Hydraulic Diameter Explained: 4.4 vs 4.5

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SUMMARY

The discussion clarifies the definitions of hydraulic diameter in two contexts: in section 4.4, the hydraulic diameter is defined as D = 4Rh, while in section 4.5, it is incorrectly stated as D = 2Rh. The hydraulic radius (Rh) is consistently defined as the area divided by the wetted perimeter (S/Lp). The author mistakenly uses the subscript "H" in section 4.5, which should simply be "R," leading to confusion regarding the relationship between the hydraulic radius and the radius of the cylinder (R).

PREREQUISITES
  • Understanding of hydraulic radius and its calculation (S/Lp)
  • Familiarity with the concept of hydraulic diameter
  • Basic knowledge of fluid mechanics
  • Ability to interpret mathematical equations in engineering contexts
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  • Study the derivation of hydraulic diameter in fluid mechanics
  • Learn about the implications of hydraulic radius in open channel flow
  • Research common mistakes in hydraulic calculations
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foo9008
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Homework Statement


why in 4.4 the author gave D =4Rh? in 4.5, D= 2Rh ?

Homework Equations

The Attempt at a Solution

 

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In some developments, the hydraulic radius is defined as the area divided by the wetted perimeter. Get used to the idea.
 
Chestermiller said:
In some developments, the hydraulic radius is defined as the area divided by the wetted perimeter. Get used to the idea.
why in 4.4 the author gave D =4Rh? in 4.5, D= 2Rh ? can you explain?
 
foo9008 said:
why in 4.4 the author gave D =4Rh? in 4.5, D= 2Rh ? can you explain?
Yes. He is consistent in defining the hydraulic radius as S/Lp, and the equivalent diameter as 4S/Lp. However, in 4.5, he makes the mistake of calling the radius of the cylinder RH. The term in brackets should not have a subscript H. It should just have an R. And, for a cylinder, RH=R/2.
 

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