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BI TP CHNG 8
8.14
Tm m thy tnh (hydrostatic bearing) chu mt ti
phn bu ft-chieu-dai (tm m hnh chnht t vung gc vi mt phng t giy). Du s
dng l SEA 30, 100F v 100 psig.
Tm : (a) b rng cn thit ca tm m chu ti, (b) phn b p sut dc tm
m v (c) b dy k h nu
ft-chieu-dai.
Gii:
Coi l dng lu cht chuyn ng gia 2 tm phng t song song l fully
developped , chy tng (1), t ta c (8.2): Suy ra phn b p sut l tuyn tnh theo phng
(Hnh
v).
Mt khc, ta c iu kin bin , do :
.
/ Gi l phn b ti, ft-chieu-dai, l chiu su tm m (tnh vomt phng t giy).p lc sinh ra trn tm m (bearing) :
. /
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* +
p dng cng thc cho dng chy loi (1) (cng thc 8.6b trang 315) ta c :
*
+
Tra Hnh A.2 (ph lc A-3 trang 722), ta c .
(
)
* + * +
Kim tra li gi tr s Reynolds :
Tra Hnh 4.3 ph lc A-3 trang 723, . Vy hon ton ph hp vi gi thit chy tng.
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8.15
Thnh phn c bn ca thit b kim tra p sut d (pressure
gage tester) bao gm h thng piston-cylinder nh hnh v.
Piston - ng kinh 6mm, chiu di 25mm - c t ti to
ra p sut theo gi trcho trc.
Tnh khi lng M to ra p sut 1,5MPa (p sut d) trong
cylinder. Xc nh vn tc dng r theo hm ca bn knh h a,
vi ti nh trn trong mi trng lu cht l du SAE 30
200C. Xc nh gi tr ti a cho php ca bn knh h chuyn
ng dc trc ca piston do dng r nhhn 1mm/min
Gii:
a) Tnh khi lng M:
Phng trnh nh lut II Newton cho piston:
T, khi lng ca vt
b) Biu thc xc nh lu lng dng r theo a:
Gi s khong h rt nh so vi ng knh piston, b qua chuyn ng ca
piston, ta c th xem dng r chy qua khong hnh l dng lu cht chy qua 2
tm phng, do lu lng dng r c tnh theo cng thc:
Trong l chiu di ca 2 thnh phng nn , cng thc lulng dng
r c vit li:
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c) Khong h a ln nht vn tc theo phng thng ng ca piston do c dng
r nhhn 1mm/pht:
Khi piston i xung vi vn tc , lu lng ca dng r: Do nn max khi max:
T khong h ln nht (vi du SAE30 c ):
[ ] [ ]
Kim tra li gi thit:Vn tc trung bnh ca dng r:
Do c thxem piston ng yn
Tnh s Reynolds:
Cng thc nh ngha trong phn ph lc (SG: special gravity):
T tnh nht ng hc thng qua nht ng lc hc (tra bng A.2 ph
lc A c SG ca du bng 0.92):
T tnh c:
Nn dng r l dng chy tng.
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8.16
Lu cht nht chy trong khe hp gia hai a song song nh hnh v. Lu lng
chy
, gia tc khng ng k. Profile vn tc coi nh pht trin hon chnh.
(a)Tm biu thc (b)Tm trong khe hp(c)Tm biu thc (d)Chng t rng net force cn gicho a bn trn (lc cn bng vi p lc
tc dng ln a bn trn) nm cn bng l
*
+
Gii:
(a) Ta c suy ra
(b) Coi dng chy trong khe l chy tng, pht trin y , phng ca dng
chy l phng ly tm (p sut thay i theo hng knh)
Vi (tnng, l lu lng qua mt tr bn knh ), t (c) Tch phn t n :
| Ta c iu kin bin ca trng p sut : ( l
p sut u vo).
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(d) Ta s dng p sut d tnh ton. p sut d ti bin , ti vngtrung tm .
