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Solid cylinder of radius r, height h and mass m. This is a special case of the thick-walled cylindrical tube, with r 1 = 0. = [1] = = (+) Thick-walled cylindrical ...
For the thin-walled assumption to be valid, the vessel must have a wall thickness of no more than about one-tenth (often cited as Diameter / t > 20) of its radius. [4] This allows for treating the wall as a surface, and subsequently using the Young–Laplace equation for estimating the hoop stress created by an internal pressure on a thin-walled cylindrical pressure vessel:
(It may be necessary to calculate the stress to which it is subjected, for example.) On the right, the red cylinder has become the free body. In figure 2, the interest has shifted to just the left half of the red cylinder and so now it is the free body on the right. The example illustrates the context sensitivity of the term "free body".
Here, the function gives the mass density at each point (,,), is a vector perpendicular to the axis of rotation and extending from a point on the rotation axis to a point (,,) in the solid, and the integration is evaluated over the volume of the body . The moment of inertia of a flat surface is similar with the mass density being replaced by ...
The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV. The fluid displaced has a weight W = mg, where g is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as W = ρVg.
The bare term cylinder often refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in the figure. The cylindrical surface without the ends is called an open cylinder. The formulae for the surface area and the volume of a right circular cylinder have been known from early antiquity.
The second polar moment of area, also known (incorrectly, colloquially) as "polar moment of inertia" or even "moment of inertia", is a quantity used to describe resistance to torsional deformation (), in objects (or segments of an object) with an invariant cross-section and no significant warping or out-of-plane deformation. [1]
The term “cylinder” can refer to a three-dimensional solid or, as in this article, only the curved external surface of the solid. This is why a line piercing a cylinder's volume is considered to have two points of intersection: the surface point where it enters and the one where it leaves.