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C HC LU CHT THC GVHD: TS. NGUYN CH CNG

SV: TNG DIN H SSV: L VCT Trang1 /26

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) :

. /


2/26



* +

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.


3/26



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:


4/26



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.


5/26



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


8/26



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


9/26




10/26



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 :


11/26



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 ,


12/26




13/26



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 )


14/26



(b) Tnh ton mt nng gia u ra bm v ch xnc

Gi thuyt : (4) (5) T :

* Tnh cho mt n v trng lng :


15/26



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


16/26



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)


17/26



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):


18/26



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)


19/26



Tch phn 2 v, ta c

Do khi Do

T


20/26



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 , .


21/26



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:


22/26



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


23/26



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).


24/26



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:

[ ]


25/26




26/26


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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