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11 A P P E N D I X C C 1. Calibratin f Cpper-Cnstantan Thermcuples The thermcuples were calibrated accrding t British Standards BS 1042 (Part 4). The calibratin curve is given in Fig C.l. As expected the calibratin is 1 inear. C 2. Calibratin f the Ht-wire Anemmetrv The ht-wire prbes were calibrated using the DISA type 55D90 calibratin equipment. With this equipment a knwn air velcity may be applied t a ht-wire cnnected t an anemmeter and the resulting vltage utput is displayed directly nt a digital vltmeter. The anemmeter unit, a DISA type 55D01, was adjusted fr each prbe, prbe supprt and ''able accrding t the DISA Instructin and Service Manual [31] fr the anemmeter. The prbes were s similar that the nly alteratins that had t be made, when changing frm ne prbe t anther, was the varying f the decade resistance settings. This allwed fr slight differences in resistances between the prbes t be cmpensated fr. Anemmeter measurements are based n measuring the cnvective heat lss frm an electrically heated ht-wire. The respnse f a ht wire t a flw field may be described by the fllwing expressin: E 2 = E* + B -Ueffn...

12 Fig C.l - thermcuple milli-vlts C a Calibratin Curve fr Ihermcuples utput

13 where: E is the bridge vltage f the anemmeter Eq is the bridge vltage f the anemmeter in the static cnditin, i e when U rr = 0,0. err is the effective cling velcity f the ht-wire. During the calibratin, measurements were made f the effective clirg velcity by means f a pressure transducer within the calibratin equipment, it was als checked externally by means f a pressure tapping and inclined water manmeter. Fr values f cling velcities ranging frm 1,0 m/s t 1 2 0,0 m/s the vltage utput frm the aremmeter unit was mnitred n a Hewlett-Packard digital vltmeter. The ht-wires were calibrated in tw rientatins fr reasns which are described in Chapter 6. The tw psitins are illustrated in Figs C.2 (a) and (b). Fig C.2 - Tw Orientatins f the ht-wires

14 The effective cling velcity n a ht-wire is defined by: U 2 = U 2 ku.?...(c.2.) ctr 1!l U1 is t\e velcity perpendicular t the ht-wire U is the velcity parallel t the ht-wire k is nt cnstant but varies with U,(, it is always <1,0. Calibratin curves fr the fur ht-wires are pltted in Figs C.3 t C.6. fhe upper line n these cuives gives the anemmeter uput vltage fr the cling velcity perpendicular t the prbe and s: U rr2 ef f = Uf i The lwer line gives the anemmeter vltage fr the cling velcity parallel t the prbe and hence: W * kuj The difference between the tw curves bviusly gives a measure f the magnitude f k at different velcities.» Frm equatin (G.l) taking the lgarithm f bth sides yields: lg(e2-e*) * lg B + n lg Ucff.... (C.3.) If lg(e -Eq ) is pltted against lg(^eff) then the result shuld be a straight line f slpe n. This was dne fr the prbe 1 calibratin curves and the resulting lines are illu trated in Fig C.7. The value f n was fund t be 0,5.

15 Prbe 1 Calibratin Curves

16 170-2 I Prbe 2 Calibratin Curves u a H u. O <> ID 2 «9 a 3 >0 <r

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18 20,0 40,0 60,0 80,0 100,0 120,0 tig C.6 - Prbe 4 Calibratin Curves U m/s

19 Fig C.7 - (E2-Eq) Versus Velcity fr Prbe

20 The shapes f the calibrat-n curves fr all the prbes were s similar that it was thught acceptable t use the index n = 0,6 fr all f them. The tp curves in the calibratin charts are thus apprximated t by the equatin E* * E2 * B (U) 6... (C.4) and the lwer curves by: E2 «E 2 * B (/Tell) 0, 6... (C.5) 2 O Cmbining equatins (C.4) and (C.5) yields an expressin fr k: IlirlAi «k.3 (E^-Ej) k, (IlldEil) (C.6 ) (e ;-ej) where fr a given velcity U, Ei is the utput vltage frm the prbe in psitin a), (see Fig C.2) and is read frm the upper curve. E2 is the utput vltage frm the prbe in psitin b) and is read frm the lwer curve. Thus a graph f k versus U may be btained fr each prbe, they are illustrated in Fig C.8. The curves fr prbes 1,3 and 4 are similar, the curve fr prbe 2 is vastly different. It is expected that prbe 2 was faulty, as it brke during the preliminary tests fr n apparent reasn.

