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Preliminary Mathematics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
A sphere is a 3D object where all the points on the surface of the object are equidistant from a common center. If d is the diameter, r is the radius, and C is the circumference of the sphere, Surfacearea,A=πd2=4πr2=Cd=0.3183C2Volume,V=(A/6)d=πd3/6=0.5236d3=4/3πr3
Flow over Immersed Bodies
Published in William S. Janna, Introduction to Fluid Mechanics, Sixth Edition, 2020
The difference between a laminar and a turbulent velocity profile has a significant effect on where separation occurs, and on the drag force exerted. The turbulent profile can offer more resistance to an adverse pressure gradient. For a turbulent boundary layer, we therefore expect that separation will occur farther downstream than that for a laminar boundary layer. To see how the location of the point of separation affects flow past a cylinder, refer to Figure 6.12. In the laminar case, the boundary layer remains laminar to the point of separation. In the turbulent case, the laminar boundary layer experiences a transition to a turbulent boundary layer; as a result, the point of separation is moved farther downstream on the cylinder surface, and the form drag is thus reduced. A common technique of inducing transition is to roughen the surface of the object. A familiar example for a sphere is the surface of a golf ball.
Digital Image Fundamentals
Published in Sheila Anand, L. Priya, A Guide for Machine Vision in Quality Control, 2019
Common 3D shapes include cube, cylinder, sphere, cone, and pyramids, as shown in Figure 2.12. In 3D, we have the concept of faces, edges, and corners. Corners are also called vertices. A face is a large surface area that can be curved or flat. For example, a cube has 6 flat faces and 12 straight edges. A cylinder has 2 flat faces, 1 curved face, and 12 straight edges. A sphere has one curved surface and no edges or corners.
An alternative way of defining integration in multivariable calculus
Published in International Journal of Mathematical Education in Science and Technology, 2022
Fix r>0. In , let . Using a spherical coordinate transformation (7), we deduce that and . We see that for every . Therefore which is the formula for the volume of a sphere with radius r.