70-kg pig via the metabolic body-size relation. Heat production does not scale linearly with mass; ASABE's convention is $Q \propto M^{b}$ with $b=0.75$, so the ratio of a 70-kg pig's heat production to the 60-kg reference is $$\frac{Q_{\text{pig}}}{Q_{\text{ref}}} = \left(\frac{M}{M_{\text{ref}}}\right)^{b} = \left(\frac{70}{60}\right)^{0.75} = 1.1226$$ so one 70-kg pig at 18°C produces $$Q_{\text{pig}} = Q_{\text{ref}}(1.1226) = (86.4)(1.1226) = \boxed{97.0\ \text{W}}$$
  4. Scale up to the whole barn. With 1000 such pigs, $$Q_{\text{total}} = n\,Q_{\text{pig}} = (1000)(97.0\ \text{W}) = \boxed{97{,}000\ \text{W} \approx 97.0\ \text{kW}}$$
Question 5 — results
QuantityValue
Interpolated rate at 18°C, $q_{18}$1.44 W/kg (of the 60-kg reference pig)
Heat production of one reference (60-kg) pig, $Q_{\text{ref}}$86.4 W
Body-size scale factor, $(70/60)^{0.75}$1.123
Heat production of one actual (70-kg) pig, $Q_{\text{pig}}$97.0 W
Total sensible heat production, 1000 pigs, $Q_{\text{total}}$≈97,000 W ≈ 97.0 kW
Check: assumes the ASABE tabulated W/kg values are defined on the 60-kg reference pig's own body mass (so the reference total is obtained by multiplying, not by reading a "per-actual-kg" rate directly), and that linear interpolation between the two tabulated temperatures is an adequate approximation of the true (mildly curved) ASABE heat-production curve over this narrow 10°C span.