21 175! </).s f-h <u, > 3 O rh m > -> r.c u ctl u <u 3 rh 03 > I 00 CJ c H u- 4.i

22 C 3. Crrectin f Ht-wire Readings fr the Influence f Temperature Variatins The calibratin charts fr the ht-wire prbes were btained fr ne calibratic^ temperature. The calibratin was carried ut at 21 C. In rder t be able t use the calibratin curves fr the determinatin f velcities at ther temperatures it is neces^ry t crrect the ht-wire eadings btained. Fr small temperature changes, apprximately C arund the calibratin temperature, the changes in the Prandtl number, viscsity and heat cnductivity can be neglected accrding t Kanevce [28]. Frm the Nusselt number crrelatin the heat transfer cefficient is thus als unchanged fr the same velcity. The heat balance equatin fr a ht-wire is: ''w jp = (Tw - T)h... (C.7) where E is the rltage drp acrss the ht-wire Rw is the wrking resistance f the ht-wire Tw is the wrking temperature f the ht-wire T h is the fluid temperature is the heat transfer cefficient. If h is cnstant then an expressin may be btained fr the crrectin f ht-wire readings fr the change f fluid temperature: (T -T ] c 2 2 '-wnj fr n ~ TT - TT...* (^*8) w where En is the crrected vltage reading and T^ is the

23 temperature at which calibratin was carried ut. By using the relatinship between electrical resistance and temperature: R = Rn (l + a(t-tn))...(c.9) where R dentes resistance and ct is the thermal resistance f the ht-wire which fr the platinum is 0,0026 ft/ C equatin (C.4) may be rewritten: K - E 1 * (c -10> Thus knwing the temperature f the air, equatin (C.9) is used t calculate the resistance f the ht-wire, and equatin (C.10) is then used t crrect the vltage readfngs btained. Values f R, w and R n btained fr the fur ht- res during calibratin are given in table C.l. Ht-wire Number V (Calibratin resistance) Rwn (Wrking resistance) 1 4,52 9,14 2 4,17 7,92 3 4,14 7,52 4 4,09 7,3 Table C.l - Values f Wrking and Calibratin Resistances fr the Ht-wires

24 A P P E N D I X D D 1. Calculatin f the Vlume flw Rate thrugh a Pipe by means f the velcity Prfile The vlume flw rate thrugh the prus pipe was calculated using a numerical integratin technique. The radius f the pipe was 31,75 mm. Fr ease f cmputing the x-sectin f the pipe was fictitiusly divided int a series f annular shapes and ne inner disc. The annular shapes were f thickness Ar (except fr the uter ne) and the inner disc was f radius Ar. The velcities at the edges f these shapes are defined as shwn in Fig D.l. Fig D.1 - Velcity Prfile superimpsed n the annular shapes

25 Ar was chsen t be 2,5 mm as this prved t give sufficient accuracy. This required defining furteen velcities as shwn in Fig D.l. The thickness f the uter annulus was 1,75 mm t allw fr the ttal x-sectinal area t be scanned. The ttal vlume flw rate is btained by summing the individual effects f flw thrugh the annular elements. The vlume flw rate thrugh a thin annulus f radius r and thickness fir is: Vlume flw rate = 2nr fir x V.... (D.l) where V is the nrmal velcity thrugh the annulus. The velcities are defined at the fllwing psitins (see Fig D.l) V at 0 = 0 0 V j at A r = 2,5 mm V 2 at 2Ar = 5,0 mm Vi 2 at 12Av = 30,0 mm V 1 3 at 12Ar +1,75 = 31,75 mm The vlume flw rate thrugh a typ equatin (D.l) is thus: xnnulus using A (V *V Vlume flw rate = 2tt(nAr+^JAr *" (V +V ) = TTAr?(2n+l)... (D.2) The vlume flw rate thrugh the central disc is simply

