Chte odel heo.. Intoduction Phsicl siultion of hdulic henoenon, such s the flow ove sillw, in the lboto is clled hsicl odel o onl odel. Potote is the hdulic henoen in the ntue like the sillw ove d. odels nd ototes hve geoetic, ktic nd dnic siilities. Geoetic Siilit is the geoetic elic of the otote nd it is siilit in fo. If A length on the odel, he length of tht hsicl length on the otote, the ength Scle ( of the odel is, (. If the length scle of otote nd its odel is tken s constnt, the e geoeticll siil. he choose of length scle fo odel deends uon to the hsicl ccit of the lboto nd lso to the oble to be ed. Usull /0, /0, /00 scles e used fo hdulic odels. Ktic Siilit denotes siilit of otion, i.e. siilit of velocit nd cceletion coonents long the,, es. et s tke the velocities t conjugnt oints on the odel nd the otote s elocit on the odel, elocit on the otote, elocit Scle is couted b, (. he odel nd otote is kticll siil if the velocit scle is constnt. elocit scle is lso cn be deived s, Pof. D. Atıl BUU
Pof. D. Atıl BUU, (. Whee is the ie Scle. (.4 Acceletion Scle cn be deived siill s, (. Acceletion scle will be constnt nd the ths of fluid ticles will be siil when the ktic siilit is sulied in the odel nd the otote. Dnic siilit denotes the siilit of foces. If thee is constnt tio between the foces on the conjugnt oints on the odel nd the otote then the two sstes is dnicll siil. oce Scle cons (.6
Genell, ti, essue, sheing, gvittionl foces e seen on the hdulic odels... Siilit Conditions odel eeients e lied fo lost eve iotnt hdulic stuctue. Otiu solutions be obtd b the obsevtions nd the esueents of the hsicl event on the odel which cn not lws be seen nd undestood duing the nlticl solution of the stuctue. Hdoowe lnts, ive ioveent, costl engeing nd lso in vition nd in shi constuction sectos e whee the odel eeients e lied. Siilit conditions should be sulied to find the esued vlues between the conjugnt oints on the odel nd on the otote. o instnce the esued wve height t hbo odel will coesond which height on the otote is the question to be nsweed. Dnic ethod is lied to sul the siilit conditions.... Dnic ethod Dnic ethod deends on the constnt vition of foces on the odel nd on the otote which is oce Scle is ket constnt. Doinnt foces on hdulic stuctues e Ineti, Gvittionl nd iscosit foces. Denoting s Ineti oce, Gvittionl oce g, iscosit oce vis, the siilit of the tio of foces cn be witten s, ( ( ( g ( g ( vis ( vis (.7 his equlit of foce tios eqution cn lso be witten s, ( g ( ( vis ( ( g ( ( vis ( (.8 Ineti foce cn be defd b using Newton s nd lw s, Ineti oce ss Acceletion Pof. D. Atıl BUU
B using the diensions of these hsicl vlues, the diension of the ti foce cn be deived s, [ ] [ ] [ g] [ ] 4 [ ] [ ] [ ] [ ] [ ] [ ] (.9 Gvittionl foce is the weight of the bod nd cn be defd s, Gvittionl foce Secific weight olue [ g ] [ ] [ ] [ ] [ ] g (.0 he tio of foces cn be witten gin b using the bove deived equtions s, ( ( g g ( ( g g (. g g Since diension of velocit is, [ ] [ ] [ ] [ ] [ ] [ ] g g king the invese of this eqution gives, 4 Pof. D. Atıl BUU
g (. g Since oude nube ( is, g Eqution (. shows tht oude nubes clculted fo the odel nd the otote t oint should be the se. (. he equlit of the tio of the gvit foces to the ti foces esults in to the equlit of oude nubes. iscosit foce cn be defd s, iscosit foce Sheing stess Ae vis vis τ A du d A [ ] [ ] vis [ ] [ ] (.4 he equlit of the tio of viscosit foces to ti foces is then, ( vis ( ( vis ( ( ( ( ( (. Pof. D. Atıl BUU
Since, [ ] [ ] [ ] [ ] [ ] [ ] Eqution cn be witten s, king the invese of this eqution ields, (.6 Since Renolds nube (Re is, Re Eqution (.6 shows the equlit of Renolds nubes fo the odel nd the otote t the oint tken. Re Re (.7 he deived esults e,. oude nd Renolds nubes e the tio of, oude nube Inetil foce / Gvittionl foce Renolds nube Re Inetil foce / iscosit foce 6 Pof. D. Atıl BUU
