# Circular ring

Circular ring with designations

A circular ring is the area between two concentric circles , i.e. H. between two circles with a common center. Its area is

${\ displaystyle A = \ pi \ cdot (R ^ {2} -r ^ {2}) = {\ frac {\ pi} {4}} \ cdot (D ^ {2} -d ^ {2})}$,

where is the number of circles and and mean the radii as well as and the diameter of the outer and inner circle. ${\ displaystyle \ pi}$${\ displaystyle R}$${\ displaystyle r}$${\ displaystyle D = 2R}$${\ displaystyle d = 2r}$

The area can also be calculated from the inside diameter or outside diameter and ring width : ${\ displaystyle d}$${\ displaystyle D}$${\ displaystyle b}$

${\ displaystyle A = \ pi \ cdot (Db) \ cdot b = \ pi \ cdot (d + b) \ cdot b}$

This information can be found e.g. B. with pipe cross-sections; where is the wall thickness. ${\ displaystyle b}$

Furthermore, the area can be calculated using the annulus width and the mean annulus diameter${\ displaystyle b}$${\ displaystyle d_ {m} = (D + d) / 2}$${\ displaystyle A}$

${\ displaystyle A = \ pi \ cdot d_ {m} \ cdot b}$.

The effective hydraulic diameter for a circular ring for hydraulic applications is ${\ displaystyle d_ {H}}$

${\ displaystyle d_ {H} = {\ frac {D ^ {2} -d ^ {2}} {D + d}} = Dd}$.

Should z. For example, for brake discs , a frictional torque to the axial force and the coefficient of friction by ${\ displaystyle M_ {t}}$${\ displaystyle F_ {ax}}$ ${\ displaystyle \ mu}$

${\ displaystyle M_ {t} = \ mu \ cdot F_ {ax} \ cdot r _ {\ mu}}$

are determined, the friction-relevant radius calculated or diameter by ${\ displaystyle r _ {\ mu}}$${\ displaystyle d _ {\ mu}}$

${\ displaystyle r _ {\ mu} = {\ frac {2 \ cdot (R ^ {3} -r ^ {3})} {3 \ cdot (R ^ {2} -r ^ {2})}}}$or .${\ displaystyle d _ {\ mu} = {\ dfrac {2 \ cdot (D ^ {3} -d ^ {3})} {3 \ cdot (D ^ {2} -d ^ {2})}}}$