A Course in Classical Physics 2—Fluids and Thermodynamics by Alessandro Bettini

By Alessandro Bettini

This moment quantity covers the mechanics of fluids, the rules of thermodynamics and their functions (without connection with the microscopic constitution of systems), and the microscopic interpretation of thermodynamics.

It is a part of a four-volume textbook, which covers electromagnetism, mechanics, fluids and thermodynamics, and waves and light-weight, is designed to mirror the common syllabus through the first years of a calculus-based college physics application.

Throughout all 4 volumes, specific consciousness is paid to in-depth explanation of conceptual facets, and to this finish the ancient roots of the crucial strategies are traced. Emphasis is additionally continually put on the experimental foundation of the options, highlighting the experimental nature of physics. each time possible on the common point, ideas appropriate to extra complex classes in quantum mechanics and atomic, stable kingdom, nuclear, and particle physics are incorporated. each one bankruptcy starts with an advent that in brief describes the topics to be mentioned and ends with a precis of the most effects. a few “Questions” are incorporated to aid readers payment their point of understanding.

The textbook bargains a fantastic source for physics scholars, teachers and, final yet now not least, all these looking a deeper knowing of the experimental fundamentals of physics.

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Example text

It is standard to divide it by two, and we shall use 12 qt2 =D (that is, the kinetic energy per unit mass divided by the tube diameter). We can conclude that Dp qt2 ¼ f ðReÞ 2D l ð1:49Þ where f is a dimensionless coefficient, called the Darcy friction factor after Henry Darcy (1803–1858). The friction factor is a function of the unique dimensionless quantity of the problem, namely the Reynolds number. Written explicitly, the Darcy friction factor defined by Eq. 49) is f ðReÞ ¼ 2DDp : lqt2 ð1:50Þ We notice here that, even if the viscosity does not have an effect on the relation between the pressure gradient and flow velocity, its effects are relevant within the boundary layer.

First, we observe that the dimension of the mass can be eliminated only by taking the ratio between viscosity and density, namely the kinematic viscosity ν = η/ρ. Its dimensions are ½mŠ ¼ m2 sÀ1 . Once more, we have only one way to eliminate the dimension of time, namely dividing υ by ν: ½t=mŠ ¼ mÀ1 . Finally, we eliminate the length, multiplying by the diameter D. We have thus found the unique dimensionless combination of the four quantities Re ¼ tD qtD ¼ ; m g ð1:48Þ which is called the Reynolds number, after Osborne Reynolds (1842–1912).

This is just what we expect, because the drag is proportional to the velocity when the Stokes law holds (for shapes other than a sphere, the drag force in this regime is proportional to the velocity and to the linear dimensions of the body anyway). Indeed, if we substitute the Stokes Eq. 52) for the drag in Eq. 57) and A = πD2/4 for the cross-section of the sphere of diameter D, we obtain CD ðReÞ ¼ 24=Re: ð1:58Þ Under these conditions, as we have seen, the drag force is almost completely a viscous drag.

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