ALBERT

Description: It has been observed by Walters & Davidson (1963) that release of a mass of gas in water sometimes produces a rising toroidal bubble. This paper is concerned with the history of such a bubble, given that at the initial instant the motion is irrotational everywhere in the water. The variation of its overall radius a with time may be predicted from the vertical impulse equation, and it should be possible to make the same prediction by equating the rate of loss of combined kinetic and potential energy to the rate of viscous dissipation. This is indeed seen to be the case, but not before it is recognized that in a viscous fluid vorticity will continually diffuse out from the bubble surface, destroying the irrotationality of the motion, and necessitating an examination of the distribution of vorticity. The impulse equation takes the same form as in an inviscid fluid, but the energy equation is severely modified. Other results include an evaluation of the effect of a hydrostatic variation in bubble volume, and a prediction of the time which will have elapsed before the bubble becomes unstable under the action of surface tension.

Description: The stability is considered of the flow with velocity components [ {0,Omega r[1+O(epsilon^2)],;2epsilonOmega r_0f(r/r_0)} ] (where f(x) is a function of order one) in cylindrical polar co-ordinates (r, ϕ, z), bounded by the rigid cylinders r/r0 = x1 and r/r0 = 1 (0 [les ] x1 〈 1). When ε [Lt ] 1, the flow is shown to be unstable to non-axisymmetric inviscid disturbances of sufficiently large axial wavelength. The case of Poiseuille flow in a rotating pipe is considered in more detail, and the growth rate of the most rapidly growing disturbance is found to be 2εΩ.

Description: The stability to small inviscid disturbances of a rotating flow, whose velocity components in cylindrical polars (r, 0, z) are (0, V(r), 0), is investigated when one boundary of the flow (r = b) is a free surface under the action of surface tension (γ), and the other is either at infinity, or a rigid cylinder (r = a ≠ b), or at the axis (r = 0). The free surface may be the inner or the outer boundary. A necessary and sufficient condition for stability to axisymmetric disturbances is derived, which requires that Rayleigh's criterion of increasing circulation be satisfied, and otherwise depends only on b, V(b), γ and the density of the swirling liquid. This condition may be extended to include non-axisymmetric disturbances when V ∝ 1/r and when V ∝ r although in the latter case it is no longer a necessary one. It is shown that, in the case V ∝ r, as well as V ∝ 1/r, the ‘most unstable’ disturbance on a rotating column of fluid will be non-axisymmetric if the rotation speed at the surface is sufficiently great. Several applications of the theory are suggested, and a possible experiment to test it is described.

Description: The flow under discussion represents an idealization of the bath-tub vortex; distortions of the free surface, finite sink size, and all rigid boundaries have been eliminated from the problem in order to isolate the effect of the non-uniform stretching of vortex lines produced by the sink flow. A boundary-layer type of approximation is made about the axis, which requires that the meridional Reynolds number (N) be large, and since the problem is still intractable, an expansion is made in powers ofK=R2/N(whereRis the swirl Reynolds number), which measures the strength of the interaction between the swirl and meridional velocity fields. In the limit of zeroKthe flow is a modified Burgers vortex whose radius decreases to zero at the sink. For non-zeroK, the interaction is not restricted to the vortex core, because the presence of the vortex modifies the outer irrotational flow, inducing a radial mass flux into the core, whose dependence on the axial co-ordinate is calculated to the first order inK.The structure of the core is obtained, again to the first order inK, from two co-ordinate expansions, one near the stagnation point on the axis, and the other near the sink, although only the first few terms of the latter can be determined explicitly. It is shown how the methods can be extended not only to higher orders inK, but also to any other narrow viscous vortex in which the vortex lines are stretched non-uniformly away from an internal stagnation point.

Description: The stability of almost fully developed viscous flow in a rotating pipe is considered. In cylindrical polar co-ordinates (r, ø, z) this flow has the velocity components [ {W_0o(1),quadOmega r[1+o(epsilon)],quad W_0[1-r^2/r^2_0+o(1)]},_{+}^{+} ] where ε = Wo/2Ωr0 and is bounded externally by the rigid cylinder r = r0, which rotates about its axis with angular velocity Ω. In the limit of small ε, the disturbance equations can be solved in terms of Bessel functions and it is shown that, in that limit, the flow is unstable for Reynolds numbers R = Wor0/v greater than Rc [asymp ] 82[sdot ]9. The unstable disturbances take the form of growing spiral waves, which are stationary relative to the rotating cylinder and the critical disturbance at R = Rc has azimuthal wave-number 1 and axial wavelength 2πr0/ε. Furthermore, it is shown that the most rapidly growing disturbance for R 〉 Rc has an azimuthal wave-number which increases with R. Some of the problems involved in testing the results by experiment are discussed and a possible application to the theory of vortex breakdown is mentioned. In an appendix this instability is shown to be an example of inertial instability.

