Related papers: The physical leaky tank car problem, revisited
I present two toy models for the motion of a tank car as fluid drains out of an off-center opening, based on replacing the fluid with particles. No knowledge beyond simple Lagrangian mechanics is required. The first toy model is solved…
This work is basically about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics.…
In the first part of the article, we will outline the paradoxical picture that arises when attempting to calculate the recoil force of the water leakage from a hole at the bottom of a water tank. We will present three different options for…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…
Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that…
A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits…
The low-Reynolds-number Stokes flow driven by rotation of two parallel cylinders of equal unit radius is investigated by both analytical and numerical techniques. In Part I, the case of counter-rotating cylinders is considered. A numerical…
This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…
We aim to reconstruct the shape of an exogenous, heavy solid contained in a tank from measurements of the liquid level in the tank as it drains (driven by gravity) through a small orifice in its side. (Because the solid displaces liquid,…
The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of…
Loss of circulation while drilling is a challenging problem that may interrupt operations, reduce efficiency, and may contaminate the subsurface. When a drilled borehole intercepts conductive faults or fractures, lost circulation manifests…
Fluid motion in tanks is usually described in space industry with the so-called Lomen hypothesis which assumes the vorticity is null in the moving frame. We establish in this contribution that this hypothesis is valid only for uniform…
Despite its apparent simplicity, Newtonian Mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtleties concern fundamental issues such as, e.g., the number of independent laws needed…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
The existence of radial solutions of a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
The biological fluids encountered by self-propelled cells display complex microstructures and rheology. We consider here the general problem of low-Reynolds number locomotion in a complex fluid. {Building on classical work on the transport…
We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to re-derive, in the first post-Newtonian approximation, the well known geometric dragging of frames. We…
The creeping flow of a generalized Newtonian fluid in a non--uniform pore throat is investigated analytically. The analytical solution determines the flow regimes and the transition point from Newtonian to the power law flow regime. As an…
We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research,…