Theodore A. Wilson

Vortex growth in jets

Observations are reported on the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a sharp-edged circular orifice. A regular periodic flow is observed near the orifice for both configurations when the Reynolds number of the jet lies between about 500 and 3000. The two-dimensional jet produces a symmetric pattern of vortex pairs with a Strouhal number of 0·43. Vortex rings are formed in the circular jet with a Strouhal number of 0·63. Computer experiments show that a growing pair of vortices in two parallel vortex sheets produces a symmetric pattern of vortices upstream from the original disturbance.

Respiratory effects of the external and internal intercostal muscles in humans

1 The current conventional view of intercostal muscle actions is based on the theory of Hamberger (1749) and maintains that as a result of the orientation of the muscle fibres, the external intercostals have an inspiratory action on the lung and the internal interosseous intercostals have an expiratory action. Recent studies in dogs, however, have shown that this notion is only approximate. 2 In the present studies, the respiratory actions of the human external and internal intercostal muscles were evaluated by applying the Maxwell reciprocity theorem. Thus the orientation of the muscle fibres relative to the ribs and the masses of the muscles were first assessed in cadavers. Five healthy individuals were then placed in a computed tomographic scanner to determine the geometry of the ribs and their precise transformation during passive inflation to total lung capacity. The fractional changes in length of lines with the orientation of the muscle fibres were then computed to obtain the mechanical advantages of the muscles. These values were finally multiplied by muscle mass and maximum active stress (3.0 kg cm−2) to evaluate the potential effects of the muscles on the lung. 3 The external intercostal in the dorsal half of the second interspace was found to have a large inspiratory effect. However, this effect decreases rapidly in the caudal direction, in particular in the ventral portion of the ribcage. As a result, it is reversed into an expiratory effect in the ventral half of the sixth and eighth interspaces. 4 The internal intercostals in the ventral half of the sixth and eighth interspaces have a large expiratory effect, but this effect decreases dorsally and cranially. 5 The total pressure generated by all the external intercostals during a maximum contraction would be ‐15 cmH2O, and that generated by all the internal interosseous intercostals would be +40 cmH2O. These pressure changes are substantially greater than those induced by the parasternal intercostal and triangularis sterni muscles, respectively.

Operating modes of the clarinet

Operating modes of the clarinet are investigated via a simple model consisting of a uniform flat reed coupled to a constant‐area tube as a resonator. The analysis shows that, for lightly damped reeds, the operating frequency which is closest to the natural frequency of the reed is excited at the lowest blowing pressure. Further, the reed must be very heavily damped in order for the lowest resonance frequency of the tube to be preferentially excited. Experiments on a model clarinet, using metal reeds with different amounts of damping applied to the reed, confirm the pattern predicted by the analysis. There is close agreement between the measured and predicted values of the frequency ratio, but in many of the experiments the observed blowing pressure ratios were somewhat higher than the predicted values, the deviation being as high as 40% for the more heavily damped reeds.

Effect of acute inflation on the mechanics of the inspiratory muscles

When the lung is inflated acutely, the capacity of the diaphragm to generate pressure, in particular pleural pressure (Ppl), is impaired because the muscle during contraction is shorter and generates less force. At very high lung volumes, the pressure-generating capacity of the diaphragm may be further reduced by an increase in the muscle radius of curvature. Lung inflation similarly impairs the pressure-generating capacity of the inspiratory intercostal muscles, both the parasternal intercostals and the external intercostals. In contrast to the diaphragm, however, this adverse effect is largely related to the orientation and motion of the ribs, rather than the ability of the muscles to generate force. During combined activation of the two sets of muscles, the change in Ppl is larger than during isolated diaphragm activation, and this added load on the diaphragm reduces the shortening of the muscle and increases muscle force. In addition, activation of the diaphragm suppresses the cranial displacement of the passive diaphragm that occurs during isolated intercostal contraction and increases the respiratory effect of the intercostals. As a result, the change in Ppl generated during combined diaphragm-intercostal activation is greater than the sum of the pressures generated during separate muscle activation. Although this synergistic interaction becomes particularly prominent at high lung volumes, lung inflation, either bilateral or unilateral, places a substantial stress on the inspiratory muscle pump.

