Explanation and discovery in aerodynamics

The purpose of this paper is to discuss and clarify the explanations commonly cited for the aerodynamic lift generated by a wing, and to then analyse, as a case study of engineering discovery, the aerodynamic revolutions which have taken place within Formula 1 in the past 40 years. The paper begins with an introduction that provides a succinct summary of the mathematics of fluid mechanics

Development of the Bélanger Equation and Backwater Equation by Jean-Baptiste Bélanger (1828)

A hydraulic jump is the sudden transition from a high-velocity to a low-velocity open channel flow. The application of the momentum principle to the hydraulic jump is commonly called the Bélanger equation, but few know that Bélanger's (1828) treatise was focused on the study of gradually varied open channel flows. Further, although Bélanger understood the rapidly-varied nature of the jump flow, he applied incorrectly the Bernoulli principle in 1828, and corrected his approach 10 years later. In 1828, his true originality lay in the successful development of the backwater equation for steady, one-dimensional gradually-varied flows in an open channel, together with the introduction of the step method, distance calculated from depth, and the concept of critical flow conditions

A Type of “Bubble” Water-saving Faucet

At present, many places are seriously short of freshwater resources. Thus, saving water is the universal responsibility of contemporary citizens. Now faucet products such as ordinary washing nozzle, kitchen nozzle, face-washer nozzle, bathtub nozzle and washing machine nozzle are widely used in urban and rural households. Most have poor water-saving abilities, and much water is wasted through daily washing. Our bubble-type water-saving device is a brand-new water-saving device with a simple structure and low cost. It uses the Bernoulli principle and the bubble atomizing principle to inhale air naturally in water flow to atomize water flow. It can help achieve more than 50% water-saving efficiency in daily washing behavior

Beyond Bernoulli: Improving the Accuracy and Precision of Noninvasive Estimation of Peak Pressure Drops

Background: Transvalvular peak pressure drops are routinely assessed noninvasively by echocardiography using the Bernoulli principle. However, the Bernoulli principle relies on several approximations that may not be appropriate, including that the majority of the pressure drop is because of the spatial acceleration of the blood flow, and the ejection jet is a single streamline (single peak velocity value). Methods and Results: We assessed the accuracy of the Bernoulli principle to estimate the peak pressure drop at the aortic valve using 3-dimensional cardiovascular magnetic resonance flow data in 32 subjects. Reference pressure drops were computed from the flow field, accounting for the principles of physics (ie, the Navier–Stokes equations). Analysis of the pressure components confirmed that the spatial acceleration of the blood jet through the valve is most significant (accounting for 99% of the total drop in stenotic subjects). However, the Bernoulli formulation demonstrated a consistent overestimation of the transvalvular pressure (average of 54%, range 5%–136%) resulting from the use of a single peak velocity value, which neglects the velocity distribution across the aortic valve plane. This assumption was a source of uncontrolled variability. Conclusions: The application of the Bernoulli formulation results in a clinically significant overestimation of peak pressure drops because of approximation of blood flow as a single streamline. A corrected formulation that accounts for the cross-sectional profile of the blood flow is proposed and adapted to both cardiovascular magnetic resonance and echocardiographic data

Gas Kinematics on GMC scales in M51 with PAWS: cloud stabilization through dynamical pressure

We use the high spatial and spectral resolution of the PAWS CO(1-0) survey of the inner 9 kpc of the iconic spiral galaxy M51 to examine the effect of gas streaming motions on the star-forming properties of individual GMCs. We compare our view of gas flows in M51 -- which arise due to departures from axi-symmetry in the gravitational potential (i.e. the nuclear bar and spiral arms) -- with the global pattern of star formation as traced by Halpha and 24\mu m emission. We find that the dynamical environment of GMCs strongly affects their ability to form stars, in the sense that GMCs situated in regions with large streaming motions can be stabilized, while similarly massive GMCs in regions without streaming go on to efficiently form stars. We argue that this is the result of reduced surface pressure felt by clouds embedded in an ambient medium undergoing large streaming motions, which prevents collapse. Indeed, the variation in gas depletion time expected based on the observed streaming motions throughout the disk of M51 quantitatively agrees with the variation in observed gas depletion time scale. The example of M51 shows that streaming motions, triggered by gravitational instabilities in the form of bars and spiral arms, can alter the star formation law; this can explain the variation in gas depletion time among galaxies with different masses and morphologies. In particular, we can explain the long gas depletion times in spiral galaxies compared to dwarf galaxies and starbursts. We suggest that adding a dynamical pressure term to the canonical free-fall time produces a single star formation law that can be applied to all star-forming regions and galaxies, across cosmic time.Comment: 28 pages, 14 figures, accepted for publication in Ap

Membrane flutter induced by radiation of surface gravity waves on a uniform flow

We consider stability of an elastic membrane being on the bottom of a uniform horizontal flow of an inviscid and incompressible fluid of finite depth with free surface. The membrane is simply supported at the leading and the trailing edges which attach it to the two parts of the horizontal rigid floor. The membrane has an infinite span in the direction perpendicular to the direction of the flow and a finite width in the direction of the flow. For the membrane of infinite width we derive a full dispersion relation that is valid for arbitrary depth of the fluid layer and find conditions for the flutter of the membrane due to emission of surface gravity waves. We describe this radiation-induced instability by means of the perturbation theory of the roots of the dispersion relation and the concept of negative energy waves and discuss its relation to the anomalous Doppler effect