Chapter 3 - Fluid Dynamics and Hemodynamic - 2022-2023 Final PDF

An-Najah National University Faculty of Medicine and Health Science Department of Biophysics and Medical Imaging Biomedical physics Course (7108101) 1 File no.4 Ch.3 : Fluid Dynamics and Hemodynamic...

An-Najah National University Faculty of Medicine and Health Science Department of Biophysics and Medical Imaging Biomedical physics Course (7108101) 1 File no.4 Ch.3 : Fluid Dynamics and Hemodynamic 2 Jehad Ahmed ALSHANTY 3  19 5 S. gas - Liquid 8 s D , 2545 any & - - -- - i Isis [15 - Sjg0 - - Jehad Ahmed ALSHANTY 4  : I - mass-guil -1 Volume i constant -4 o 4. 5 %I -- - , , pressures is 4 5) 1 & jj Bjd : Joe - , ,0 3 ↑ 7 -2011 sh I 49. incompressible fluid 11 -v -2 - i9 5 i - ,. - &is I4. compressible &Je - temprature /g pressuresis 5 : Gases 11 etwich - - incom... * is :9 isis55) : Liquids incompressible o C & fluid N45 ,i is i 7  · Song : + -P. S As Az 4 g,Sissi,,6 = W sin i - - - = Spressure is + 5 A, 99%4 2 =2 Aid F An - , & Y P2 = Pi 57 = A, = ps Az · A , -3 %. & % force Azig si 6it F i P2 ↑ = p pI = = Az 2 F S & E ↓ Az A I A (A I , z 7 , 75z · NB & 5 2 ration A & e I -ji E gitsj" -- & Fi A &  agg & jnfljs - jivi judisvid's is is & jvyj. 3 I 2 ⑳Is # 5861 I s ↳ viscosity - & Jehad Ahmed ALSHANTY 5  01/1541 : - velocity - > & I 1 slow joins u smooth sisid DI5 [SgE= i 15 35 : 8 Isl - - - b - JWtg > -541 &5 # 9 randomj6. randonijs j is Jehad Ahmed ALSHANTY 6  Si E - 4=-1 => Liquid in as i "Gl > Laminar - flow O - - 9955s6 Viscosity 6 - 34m + -9-y Viscosity - ↑ ei il g(1 55 48 d Iss gbse Do y los flow I returbulent dis Jehad Ahmed ALSHANTY 7  d real Ideal 11 9 · is " ↑ S Ideal p Jehad Ahmed ALSHANTY 8 Jehad Ahmed ALSHANTY 9  ‫‪-‬‬ ‫·‬ ‫‪↳ener‬‬ ‫‪d‬‬ ‫‪-‬‬ ‫‪S‬‬ ‫‪Q‬‬ ‫‪:q‬‬ ‫‪j09‬‬ ‫‪Volume‬‬ ‫‪flow rate-‬‬ ‫‪Q‬‬ ‫=‬ ‫&‬ ‫‪Q‬‬ ‫‪9‬‬ ‫"‪ity‬‬ ‫‪S.‬‬ ‫‪He‬‬ ‫‪#j‬‬ ‫*‬ ‫‪6‬‬ ‫‪·...‬‬ ‫بالنسبة للسائل غير القابل للضغط‪ ،‬يكون معدل التفريغ مساوًيا ملنتج مساحة املقطع العرضي لألنبوب وسرعة السائل‪.‬‬ ‫‪Jehad Ahmed ALSHANTY‬‬ ‫‪10‬‬  I comprissible Luid & => conservation of mass m I is constant & - V , /I - * = Jil. Incompressibl H 2 5 a = a m 2 , 1558 Axv 2 2. = A , xv , -at % s - jage / · - & b Sis gid -jiji Q4 &54u Sis C : 0 g ② A 3A 2 , Jehad Ahmed ALSHANTY V , 2 Uz 11  pipei is i jag · = 21 d 35 ar And M gijd -15 Q , = e = jig) EQ , = [Q2 · 074 a = Q85ds - befor After Jehad Ahmed ALSHANTY 9 + Q = Q , + q , 12 *V. AUz ↑ , V * 44 & It i & % IS -- ja55 3 - - b Jehad Ahmed ALSHANTY 13 Q1 : = 10002 = 1m 1 minute = 60s Q Volume = bo a 0 % 10 joi - radius 11 = Time & · less rilgiri 1 ,5.55r i siSj m ms · = = gold r , % % 10 so y - r -ju -9/12 r25/Jsi radius a8 V = 2 m/s of pipe ?? jjnarz. [ r2 m - = E D j)v A V = = Q = + M E = 99r gold = Ax 2 Q Q & A = 9008mh , = Q2 jls A k AzV ↳ Sjgr , Jiwsss = Tr2 , r = 514 900g. jS ! Sin pipe si il &3 0 # 981 Ve , Egg N = 3j 610lg N / a r= g05m - = Ye - -v - a VI Sisjej8 5. U = 2. 46 wis - V3b Co. Qbefore functions is = Q ↑ after b es v -ev1, j AcV = Anza +A Va b 2 46. = 1449v V = V + Y 3a b V 2u E 246 = 1 , 23r u = 3 =  -9 & -Wgjdi & - - - & P E = p E. ↑ & ↳p t !. = j. constant a & Sisj 110 This horizontal is area 01s [ [. A) A [1, 9. 98 53, , I 11 I S E - V V2. P Prizes > = 62500 pa ↑ P = - 4595. > - i gi's & - · swinging His slido O hi ge Jehad Ahmed ALSHANTY 22  8 -% St & /Jy A N 55165 - Laminur 9 Eigh /19591515- - How & Turbulent 5 ? How : 911 - Sjas I 2 asteinid glysis &Nas" El [ D 2 S r , S Te p[Pr 3 r < r 2 2 V 27V continuity equation 31 +9 + A2LA. [Velocity/I A =Sta - - 2 & 30-5 " & plg , (i) & &5 - -55 i I Z 3 & > 2 ri & b Posts 9 j ,  join Vi > & - & Ap ? - r E = n , + a do garage r rz = (n + [ 555 192v, % 2909 : Vz = Q 501]) a.. = ·s ~ S = 1060 kgim 155- -Y , P* VLV 3m/s 3v , P +I V ? = = h, = his gen , ↳ ↳ er jg , 2 = Vz(1 , 25 P. - Pe = * IV - ASV , V2 (1, 2) 3 - t (v v2) 2 up 08 mis Ve 2 = - =. , 87 =(106) (3 - 2. = -p = 2477pa > & P , Jehad Ahmed ALSHANTY 26  - real 11 % Jess - > GlVisss1 - - ~ fluid Jehad Ahmed ALSHANTY 27  & Niss 05581s - - -- Jansw - , - - 08 555. ~ - SI unit & -401's & ,Si O ↑ 3.j j)i %, - - -jeyin g. - -ma => *5.9 Sjl. &" ↑i s i i Wi Supis gives & , sil- > & & / +j :;310 - > ⑤ · & - - & => & & & siglsm&, · & sigej - Sign ⑮ & · sig 45 , 55941j - - Jehad Ahmed ALSHANTY.Sis TridisI1 & 28 * = sigis I  04 =j Pz(p,; 43 · p 25.. 12 eid44?. pushing xp pressur 11 is f = Ap pressures/jj 100 force. - - f - = xp Miss Solj8 I R * 2 I i S - 08 & gina is 3 = Z - & ga &: s Dri 9 %Sin Ji ggi zis'i res idi jsE s dig pipe jo 19 MJj & as 6 3 · 58 ·4 j , Y6'id3 /jks ! [ : # - i wei pipes Jehad Ahmed ALSHANTY - 29 resistence js; Length/Ji S-&12  S ↑ -8756 & - & 50 8 _ - 14, resistances/Tilj Viscosity Selj 15 i l; (1 1) , &51 Sj j51Jg 1; , ↳ Gas / Forcellig pressurslog 156 Ap EklsmS o /! G && Sxd ⑳O- b Hiking resistances/s9 Jxjb , s /.. % 51 /115514 - Ap Jehad Ahmed ALSHANTY 30  ‫‪me‬‬ ‫‪mL‬‬ ‫‪-‬‬ ‫‪JS‬‬ ‫‪.