. Dnic siilit cn be sulied b the equlit of oude nd Renolds nubes siultneousl t the odel nd the otote... Selection of odel Scle, Re Re Using the equlit of oude nubes, g g g g g (.8 S the odel nd the otote will be constucted on the se lnet (eth, gvittionl cceletion scle is g. he bove eqution gives the theticl eltion between the velocit nd geoetic scle s, (.9 his theticl is the esult of the equlit of oude nubes t the odel nd the otote. Using the equlit of Renolds nubes, 7 Pof. D. Atıl BUU
Re ν ν ν Re ν ν ν (.0 Since the se fluid (wte will be used t the odel nd the otote, ktic viscosit scle is υ. he equlit of Renolds nubes ields the theticl eltion between velocit nd geoetic scle s, (. Since the equlit of Renolds nd oude nubes ust be sulied siultneousl, using the deived eltions between the velocit nd geoetic scles, (. his esult shows tht the odel nd the otote will be t the se sie which does not hve n cticl ening t ll. he tio of gvittionl, til nd viscosit foces cn not be sulied t the se tie. One of the viscosit o gvittionl foces is tken into considetion fo the odel lictions..4. oude odels oude odels denote suling the equlit of oude nubes t the odel nd the otote. Oen chnnel odels e constucted s oude odel since the otive foce in oen chnnels is gvit foce which is the weight of wte in the flow diection. D 8 Pof. D. Atıl BUU
Pof. D. Atıl BUU 9 sillws, hbos, wte intke stuctues nd eneg dissitos e the eles of hdulic stuctues. king the deived eltion between the velocit nd geoetic scles, (. he scles of the othe hsicl vibles cn be deived in geoetic scle. he diension of hsicl vible A, [ ] [ ] [ ] [ ] A he diension of this hsicl vlue A is then, A (.4 Since, (. (.6 he scle of the hsicl vlue of A is, A A + + (.7 he dischge scle cn be found s b using the bove deived eqution s,
Pof. D. Atıl BUU 0 [ ] [ ][ ][ ] 0 (.7 Ele.: Geoetic scle of sillw odel is chosen s /0. If the dischge on the otote is 00 /sec, wht will be the dischge on the odel? Since, 6. 0 sec / 0.6 6. 00 b If the velocit t oint on the odel is esued s /sec, wht will be the velocit on the otote t tht hoolog oint?.6 0 sec / 9.49.6
c If the eneg dissited with hdulic ju on the bsin of the sillw is N 00 kw, wht will be the dissited eneg on the otote? Eneg eqution is, N γh [ N] [ ][ ][ ] [ N] [ ] Using the deived scle eqution, A + + + N 7 Powe scle is, N 0 7 6 he dissited eneg on the bsin is, N N N N 00 6 600kW Ele.: Potote dischge hs been given s /sec fo oude odel. elocit nd foce t oint on the odel hve been esued s 0. /sec nd N. Clculte the dischge fo the odel nd velocit nd foce t the conjugte oint on the otote. Geoetic scle hs been s /00. he se liquid will be used t both odel nd otote. Solution: 00 Dischge fo the odel is, Pof. D. Atıl BUU
Pof. D. Atıl BUU sec 0.0 sec 0 0 0 00. lt elocit scle is, sec 0 0. 0 0 00 0. oce scle is, kn N 6 6 6 0 0 0 0 00
Pof. D. Atıl BUU.. Renolds odels If the govening foces of the otion e the viscosit nd the ti foces like in essued ie flows, Renolds odels e used. In Renolds odels the equlit of the Renolds nubes e sulied. Using the deived eltion between the velocit nd the geoetic scle, the scle of n hsicl vlue cn be deived. A (.8 Since, A A + + (.9 he dischge scle fo Renolds odels is, [ ] [ ][ ][ ] 0 (.0 Dischge is equl to the geoetic scle fo Renolds odels. Ele.: 0.0 /sec, D 0.0, nd D 0. e in ventuiete. A odel of it will de in / geoetic scle. ind out tie, velocit, dischge, nd essue scle of this entuiete. igue Solution: Renolds odel will be lied since the flow is essued flow in entuiete.
Pof. D. Atıl BUU 4 Geoetic hs been given s, ie scle is; + + [ ] [ ] 0, 0, 0 0 (. elocit scle is; + + [ ] [ ] 0,, 0 (. Pessue scle is; [ ] [ ] + +
Pof. D. Atıl BUU [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ],, 4 + (. Dischge scle is, [ ] [ ] + [ ] [ ] [ ] [ ] [ ] 0,, 0 0 +