Problem 4: Study the effects pf hydraulic diameter. A rectangular duct with air

Question

Problem 4: Study the effects pf hydraulic diameter. A rectangular duct with air flowing measures 1 foot by 3 foot (so that it can fit in a ceiling crawl space) and it is to be compared to a 2 foot diameter round duct, which has a similar cross- sectional area, meaning it carries a similar mass flow of air for the same velocity. Use the round duct as the base case Note that hydraulic diameter is equal to 4 times cross-sectional area divided by the wetted perimeter (verify this relationship by finding the hydraulic diameter of a round duct which should be equal to diameter).

Explanation / Answer

The hydraulic diameter, DH, is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. It is defined as

Dh = (4*A)/P

where

A is the cross-sectional area of the flow,

P is the wetted perimeter of the cross-section.

For round duct A = Pi*(r^2) and P=2*Pi*r hence Dh = (4*A)/P = 2r = Diameter of round duct.

For rectangle Area = 3 and Perimeter = 8 so Dh = 1.5 foot.

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