continuity

Examples of continuity in the following topics:

• Flow Rate and the Equation of Continuity

  • The equation of continuity works under the assumption that the flow in will equal the flow out.
  • The equation of continuity applies to any incompressible fluid.
  • You can observe the continuity equation's effect in a garden hose.
  • This is a consequence of the continuity equation.
  • For example, if the nozzle of the hose is half the area of the hose, the velocity must double to maintain the continuous flow.

• Equipotential Lines

  • If charges are distributed across two conductor plates in static equilibrium, in which charges are continuous and distributed in a straight line, the equipotential lines will be approximately straight .
  • This is because the continuity of charges results in a continuity of action upon any point a certain distance from either plate.
  • This continuity is broken towards the ends of the plates, however, which causes curvature in these areas.
  • When charges are lined up and continuous on conducting plates, equipotential lines are straight between them.

• Convergence Theorems

  • One has to be a little careful about saying that a particular function is equal to its Fourier series since there exist piecewise continuous functions whose Fourier series diverge everywhere!
  • If $f$ is piecewise continuous and has left and right derivatives at a point $c$ (A right derivative would be: $\lim _{t\rightarrow 0} (f(c+t) - f(c)) /t$ , $t>0$ .
  • If $f$ is continuous with period $2\pi$ and $f'$ is piecewise continuous, then the Fourier series for $f$ converges uniformly to $f$ .

• Basic Map Types

  • Isoline (meaning "equal line") maps use continuous lines (sometimes called isolines or contours) to represent regional differences across a continuous surface.
  • Non-continuous cartograms are simpler.
  • Density maps depict the concentration of points across a continuous surface by joining adjacent points together and shading more concentrated clusters more darkly.

• What is a Fluid?

  • A fluid is a substance that continually deforms (flows) under an applied shear stress.
  • A fluid is a substance that continually deforms (flows) under an applied shear stress.

• X-Ray Diffraction

  • These XRD machines record images in two ways, either continuous scans or step scanning.
  • In continuous scans, the detector moves in circular motions around the object, while a beam of x-ray is constantly shot at the detector.
  • It is much more efficient than continuous scans.
  • To ensure that the incident beam is continuous, XRD machines are equipped with a Soller slit.

• The Ray Aspect of Light

  • Even when passing through a material, or bouncing off of a material in a reflection, the light continues to travel in a straight line, even if that line has changed direction.
  • Direct light travel is when a ray of light starts at a source, and continues to travel from that source to its destination without encountering any interference.
  • The light will continue in a straight line or ray until it reaches the observer.
  • This is only a directional change and will continue in this new path, but still as a straight line, or ray.

• Locating the Center of Mass

  • If the mass distribution is continuous with the density ρ(r) within a volume V, the position of COM is given as
  • If a continuous mass distribution has uniform density, which means ρ is constant, then the center of mass is the same as the center of the volume.
  • Identify the center of mass for an object with continuous mass distribution

• Ideal Fluids

  • for a bunch of fluid; therefore, we also have a continuity equation for the entropy
  • We can use the continuity equation for particle number to simplify this further,

• Blood Flow

  • Blood flow is the continuous running of blood through the cardiovascular system, which consists of the vessels and the heart.
  • Blood flow is the continuous running of blood through vessels in the cardiovascular system (the mammalian cardiovascular system is shown in ).