American Journal of Physics
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Experimental study of Bernoulli’s equation with losses We present a simple and inexpensive experiment to study the drainage of a cylindrical vessel. The experiment consists of a transparent cylinder and a webcam or a digital camera connected to a computer. The model proposed to explain the results makes use of Bernoulli’s equation for real flows including energy losses. The experimental results are well explained by the model, which is a generalization of Torricelli’s expression.
American Journal of Physics - Tập 73 Số 7 - Trang 598-602 - 2005
Surface tension influence in vessel discharge: Comment on “Experimental study of Bernoulli’s equation with losses,” by Martín Eduardo Saleta, Dina Tobia, and Salvador Gil [Am. J. Phys. 73 (7), 598–602 (2005)]
American Journal of Physics - Tập 77 Số 5 - Trang 477-478 - 2009
Mechanics of the slow draining of a large tank under gravity
American Journal of Physics - Tập 71 Số 11 - Trang 1204-1207 - 2003
On combining the Bernoulli and Poiseuille equation—A plea to authors of college physics texts A generalized form of the Bernoulli equation is presented. The assumptions involved in the derivation and its limitations are identified. The usual form of the Bernoulli and Poiseuille equations is shown to be a special case of this generalized equation. Various implications in the teaching of college physics are discussed.
American Journal of Physics - Tập 57 Số 11 - Trang 1013-1019 - 1989
Efficiency of a Carnot engine at maximum power output The efficiency of a Carnot engine is treated for the case where the power output is limited by the rates of heat transfer to and from the working substance. It is shown that the efficiency, η, at maximum power output is given by the expression η = 1 − (T2/T1)1/2 where T1 and T2 are the respective temperatures of the heat source and heat sink. It is also shown that the efficiency of existing engines is well described by the above result.
American Journal of Physics - Tập 43 Số 1 - Trang 22-24 - 1975
A class of one-dimensional relativistic band models The solution to the Dirac equation is worked out for a nonlocal separable periodic potential which varies in one direction. The relativistic version of the Kronig–Penney model is obtained as a special case.
American Journal of Physics - Tập 51 Số 10 - Trang 936-939 - 1983
Use of the Laplace Transform Method to Solve the One-Dimensional Periodic-Potential Problem The one-dimensional periodic-potential problem is solved using the Laplace transform method. This method allows an easy generalization of the Kronig-Penney model so that it is applied to solve far more complex one-dimensional periodic structure.
American Journal of Physics - Tập 41 Số 10 - Trang 1138-1144 - 1973
Proper treatment of the delta function potential in the one-dimensional Dirac equation It is pointed out that the usual treatment of the delta function potential in the one-dimensional Dirac equation is incorrect. Steps leading to such incorrect results are identified. The delta function potential is also examined from the limiting case of a nonlocal potential V(x,x′). In this general case, the strength g=∫dx ∫dx′V(x,x′) is no longer a sufficient parameter to characterize a potential.
American Journal of Physics - Tập 55 Số 8 - Trang 737-739 - 1987
Partition functions and symmetric polynomials We find a close correspondence between the partition functions of ideal quantum gases and certain symmetric polynomials. From this correspondence, it can be shown that a number of thermodynamic identities that have recently been considered in the literature are essentially of combinatorial origin and have been known for a long time as theorems on symmetric polynomials. For example, a recurrence relation for partition functions in the textbook by P. Landsberg is Newton’s identity in disguised form. Conversely, a theorem on symmetric polynomials translates into a new and unexpected relation between fermion and boson partition functions, which can be used to express the former by means of the latter and vice versa.
American Journal of Physics - Tập 70 Số 1 - Trang 53-57 - 2002
Momentum of light in a refracting medium It is pointed out that neither Minkowski’s nor Abraham’s proposal gives correctly the momentum density of light in a refracting medium. The correct result due to Peierls is simply derived. The imbalance of momentum flux at an interface corresponds to a force on the surface, and this is contrasted with a delayed force due to a finite beam width.
American Journal of Physics - Tập 45 Số 2 - Trang 195-198 - 1977
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