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Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution. This method models the resulting three-dimensional shape as a stack of an infinite number of discs of varying radius ...
For example, the solution to the Dirichlet problem for the unit disk in R 2 is given by the Poisson integral formula. If f {\displaystyle f} is a continuous function on the boundary ∂ D {\displaystyle \partial D} of the open unit disk D {\displaystyle D} , then the solution to the Dirichlet problem is u ( z ) {\displaystyle u(z)} given by
In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [2] For a radius, , an open disk is usually denoted as and a closed disk is ¯.
For example, we can calculate the effective transfer speed for a floppy disc by determining how fast the bits move under the head. A standard 3½-inch floppy disk spins at 300 rpm, and the innermost track is about 66 mm long (10.5 mm radius). At 300 rpm the linear speed of the media under the head is thus about 66 mm × 300 rpm = 19800 mm ...
In other words, the solution of equation 2, u(x), can be determined by the integration given in equation 3. Although f ( x ) is known, this integration cannot be performed unless G is also known. The problem now lies in finding the Green's function G that satisfies equation 1 .
The harmonic capacity can also be understood as a limit of the condenser capacity. To wit, let S r denote the sphere of radius r about the origin in . Since K is bounded, for sufficiently large r, S r will enclose K and (Σ, S r) will form a condenser pair. The harmonic capacity is then the limit as r tends to infinity:
The essence of the actuator-disc theory is that if the slip is defined as the ratio of fluid velocity increase through the disc to vehicle velocity, the Froude efficiency is equal to 1/(slip + 1). [2] Thus a lightly loaded propeller with a large swept area can have a high Froude efficiency.
In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions . The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region.