Ceramics are an important material for precision engineers. Ceramics are often used for their low coefficients of thermal expansion, high Young’s modulus, as well as other properties. The text Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection by Dietrich Munz and Theo Fett (google books link, amazon.com link) is a very good reference for ceramics and for their failure in particular. The text derives formulas for lifetime (time to failure) under constant and cyclic loads. The text also provides extensive information on materials testing, statistical methods (Weibull distributions), and probability of fracture for ceramics.
In a previous post, we built a quick model for eddy currents in a plate stationary in a time-varying magnetic field. Here we examine the induced currents and damping force that result from motion of the plate relative to the magnetic field.
In electric machines, there are two common causes of eddy currents: (1) time-varying currents in coils, and (2) motion of conductors relative to sources of magnetic field. In this post, we show how to estimate the current density arising from a time-varying magnetic field passing through a plate.
Low Reynolds number flow can be a very interesting topic. Low Reynolds number flow (Re ) is also called Stokes flow. At very low Reynolds number, the Navier-Stokes equations can be greatly simplified. Fluid mechanics at human length scales, such as swimming, is generally not very low Reynolds number. Developments in microfluidics, nanotechnology, and biomimicry has increased the frequency with which engineers encounter low Reynolds flows problems. Because humans often encounter fluids at moderate of high Reynolds numbers, our intuition can deceive us. Two of the most basic results of low Reynolds flow is that it is fully reversible and independent of time.
As a refresher, the Reynolds number is the ratio of inertial to viscous forces and is given by
where is the fluid density, is the velocity, is a characteristic length such as a diameter, and is the viscosity. The Reynolds number can also be thought of as the ratio of the momentum diffusion rate to the viscous diffusion rate. At Reynolds numbers less than approximately 2000, the flow is laminar. For Reynolds numbers greater than approximately 4000, the flow is turbulent. Continue reading Low Reynolds Number Flow
A great set of video lectures by Ascher Shapiro of MIT on Fluid Mechanics is available on youtube. The videos are old, but fluid mechanics hasn’t changed. Each video is presented by a world renowned fluids expert such as Ascher Shapiro (wikipedia link) or G.I. Taylor (wikipedia link). An accompanying set of notes is available at http://web.mit.edu/hml/notes.html. He uses experiments to explain the topics in a way which helps develop one’s intuition for understanding and solving fluids problems.