p lc trong vng trung tm l . Vi phn p lc tc dng ln atrn vng l :
Ly tch phn trn ton ba, ta c p lc tng cng :
i bin :
(1) tr thnh :
[ ] , [ ] [ ]-
, -
*
+ pcm
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8.25
u c ca a my tnh t trn 1 a quay v cch mt lp mng khng kh (coi
dy ca lp khng kh l 0,5m). V tr ca u c cch tm a quay 150mm,
vn tc quay ca a l 3600rpm. u c l c kch thc 10mm mi chiu. Cho
khng kh ti khong h gia u c v a iu kin chun, tnh: a) s Reynolds
ca dng khng kh; b) ng sut nht dc; c) cng sut yu cu thng lc nht
Gii:
Ta c: Ti , ta c Gi thitkhng kh iu kin chun Vi khong h nh
Lc cn thit:
v moment xon l:
Cng sut tiu tn
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8.32
Mt cng dy nt c ko ln trong mt bn ha hc
vi vn tc U0, ko theo mt lp cht lng dy h, khi
lng ring , nht ng lc hc . Trng lc c xuhng ko cht lng xung nhng s di chuyn cacng dy lm cht lng btrt ra. Dng l pht trin
hon ton, chy tng v gradient p sut bng 0 v
ng sut trt ti b mt cht lng l 0. Lp biu thc
profile vn.
Gii:
ch co l c tr tDong on inh Do ng fully-developed
iu kin bin : ; a y: Lu y ta i
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8.38
Gii:
Co ng th c slide 12 chng nternal:
Do ng gi a 2 tam phang, 1 tam ng ye n,1 tam chuyen o ng va n toc do a
i va Moment va
Trong o
[
]
[
]
[ ] [ ]
Co ng suat h u ch la p, nen hie u suat la :
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8.43
Trong thit kxe hi, xu hng truyn ng tt ccc bnh xe ang pht trin nhm
tng hiu sut hot ng v an ton khi xe mt ma st. Nhng xe ny c b vi sai c
th hot ng trn ng kh. Trong qu trnh phn tch v thit k cn phi xc
nh truyn ng xon bi b vi sai vi tc khc nhau. Xc nh kch thc ca
b truyn ng vi sai vi monen xon 150Nm ti tc quay 125 vng/pht th s
dng du bi trn loi SAE 30.
Gii:
Ta c:
t
Gi tr 1 khe h.
Vi n khe h:
Vi ,
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8.77
Nc c bm t mt b cha cao 20 ft so vi bm x v mt ni cao hn bm 90
ft vi lu lng
. p sut pha u vo bm l 5 psig, p sutu ra l 50
psig. Cc ng u l ng thp thng mi (commercial steel) ng knh 6 in. Xc
nh (a) cng sut cung cp (head supplied) bi bm v (b) mt nng dc ng
(total head loss) gia u ra bm v ch xnc.
Gii:
(a) p dng phng trnh nng lng cho th tch kim sot quanh bm(phng
trnh tng qut 8.45 trang 347) :
* + Gi thuyt : (1) dng khng nn c
(2) (do vi dng chy trong ng (trang 335) vbo ton lu lng nn khng i)
(3)
T cc gi thuyt trn ta n gin phng trnh (1). Cng sut bm (head) tnh
bng nng lng trn mt n v khi lng (energy/mass) :
( ba ng A.7 )
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(b) Tnh ton mt nng gia u ra bm v ch xnc
Gi thuyt : (4) (5) T :
* Tnh cho mt n v trng lng :
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8.137
Mt h cha cung cp nc c h thng dn nc nh hnh v. Nc c bm t
h vo mt b cha nc trc khi c x l. H thng c thit k cung cp
1310 L/s nc 20oC
T B C h thng gm ming vo cnh vung (square-edged entrance), ng di
760m, 3 van ca, 4 ch un 45o v 2 ch un 90o. p sut d ti C l 197kPa.
T F G h thng gm 760m chiu di ng, 2 van ca, 4 ch un 90o. Tt cng
u c ng knh 508mm, lm bng gang.
Tnh vn tc trung bnh ca nc trong ng, p sut d ti F, cng sut cn cung cp
cho bm (hiu sut 80%) v w ti phn ng FG
Gii:
Vn tc trung bnh ca nc trong ng
xc nh p sut d ti F, ta s dng phng trnh nng lng cho dng n
nh, khng nn c gia F v G
Phng trnh nng lng c bn
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Gi thit :
(b ln);
;
T
*
+
Tra bng: S Reynolds
ng lm bng gang nn T th 8.12 vi gi tr
v tnh, ta thu c h s ma st Th svo phng trnh trn
[ ] * +* + (p sut d)
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p dng phng trnh nng lng cho bm Do Cng sut cn cung cp cho bm
p dng phng trnh nng lng cho on ng tF n G, ta c: Hay
Ta c:
Vy (theo phng trnh 8.15):
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BI TP CHNG 9
9.45
Profil vn tc ca lp bin ri khng c gradient p sut c m hnh ha thnh
mt hm m bc 1/6: vi
S dng phng trnh ng lng cho lp bin hy xc nh /x v Cf ca lp bin
ri ny.