26 given by:, ( W Vlume flw rate = ttai2---^... (D.3) this can be seen t be exactly the same as thse fr the annulae with n = 0. The flw thrugh the uter annulus is given by: Vlume flw rate * 2tt (12Ar+1-^ -)1,7 As V 13 is defined at the wall f the pipe its value is zer and s the expressin may be rewritten as fllws: Vlume flw rate = rr( 30,8 7 5) 1,7 5V (D*4) The ttal vlume flw rate thrugh the pipe is given by cmbining equatins (D.2) t (D.4). 11 (V_+V +.) Ttal vlume flw rate * rrr2(2n+l)----*---- n=0 7(30,875)1,7 5 V i (D.5)

27 A P P E N D I X E E 1. Results frm the Cmputer Prgramme Tables E.l t E.IO give the calculated flw fields fr varius flw situatins. The velcity prfiles are flat and the suctin rates are unifrm alng the length f the pipe. The prus sectin is preceeded and fllwed by lengths f nn-prus piping. Table E.ll gives th results fr variable suctin alng the prus pipe in.ccrdance with the pressure balances described in sectin 3.10.

28 Tabic K.l - The Basic Prblem... n ttal thrugh flw n = 100 x'10 3 X Y Vx vy. CP 0, , , , , ,000 0, ,023 0,00 0-0,046 4,000 0, ,988 0, ,024 6, , ,696 0, ,515 8,000 0, ,302 0, ,909 10, , ,093 0, ,991 12, , ,488 0,00 0 0,762 14,000 0, ,873 0, ,238 16,000 0, ,985 0, ,029 18,000 0, , , , ,000 0, ,000 0,00 0 0, ,00 0 0,250 1,000 0, , ,000 0,250 1,02 3 0,003-0,04 5 4,000 0,250 0,988 0,005 0,024 6,0 00 0,250 0,690 0,02 5 0,515 8,000 0,250 0,302 0,025 0,908 10, ,250-0,09 3 0,025 0,991 12, ,2 50-0,487 0,025 0,762 14,000 0,250-0,874 0, ,236 16,000 0,250-0,9 84 0, ,031 18,000 0,250-1,011 0, , ,000 0,250-1, , , ,00 0 0,500 1,000 0, , ,500 1,023 0,004-0,047 4,000 0,500 0,987 0,007 0,026 6, ,500 0,694 0,049 0,516 8,000 0,500 0,301 0,049 0,907 10, ,500-0,092 0,050 0,989 12, ,500-0,486 0,050 0,762 14,000 0,500-0,874 0,045 0,224 16,000 0,500-0,979 0, ,039 18,000 0,500-1,0 11 0, , ,000 0,500-1, ,000 0, ,00 0 0,7 50 1, , , ,000 0,750 1,02 5 0, ,050 4,000 0, ,006 0,046 6,0 00 0,750 0,685 0,075 0,52 5 8,000 0,750 0,298 0,075 0,906 10, ,750-0,091 0,075 0,986 12, ,750-0,480 0,075 0,764 14,000 0,750-0,867 0,071 0,244 16,000 0,750-0,966 0,002 0,066 18,000 0,750-1,012 0, ,025 20,000 0,750-1, , ,00 0 0,00 0 1,000 1,000 0, ,00 0 2,250 1,000 0,99 0, ,005 4,000 1,000 0,939 0, ,118 6, ,000 0,659 0, ,556 8,000 1,000 0,287 0, ,908 10, ,000-0,088 0, , , , ,462 0, ,777 14,000 1,000-0,833 0, ,296 16,000 1, ,9 30 0, ,1^5 17,750 1,000-0,985 0,000 0,030 20,000 1, , ,000 0,001)

29 Authr Bale Barbara Anne Name f thesis Mass Transfer Thrugh A Prus Tube PUBLISHER: University f the Witwatersrand, Jhannesburg 2013 LEGAL NOTICES: Cpyright Ntice: All materials n the University f the Witwatersrand, Jhannesburg Library website are prtected by Suth African cpyright law and may nt be distributed, transmitted, displayed, r therwise published in any frmat, withut the prir written permissin f the cpyright wner. Disclaimer and Terms f Use: Prvided that yu maintain all cpyright and ther ntices cntained therein, yu may dwnlad material (ne machine readable cpy and ne print cpy per page) fr yur persnal and/r educatinal nn-cmmercial use nly. The University f the Witwatersrand, Jhannesburg, is nt respnsible fr any errrs r missins and excludes any and all liability fr any errrs in r missins frm the infrmatin n the Library website.