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The thermal entrance length for a fluid with a Prandtl number greater than one will be longer than the hydrodynamic entrance length, and shorter if the Prandtl number is less than one. For example, molten sodium has a low Prandtl number of 0.004, [12] so the thermal entrance length will be significantly shorter than the hydraulic entrance length.
L is the length Re is the Reynolds number and Pr is the Prandtl number. This number is useful in determining the thermally developing flow entrance length in ducts. A Graetz number of approximately 1000 or less is the point at which flow would be considered thermally fully developed. [2]
Here, the bar on the left side of the figure is the mixing length. In fluid dynamics, the mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a Newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century. [1]
The entrance pupil is the image of the aperture stop viewed from the front of the optical system and here it is a virtual image. Chief rays and marginal rays determine the location and the size of the entrance pupil, respectively. A camera lens adjusted for large and small aperture. The visible opening is the entrance pupil of the lens.
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where R is Earth radius, Ω is frequency of rotation of the Earth, g is gravitational acceleration, φ is latitude, ρ is density of air and ν is kinematic viscosity of air (we can neglect turbulence in free atmosphere). In synoptic scale we can expect horizontal velocities about U = 10 1 m.s −1 and vertical about W = 10 −2 m.s −1.
The entrance pupil is located at infinity, and chief rays before the objective are parallel to the optical axis. An object-space telecentric lens has the entrance pupil (the image of the lens's aperture stop, formed by optics before it) at infinity and provides an orthographic projection instead of the perspective projection in