Beyond Bernoulli

Beyond Bernoulli

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 veloc...

Congruences concerning Bernoulli numbers and Bernoulli polynomials

Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (modp), where p is an odd prime, x is a p-integral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=x ) (modp ); ∑(p−1)=2 x=1 (1=x ) (modp ); (p − 1)! (modp ) and Ar(m;p) (modp), where k ∈ {1; 2; : : : ; p− 1} and Ar(m;p) i...

Noninvasive Estimation of the Severity of Aortic Stenosis: Going Beyond Bernoulli.

Ever since the original reports by Hatle et al, echocardiography has been the mainstay for diagnosing the severity of aortic stenosis noninvasively. They reported that the modified Bernoulli equation could be applied to estimate the pressure drop across a valve and that the continuity equation could be used to estimate its area. The behavior of fluids is described by the Navier–Stokes different...

" Bernoulli " Levitation

“Bernoulli” levitation is the basis of many popular counter-intuitive physics demonstrations. However, few of these lend themselves to a quantitative description without recourse to computational fluid dynamics. Levitation of a flat plate is the exception, and we present here a straightforward analysis which illustrates several principles of fluid mechanics in a pedagogically useful way.

Bernoulli polynomials