ALBERT

Description: The problem of the stability of a fluid with time-dependent heating has been investigated by Morton (1957), Lick (1965) and Foster (1965). Morton and Lick assumed that the rate of change of the temperature profile is small compared with the growth rate of the disturbances (quasi-static assumption). This assumption is invalid near the onset of instability (as defined by ∂/∂t = 0), and Foster has therefore used an initial-value approach.In this paper the range of validity of the quasi-static assumption is discussed, and results of a time-scaled analysis and calculations based on this are compared with the work of Foster; the agreement is found to be good. We restrict our attention to a semi-infinite fluid initially at a constant temperature; at time t = 0 a temperature difference ΔT is applied at the (lower) horizontal boundary (case (A) of Foster).

Description: In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N sim R^{frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

Description: SUMMARYEwo milk yield data obtained by the lamb suckling technique from nutritional experiments were analysed statistically to obtain estimates of the several components of variation. Diurnal variation was studied. The fitting of a sinusoidal curve removed a significant amount of variation.There was a highly significant correlation between successive milk yields obtained at 4 h intervals. Number of lambs suckled and body weight of ewe at parturition had a significant effect on total daily milk yield.The variation within ewes after the removal of diurnal variation and between ewes after the removal of the effects of number of lambs suckled and body weight at parturition were computed. These sources of variation were combined in a general equation which enabled the prediction of the standard errors associated with daily milk production for a given sampling technique. The practical application of the predicted standard errors is discussed.

Description: SUMMARYThirty-six mature Finnish Landrace × Dorset Horn ewes, each suckling two lambs, were used in a comparative slaughter experiment to measure changes in body tissues during early lactation. Two levels of body fatness at lambing were established by giving ewes a complete diet containing 10 MJ metabolizable energy (ME) and 139 g crude protein (CP)/kg d.m. either close to requirements or ad libitum during the second half of pregnancy. In lactation half the ewes in each group were given a complete diet containing either 90 (diet A) or 60 (diet B) % milled hay ad libitum. These diets contained 7·9 and 9·2 MJ ME and 121 and 132 g CP/kg d.m. respectively.Ewes fed at the two levels in pregnancy contained 8·4 and 19·6 kg chemically determined fat 5 days after lambing but had similar amounts of body protein, ash and water. Over 6 weeks of lactation ewes given diet A lost 60 and 69% of these weights of fat respectively, while ewes given diet B gained 5% and lost 30% respectively. Up to 26 g of body protein was lost daily from ewes given diet A but none from ewes on diet B. During early lactation the weight of the empty digestive tract increased while the weights of most other body components, particularly the carcass, decreased. The ratio of body energy change to live-weight change varied from 24 to 90 MJ/kg. Thus live-weight change did not accurately reflect relative or absolute changes in body energy.Voluntary food intake was greater for ewes given the high-energy diet (B) than for those given diet A and was depressed in the fatter ewes. Differences in intake could be explained by the effects of body fatness and diet on the weight of gut contents. Milk yield was not significantly affected by body fat reserves but was higher on diet B than A. Fat content of milk was higher and protein content lower for ewes with the higher fat reserves at lambing.As the contribution of fat loss to energy available for milk synthesis increased there appeared to be a reduction in the energetic efficiency of milk synthesis. A number of possible reasons for this are discussed.

Description: SUMMARYThe efficacy of estimates of gut contents and total body water in increasing the precision with which the chemical composition of the body could be estimated in early lactation was evaluated in 36 Finnish Landrace × Dorset Horn ewes. The ewes were fed at two levels in pregnancy, and, in lactation, given diets of two metabolizable energy concentrations.The allometric relationships relating weight of chemical fat and protein to emptybody weight were not affected by treatment or stage of lactation. Inclusion of an index of gut contents, based on dry-matter intake, indigestibility and retention time of food residues, together with live weight in a regression equation predicting weight of body fat, only slightly increased the precision of estimate compared with equations using live weight alone.There was a close negative relationship between the proportions of water and fat in live weight. Inclusion of weight of body water with live weight in a regression equation predicting weight of body fat markedly increased the precision of estimate and the residual error (0·81 kg) was similar at different stages of lactation. However, when deuterium oxide space was used instead of body water there was only a small increase in precision of estimate and the residual error varied from 5·3 kg in early lactation to 2·1 kg in mid-lactation. The relationship between deuterium oxide space and body water was shown to be variable and altered by stage of lactation, and these differences were associated with differences in rate of water turnover in the animal's body.It is concluded that estimates of body water are unsuitable for estimating weight of body fat in early lactation.

Description: SUMMARYMilk yield data obtained by the lamb-suckling technique on twenty-four ewes over a period of 5 consecutive days in the second and third week of their lactation have been related to lamb body weights and lamb body-weight changes over the same period. The regression equation obtained wasThe equation was used to estimate the milk consumption of lambs over the range of lamb body weights and lamb body-weight changes studied. The standard errors of these estimates have been computed for comparison with those obtained directly from the lamb suckling technique.The role of the prediction equation in estimating daily milk consumption of lambs is discussed.

Description: SummaryEstimates of the energy contents of the foetuses, placentae, foetal fluids, empty uteri and maternal empty bodies at 88 and at 144 days of pregnancy were obtained from a comparative slaughter experiment on Finnish Landrace × Dorset Horn ewes. Over this period the mean daily intakes of metabolizable energy (ME) for ewes with twin, triplet or quadruplet foetuses were 11·2, 12·0 and 12·2 MJ respectively (low plane of feeding) or 14·4, 15·2 and 15·3 MJ (high plane of feeding), total numbers of ewes being 15, 23 and 7 respectively. The diet contained 8·2 MJ of ME and 153 g crude protein per kg dry matter. All six categories of ewe lost energy from maternal empty-body tissues between 88 and 144 days at mean daily rates of 2·7, 4·1 and 4·9 MJ (low plane) and 1·4, 2·7 and 3·6 MJ (high plane), according to litter size. Rates of energy deposition in the gravid uterus were 0·72, 0·93 and 1·07 MJ/day respectively, and were not affected by plane of nutrition. Estimates of heat production from these balance data were confirmed by direct measurements made on about half of the ewes.Estimates of the gross efficiency of utilization for foetal growth of the combined energy from maternal tissue and from ME intake, after allowing for maternal main–tenance, were similar for each litter size but were 0·14 and 0·11 on the low and high planes of feeding respectively. Consideration of these together with other published observations suggested that efficiency of utilization of ME in pregnancy increases linearly with the ME concentration of the diet and at concentrations below 10 MJ/kg dry matter is less than the efficiency of utilization of energy derived from maternal tissue loss.

Description: SUMMARYThe weights of 44 twin foetuses, 99 triplets and 44 quadruplets, varying in gestational age from 55 to 145 days, were studied in relation to age, sex, litter size, uterine position, placental structure and weight, and ovulation rate. Triplet and quadruplet foetuses were more variable in weight, within litters, than were twins. The difference increased with foetal age and was attributed to increased competition between foetuses which were located within the same horn of the uterus. The effect was largely associated with differences in placental development, i.e. numbers of cotyledons and weight, but those differences did not entirely account for the reduction in foetal weight with increasing litter size. Differences in placental development, arising from embryo mortality, also accounted for the reduction in foetal weight when ovulation rate exceeded litter size. In contrast, differences in foetal weight associated with the sex of the foetuses were only partly mediated by differences in cotyledon weight. Foetuses in the larger litters are thus not only lighter in weight but are more variable in weight, the increased variability being controlled by events in early pregnancy.