Mechanical advantage of the human parasternal intercostal and triangularis sterni muscles

1 Previous studies in dogs have demonstrated that the maximum change in airway pressure (ΔPao) produced by a particular respiratory muscle is the product of three factors, namely the mass of the muscle, the maximal active muscle tension per unit cross‐sectional area (∼3.0 kg cm−2), and the fractional change in muscle length per unit volume increase of the relaxed chest wall (i.e. the muscles mechanical advantage). In the present studies, we have used this principle to infer the ΔPao values generated by the parasternal intercostal and triangularis sterni muscles in man. 2 The mass of the muscles and the direction of the muscle fibres relative to the sternum were first assessed in six cadavers. Seven healthy individuals were then placed in a computed tomographic scanner to determine the orientation of the costal cartilages relative to the sternum and their rotation during passive inflation to total lung capacity. The fractional changes in length of the muscles during inflation, their mechanical advantages, and their ΔPao values were then calculated. 3 Passive inflation induced shortening of the parasternal intercostals in all interspaces and lengthening of the triangularis sterni. The fractional shortening of the parasternal intercostals decreased gradually from 7.7% in the second interspace to 2.0% in the fifth, whereas the fractional lengthening of the triangularis sterni increased progressively from 5.9 to 13.8%. These rostrocaudal gradients were well accounted for by the more caudal orientation of the cartilages of the lower ribs. 4 Since these fractional changes in length corresponded to a maximal inflation, the inspiratory mechanical advantage of the parasternal intercostals was only 2.2–0.6% l−1, and the expiratory mechanical advantage of the triangularis sterni was only 1.6–3.8% l−1. In addition, whatever the interspace, parasternal and triangularis muscle mass was 3–5 and 1–3 g, respectively. As a result, the magnitude of the ΔPao values generated by a maximal contraction of the parasternal intercostals or triangularis sterni in all interspaces would be only 1–3 cmH2O. 5 These studies therefore confirm that the parasternal intercostals in man have an inspiratory action on the lung whereas the triangularis sterni has an expiratory action. However, these studies also establish the important fact that the pressure‐generating ability of both muscles is substantially smaller than in the dog.

Experiments on the Fluid Mechanics of Whistling

Experiments to investigate the fluid mechanics of whistling are reported. A model, consisting of a cylindrical cavity with rounded holes at each end, is used to simulate human whistling. It is found that the frequency is very near the Helmholtz resonator frequency, and that the resonator can be excited by flow through the smooth‐edged orifices bounding the resonant cavity. Furthermore, it is found that the flow velocity of the jet which excites the resonator must lie between limits that are proportional to frequency and that increase with both diameter and thickness of the orifice. It is concluded that whistling can be included in the same class of sound sources as the Rayleigh bird call and the Pfeifentone, since the essential mechanism for exciting them depends on the instability of a jet to the formation of vortex rings and the interaction of the rings with a rigid boundary in the flow.

Respiratory mechanical advantage of the canine external and internal intercostal muscles