Description: 1. A total of forty-two Suffolk cross-bred and 230 stud Romney Marsh ewes were used in four experiments in which pregnant mare serum gonadotrophin (p.m.s.) was used in various combinations with progesterone and oestrogen in attempts to induce fertile mating in anoestrus.2. Groups of six Suffolk cross-bred ewes were injected with 1000 i.u. p.m.s. after pretreatment, commencing 4 days earlier, with 75 mg. progesterone administered in one of four different ways. Six twice-daily injections in oil resulted in oestrus in five ewes in each of two groups treated. Single injections in oil solution, aqueous suspension, and benzyl alcohol emulsion resulted in oestrus in two, nil, and four ewes, respectively. All were served within 48 hr. of injection of p.m.s.3. Ovulation was observed in five of six crossbred ewes which received six twice-daily injections of progesterone in oil, without subsequent injection of p.m.s. Three were served.4. Divided injections of progesterone commencing 4 days before 750–1000 i.u. p.m.s. failed to induce a satisfactory oestrous response in Romney Marsh ewes. An increase to 7 days in the duration of progesterone stimulation resulted in oestrus in all of eighteen ewes treated.5. The injection of a benzyl alcohol emulsion containing 75 or 150 mg. progesterone, given as a single dose 4 or 7 days before 750 i.u. p.m.s., failed to induce a satisfactory oestrous response. Of seventy-two ewes treated, only seven were served.6. Lambing results were most unsatisfactory when progesterone-p.m.s. treatment was followed by artificial insemination. Of 144 Romneys inseminated, only twelve lambed. Successful pregnancy appeared unrelated to the type of treatment or the occurrence of oestrus.7. On the basis of the oestrous responses observed after the injection of a variety of combinations of oestrogen, progesterone, and p.m.s., and by reference to quantitative data on progesterone-oestrogen relationships in oestrous behaviour in the spayed ewe, it is concluded that the developing follicle of the Romney Marsh ewe produces an amount of oestrogen approximately equivalent, in its physiological activity, to a single injection in oil of about 20 μg. oestradiol benzoate.

Description: 1. Extracts containing hemicellulase activity were prepared from mixed rumen bacteria and Butyrivibrio fibrisolvens cells by mechanical disruption.

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: Summary1. An experiment consisting of two separate trials was carried out to study the utilization by beef cattle of high concentrate diets containing different amounts of milled barley straw and of protein. For each trial twenty-four Friesian steers, initially weighing about 270 kg, were divided into three groups and the animals within each group then allocated at random to eight dietary treatments. The treatments were based on an all-concentrate diet and three others containing 10, 20 and 30% of milled (1 in screen) barley straw. Four of the treatments consisted of giving the same concentrate mixture with each level of straw, and the other four involved giving concentrate mixtures with increasing levels of protein so that the percentage of protein in the diets was maintained. All the diets were fed ad libitum until slaughter.2. Performance in terms of live-weight gain was considered as the net result of a number of factors, notably the total intake of dry matter, the digestibility of the dry matter, the efficiency of utilization of the end products of fermentation in the rumen and the composition of the live-weight gain. The inclusions of 20 and 30% of straw in the diet were associated with lower rates of gain than on corresponding all-concentrate and 10% straw treatments but the differences obtained did not attain significance. Total intakes of dry matter were greater on treatments containing 10 and 20% of straw than on corresponding all-concentrate treatments, but then declined with further increase in level of straw to 30%. This trend was significantly curvilinear (P 〈 0·01), the equation for the relationship beingY = 5·881 + 0·131X - 0·004X2,with Y being the daily intake of dry matter (kg) and X the percentage of straw in the diet. The maximum intake of dry matter was calculated to occur with a level of 16·4% straw in the diet and represents an increase in total dry matter intake of 18·2% over that on an all-concentrate diet. Food conversion ratio, expressed as total dry matter consumed per kg live-weight gain, tended to increase with increasing proportion of straw in the diet.3. The mean digestibility of organic matter fell sharply with the inclusion of 10% straw in the ration, the decrease being 8·2% where the protein level was not maintained and 9·1% where it was maintained. Further reductions in digestibility occurred on the 20 and 30% straw diets, but the magnitude of the reductions were considerably less than those brought about by the initial introduction of straw into the ration.4. The molar percentage of acetic acid in the steam volatile acids of rumen liquor increased markedly, and that of propionic acid decreased sharply from the all-concentrate to the 10% straw treatment with a similar level of dietary protein. Increase in the level of straw to 30% gave rise to a further increase in the proportion of acetic acid and reduction in that of propionic acid. Analysis of samples taken at 3, 6, 9 and 12 h after feeding showed appreciable differences in pattern between treatments.5. Effects of treatment on killing-out percentage were different for each trial. In trial 1 the inclusion of straw in the diet did not cause any reduction in killing-out percentage, but the maintenance of protein level gave rise to a significantly higher killing-out percentage than was obtained with the lower protein groups. In trial 2 the killing-out percentages showed a significantly linear (P 〈 0·01) decrease with increasing proportion of straw in the ration, and maintenance of protein level did not give any improvement.