Gii:
Do dng chy ri khng c gradient p sut nn: v Phng trnh ng lng cho lp bin lc ny c cho bi phng trnh
(9.19)
Vi T m hnh ha
, ta c [ ]
i vi m hnh dng chy ri, ta s dng phng trnh (9.25)
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Tch phn 2 v, ta c
Do khi Do
T
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9.58
Cho ng phn k thnh phng. Dng
chuyn ng khng nn c. Gi s
dng khng nht, hy m t ng
dng chy trong ng, phn b vn tc
v phn b p sut khi gc tng t 0
. Khi c tnh n tnh nht, hy m
t li dng chuyn ng trong ng
phn k ny. Trong 2 iu kin trn
(nht v khng nht), iu kin no
cho ta p sut u ra ln hn.
Gii:
Trng hp Vi lu cht l tng, vn tc khng c sthay i, do khng c gradient p
sut. V vy, vi lu cht l tng Vi lu cht thc, lp bin s to thnh trn thnh, lm gim khu vc dng
effective (effective flow area). tha mn tnh lin tc ca dng khng nn c . Vn tc chtng khi p sut gim. V vy, vi lu cht thc Vy vi , Trng hp (no separation)Cng tng tnh trng hp trn, gradient p sut ca lu cht thc cng b
gim bi s pht trin lp bin. Lu cht l tng cho gi tr p sut ln hn Vy vi , .
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9.71
Mt tu ngm ht nhn di chuyn vi vn tc 27 hi l/gi. Thn tu xem nh hnh
tr trn vi ng knh D=11m, di L=107m. c lng phn trm chiu di ca
thn m lp bin chy tng. Xc nh lu cn ma st b mt thn v cng sut tiu
hao.
Gii:
Ta m hnh ha b mt trbng mt mt phng vi kch thc ,
,
V:
Gi s dng ri hon ton:
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9.88
Mt phong tc ko vn tc gi cu to bi bn chn hnh bn cu ng knh
50 mm, nh trn hnh v. Tm ca mi bn cu t cch tr gia mt khong
. Xc nh hng s hiu chnh l thuyt (theoretical calibration constant) trong phng trnh hiu chnh , trong l vn tc gi v l vn tc quay. Trong qu trnh phn tch, tnh ton moment quay (torque),da vo lc cn sinh ra tc thi khi hai chn trc giao v hai chn cn li t song
song (vi hng gi?), b qua lc ma st tr. Trong trng hp b qua ma st, gii
thch ti sao bt k vn tc gi cho trc no i na th phong tc kcng quay
mt vn tc xc nh m khng gia tc v hn. Thc t, nu xt n ma st (khng
i) th cn mt vn tc gi cc tiu l th mi bt u quay c, t hyso snh tc quay khi c v khng c ma st, khi vn tc gi .Gii:
Xt moment tng cng trn trc :
Khi bt u quay, , Trong : l lc cn ng lc hc (drag), l moment cn xoay do ma st
sinh ra.
Tra Bng 9.3 trang 439, ta c
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Khi vn tc gi , , vn tc tng i ca hai
chn vung gc vi lung gi l . Ta c :
Vi , (1) tr thnh Trng hp khng c ma st, ta c
(Trong sch gii :
)Trng hp c ma st,
, gii li (1a).
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9.99
Mt vt ri trong khng kh xung mt ci
mng di thng ng. Vn tc l hng s 3
m/s. p sut coi nh khng i trn tit
din 1 v 2, p sut ti tit din 1 bng p
sut kh quyn. Din tch dng thc
(effective flow area) ti tit din 2 bng
20% din tch mng. nh hng ca ma st
gia tit din 1 v 2 l khng ng k. Tnh
vn tc dng ti tit din 2, p sut tnh ti
v khi lng vt.
Gii:
Phng trnh lien tuc
Phng trnh bernoulli:
*
+Phng trnh o ng l ng:
[ ]
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C HC LU CHT THC GVHD: TS. NGUYN CH CNG
9.101
Mt bnh xe nc c t trn
dng chy ca con sng to ra
nng lng. Mi cnh c din tch A
v h s lc cn CD; tm ca cnh
c t cch tm bnh xe mt on
R. Gi thit ti thi im bt k, ch c 1 cnh chm trong nc. Vn tc ca dng
nc l V, vn tc di ca bnh xe = . Xc nh lc cn, moment xon v cng
sut to ra bi bnh xe; tm gi tr ti u ca vn tc gc
Gii:
Gi thit b qua sc cn khng kh kk
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