1 The current conventional view of intercostal muscle actions is based on the theory of Hamberger (1749) and maintains that as a result of the orientation of the muscle fibres, the external intercostals have an inspiratory action on the lung and the internal interosseous intercostals have an expiratory action. This notion, however, remains unproved. 2 In the present studies, the respiratory actions of the canine external and internal intercostal muscles were evaluated by applying the Maxwell reciprocity theorem. Thus the effects of passive inflation on the changes in length of the muscles throughout the rib cage were assessed, and the distributions of muscle mass were determined. The fractional changes in muscle length during inflation were then multiplied by muscle mass and maximum active stress (3·0 kg cm−2) to evaluate the potential effects of the muscles on the lung. 3 The external intercostals in the dorsal third of the rostral interspaces were found to have a large inspiratory effect. However, this effect decreases rapidly both toward the costochondral junctions and toward the base of the rib cage. As a result, it is reversed to an expiratory effect in the most caudal interspaces. The internal intercostals in the caudal interspaces have a large expiratory effect, but this effect decreases ventrally and rostrally, such that it is reversed to an inspiratory effect in the most rostral interspaces. 4 These observations indicate that the canine external and internal intercostal muscles do not have distinct inspiratory and expiratory actions as conventionally thought. Therefore, their effects on the lung during breathing will be determined by the topographic distribution of neural drive.

Rostrocaudal gradient of mechanical advantage in the parasternal intercostal muscles of the dog.

1. Previous theoretical studies have led to the predictions that, in the dog, the parasternal intercostal muscles in the rostral interspaces shorten more during passive inflation than those in the caudal interspaces and have, therefore, a greater inspiratory mechanical advantage. The present studies were undertaken to test these predictions. 2. The effects of passive inflation on the length of the parasternal intercostals interspaces 1 to 7 were evaluated with markers implanted in the costal cartilages. Although the muscles in all interspaces shortened with passive inflation, the fractional shortening increased from the first to the second and third interspaces and then decreased continuously to the seventh interspace. 3. To understand this peculiar distribution, a geometric model of the parasternal area was then developed and a relation was obtained between muscle shortening and the angles that describe the orientation of the muscle and costal cartilage relative to the sternum. Measurement of these angles indicated that the rostrocaudal gradient of parasternal shortening resulted from the different orientations of the costal cartilages and their different rotations during passive inflation. 4. The changes in airway pressure generated by the parasternal intercostals in interspaces 3, 5 and 7 were finally measured during selective, maximal stimulation. The fall in pressure was invariably greatest during contraction of the third interspace and smallest during contraction of the seventh. 5. These observations indicate that, in the dog, the rostrocaudal gradient in rib rotation induces a rostrocaudal gradient of mechanical advantage in the parasternal intercostals, which has its climax in the second and third interspaces. These observations also support the concept that the respiratory effect of a given respiratory muscle can be computed from its behaviour during passive inflation.

Fluid mechanics of the edgetone

A model is proposed to explain the means by which an edgetone transforms the energy of a fully developed plane jet into energy which is radiated as sound. The edgetone configuration considered consists of a flat plate located in the medial plane of a fully developed two‐dimensional jet. The flow is modeled as follows. A periodic disturbance at the jet origin leads to the formation of an asymmetric vortex street which propagates downstream with a fixed convection velocity and wavelength. The vortex strength, convection velocity, and wavelength are determined as functions of the Strouhal number by applying conservation laws and kinematic relationships. A potential flow analysis of the interaction of the vortices with the edge is used to estimate the nearfield oscillating flow at the jet exit which, in turn, is used to calculate the phase of the feedback mechanism. The phase then determines the operating frequency as a function of jet velocity and edge stand‐off distance. It is shown that the proposed model is capable of predicting the major observed features of edgetone operation. The frequency predictions of the theory are compared with experiments for a wide range of jet parameters in both air and water. The comparison indicates that the frequency predictions are as good or better than previous empirical or semiempirical formulas.

Osmotic volume changes induced by a permeable solute

Abstract A differential equation is developed describing volume changes as a function of time for a system such as a cell which is undergoing osmotically induced volume changes due to a solute which penetrates the cell membrane or boundary of the system. The parameters used to describe the membrane properties are the Staverman reflection coefficient, the water permeability coefficient and the solute permeability coefficient. The fluids bathing both sides of the membrane barrier are assumed to be spatially homogeneous with respect to water and solute concentrations. A first-order perturbation technique is used to solve the equations and obtain cell volume as a function of time. This solution is compared with data available in the literature and values for the cell membrane parameters are obtained for these cases.