A Newtonian fluid with a viscosity drains through the space between two large parallel plates as shown in the figure. The gap
distance between the plates is 2b. Obtain relations for the shear stress distribution, shear stress at the walls, velocity profile and volumetric flow rate assuming laminar flow and negligible end effects. You can begin the derivations by considering that vz=vz(x) only and pressure at the inlet and outlet is atmospheric.
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Here is the full question
Suppose there are 10,000 civilizations in the Milky Way Galaxy. If the civilizations were randomly distributed throughout the disk of the galaxy, about how far (on average) would it be to the nearest civilization?
(Hint: Start by finding the area of the Milky Way's disk, assuming that it is circular and 100,000 light-years in diameter. Then find the average area per civilization, and use the distance across this area to estimate the distance between civilizations.)
Answer:
1000 light-years (ly)
Explanation:
If we go by the hint; The area of the disk can be expressed as:
where D = 100, 000 ly
Let's divide the Area by the number of civilization; if we do that ; we will be able to get 'n' disk that is randomly distributed; so ;
The distance between each disk is further calculated by finding the radius of the density which is shown as follows:
replacing d = in the equation above; we have:
The distance (s) between each civilization =
= 2 (500 ly)
= 1000 light-years (ly)