# Circular ring

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