A water "light pipe" is created by a stream of water exiting a container through a hole with a circular cross section of diameter d=5mm. Lascr light is injected uniformly into the water stream through the hole as shown. If the water and laser light exits the container initially horizontally with a laminar flow, and we approximate the trajectory of the water as following a circular path (it would actually be parabolic) and maintaining a constant diameter for the "light pipe", find the smallest outside radius R permitted for the water path such that no laser light escapes on its first reflection with the water-air surface. Water has an index of refraction of n=1.33.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter11: Heat Transfer By Radiation
Section: Chapter Questions
Problem 11.11P
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 A water "light pipe" is created by a stream of water exiting a container

through a hole with a circular cross section of diameter d=5mm. Lascr light is injected

uniformly into the water stream through the hole as shown. If the water and laser light exits the container initially horizontally with a laminar flow, and we approximate the trajectory of the water as following a circular path (it would actually be parabolic) and maintaining a constant diameter for the "light pipe", find the smallest outside radius R permitted for the water path such that no laser light escapes on its first reflection with the water-air surface.

Water has an index of refraction of n=1.33.

 

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