Hidrouliese diameter

Sirkelvormige buis

Diameter = ${\displaystyle d}$

${\displaystyle A={\frac {\pi }{4}}d^{2}}$

${\displaystyle P=\pi d}$

${\displaystyle D_{H}={\frac {4A}{P}}={\frac {4\times {\frac {\pi }{4}}d^{2}}{\pi d}}=d}$

${\displaystyle D_{ekwivalent}={\sqrt {\frac {4A}{\pi }}}={\sqrt {\frac {4{\frac {\pi }{4}}d^{2}}{\pi }}}=d}$

Vierkant

Lengte van sye = ${\displaystyle L}$

${\displaystyle A=L^{2}}$

${\displaystyle P=4L}$

${\displaystyle D_{H}={\frac {4A}{P}}={\frac {4L^{2}}{4L}}=L}$

${\displaystyle D_{ekwivalent}={\sqrt {\frac {4A}{\pi }}}={\sqrt {\frac {4L^{2}}{\pi }}}=1.128L}$

Reghoek

Lengte = ${\displaystyle L}$ en breedte = ${\displaystyle B}$

${\displaystyle A=LB}$

${\displaystyle P=2(L+B)}$

${\displaystyle D_{H}={\frac {4A}{P}}={\frac {4LB}{2(L+B)}}={\frac {2LB}{L+B}}}$

${\displaystyle D_{ekwivalent}={\sqrt {\frac {4A}{\pi }}}={\sqrt {\frac {4LB}{\pi }}}=1.128{\sqrt {LB}}}$

Oop kanaal

${\displaystyle A=H\times W}$

${\displaystyle P=2H+W}$

${\displaystyle R_{H}={\frac {A}{P}}={\frac {HW}{2H+W}}}$

Half vol pyp

Beskou prentjie aan die regterkant vir 'n halfvol pyp:

Area van driehoek:

${\displaystyle r={\frac {D}{2}}}$            ${\displaystyle a=H-r}$

${\displaystyle a^{2}+b^{2}=r^{2}}$ (Volgens Pythagoras)

${\displaystyle \left(H-r\right)^{2}+b^{2}=r^{2}}$

${\displaystyle H^{2}-2Hr+r^{2}+b^{2}=r^{2}}$

${\displaystyle b^{2}=2Hr-H^{2}}$

${\displaystyle b={\sqrt {2Hr-H^{2}}}}$

${\displaystyle Area\ van\ driehoek={\frac {1}{2}}a.2b=ab=\left(H-r\right)\cdot {\sqrt {2Hr-H^{2}}}}$

${\displaystyle Area\ van\ driehoek=\left(H-{\frac {D}{2}}\right)\cdot {\sqrt {HD-H^{2}}}}$

Area van sirkelsegment:

${\displaystyle Area\ van\ sirkelsegment={\frac {\theta }{360}}\cdot {\frac {\pi }{4}}D^{2}}$

${\displaystyle \sin \alpha ={\frac {a}{r}}}$

${\displaystyle \alpha =\arcsin \left({\frac {H-r}{r}}\right)=\arcsin \left({\frac {H-{\frac {D}{2}}}{\frac {D}{2}}}\right)=\arcsin \left({\frac {2H-D}{D}}\right)}$

${\displaystyle \theta +\left(180-2\alpha \right)=360}$            ${\displaystyle \theta =2\alpha +180}$

${\displaystyle \theta =2\alpha +180=2\arcsin \left({\frac {2H-D}{D}}\right)+180}$

${\displaystyle \theta =2\arcsin \left({\frac {2H-D}{D}}\right)+180}$

Totale area:

${\displaystyle Totale\ area\ (A)=\left(H-{\frac {D}{2}}\right)\cdot {\sqrt {HD-H^{2}}}+{\frac {\theta }{360}}\cdot {\frac {\pi }{4}}D^{2}}$

${\displaystyle Benatte\ omtrek\ (P)={\frac {\theta }{360}}\cdot \pi D}$

${\displaystyle \theta =2\arcsin \left({\frac {2H-D}{D}}\right)+180}$

Om ${\displaystyle \theta }$ in Excel te bereken, gebruik die volgende formule:

"=2*DEGREES(ASIN((2*B4-B3)/B3)) + 180"

Hitteruiler vierkantige buiskonfigurasie

Die hidrouliese diameter word uitgewerk vir hitteruilers aan die mantelkant om die drukval oor die mantelkant en ook die filmkoëffisiënt te bepaal vir die berekening van die warmteoordragskoëffisiënt (U).

Hier volg die berekening vir 'n vierkantige buiskonfigurasie van 'n hitteruilerː

${\displaystyle A=p^{2}-{\frac {4\times 90}{360}}\cdot {\frac {\pi }{4}}d^{2}=p^{2}-{\frac {\pi }{4}}d^{2}}$

${\displaystyle P={\frac {4\times 90}{360}}\pi d=\pi d}$

${\displaystyle d_{e}={\frac {4A}{P}}={\frac {4\left(p^{2}-{\frac {\pi }{4}}d^{2}\right)}{\pi d}}={\frac {4}{\pi d}}\left(p^{2}-{\frac {\pi }{4}}d^{2}\right)}$

${\displaystyle d_{e}={\frac {1.27}{d}}\left(p^{2}-0.785d^{2}\right)}$

Hitteruiler driehoekige buiskonfigurasie

Die hidrouliese diameter word uitgewerk vir hitteruilers aan die mantelkant om die drukval oor die mantelkant en ook die filmkoëffisiënt te bepaal vir die berekening van die warmteoordragskoëffisiënt (U).

Hier volg die berekening vir 'n driehoekige buiskonfigurasie van 'n hitteruilerː

${\displaystyle p^{2}=h^{2}+\left({\frac {p}{2}}\right)^{2}}$            ${\displaystyle h^{2}=p^{2}-{\frac {p^{2}}{4}}={\frac {3}{4}}p^{2}}$            ${\displaystyle h={\frac {\sqrt {3}}{2}}p}$

${\displaystyle A={\frac {1}{2}}ph-{\frac {3\times 60}{360}}\cdot {\frac {\pi }{4}}d^{2}={\frac {\sqrt {3}}{4}}p^{2}-{\frac {\pi }{8}}d^{2}}$

${\displaystyle P={\frac {3\times 60}{360}}\pi d={\frac {1}{2}}\pi d}$

${\displaystyle d_{e}={\frac {4A}{P}}={\frac {4\left({\frac {\sqrt {3}}{4}}p^{2}-{\frac {\pi }{8}}d^{2}\right)}{{\frac {1}{2}}\pi d}}}$

${\displaystyle d_{e}={\frac {8}{\pi }}{\frac {\sqrt {3}}{4}}{\frac {1}{d}}\left(p^{2}-{\frac {\pi }{8}}{\frac {4}{\sqrt {3}}}d^{2}\right)={\frac {2{\sqrt {3}}}{\pi d}}\left(p^{2}-{\frac {\pi }{2{\sqrt {3}}}}d^{2}\right)}$

${\displaystyle d_{e}={\frac {1.10}{d}}\left(p^{2}-0.907d^{2}\right)}$

• Manningvergelyking