‬‬ ‫↑‬ ‫‪2‬‬ ‫‪Peli."T‬‬ ‫‪ :‬يتم إيصال الدواء إلى ذراع املريض بمعدل ‪ 10‬مل‪ /‬دقيقة‪.‬يتم نقل الدواء من املحقنة عبر إبرة طولها ‪ 5‬سم وقطرها الداخلي ‪ 1‬ملم إلى ذراع املريض‪.‬إذا كان ضغط دم املريض ‪ 15‬كيلو باسكال‪ ،‬فكم يجب أن يكون الضغط في اإلبرة؟ الح‬ ‫‪Q‬‬ ‫=‬ ‫‪10m x‬‬ ‫‪3‬‬ ‫& ‪box LemL‬‬ ‫‪a‬‬ ‫=‬ ‫‪(p‬‬ ‫‪,‬‬ ‫‪-‬‬ ‫‪p)πr‬‬ ‫‪L‬‬ ‫‪84L‬‬ ‫‪3‬‬ ‫‪-‬‬ ‫‪DXm‬‬ ‫‪-‬‬ ‫‪-‬‬ ‫‪-‬‬ ‫‪5cm‬‬ ‫>‬ ‫‪-‬‬ ‫‪g05m‬‬ ‫‪4‬‬ ‫‪6‬‬ ‫)‪( , 0005‬‬ ‫‪-‬‬ ‫‪radius‬‬ ‫‪916‬‬ ‫‪x10‬‬ ‫=‬ ‫‪Ap‬‬ ‫‪x 3‬‬ ‫‪.‬‬ ‫‪14‬‬ ‫‪x‬‬ ‫‪9x154)x54152‬‬ ‫‪diameter‬‬ ‫‪Imm‬‬ ‫‪5 mm‬‬ ‫&‬ ‫=‬ ‫>=‬ ‫‪-‬‬ ‫‪,‬‬ ‫‪985‬‬ ‫‪1%‬‬ ‫‪8‬‬ ‫‪x(8‬‬ ‫‪x153‬‬ ‫‪.‬‬ ‫*‬ ‫‪15290pa‬‬ ‫‪good 5 m‬‬ ‫‪0‬‬ ‫=‬ ‫‪290‬‬ ‫‪Dp‬‬ ‫=‬ ‫‪P2‬‬ ‫=‬ ‫‪15 X10 pa‬‬ ‫‪Jehad Ahmed ALSHANTY‬‬ ‫&‬ ‫‪P,‬‬ ‫‪15x103‬‬ ‫‪-‬‬ ‫‪zys31‬‬ ‫‪=-‬‬  jessie -4-.. & - Turbans ! Laminars - 55555 , ① ② Turbulent & & & & - transitional &S : E ⑤ - S g) · - Laminav Jehad Ahmed ALSHANTY 32  - ss 9 sys , ~s 4410i, & ↑ > - Re sljm · lil 5 g - diges - -. ---- Turbulantin ils ia Lamina > - 891. &S& 5 PS -12 gs S · = ↳.3 31 Laminar & Jess turb &g... % Jehad Ahmed ALSHANTY 33  Q &0 y - · : Sis & 3 Subs - & Turulent i551 Re-e & Laminars W gijb is s Q = 319 m/min :5 - 2000 s issi Ra 20 Lamina & ison 5 3 XI0m3/s & = Is. r diamet S 45 n10 Q & VA 2 , velocity s / :@ 9 Svenii = 1050 kg/m. 5 3x150 VXπ(. 5x(0) g = " 12 = 8. 9X15 pa. s V = 6. 75 m/s %8. 3 d - = 1mm = > v = , 5 mm 1050 x 6 75 X 1106 15t. Q : 585 = ,5x153 - Re - 4 8. 9 XIs 8 Tur Cow Type Re ? = 7963 > 300 , Jehad Ahmed ALSHANTY 34  G * Q= lon - 96 x15 m3/5 m - 4 n = 89X10 Pas d = Imm + u =3 J = 1078 kg/mi Re-und In 1070 x (V)(1531 Q = Ay. 8 aX754 Re 254 P capillary P > P 3 joh s s & 59. capillarysi not s S'J Oxygenated is 2 blood S -- 41g J. a *lisosmotic pressuregi capillarysils blood pressur 1 Mi Prices o big Scapillary sl is Sy J Dosmotic 11 n &I blood pressure s 5, amino acid & i 11jS ston : / capillary & bod 11 45544 / #]2j1g122 - D ↳ 1 Sloxygen % , sig3 ! Sels capillary 11 & 15. vein & s. Venules gicapillar bio venules So Capillary /1) FJi Jehad Ahmed ALSHANTY 38  egis gen p Max Capillary Starteriosling is capillary /10% cross - N 51 b, · / > - venules S 59 · S arterials 11 59 5091 , -j9 Capiliwys : 19 artery 11 Si -.. / 0 cross sections() G2/ distin S & i & 24.ja : 93 vein S1 · Venules (1 / [/99 id. & - jis artin - > 1940 1, ! ~ j 3 autrie & Egg sig ↑ & I & sectional vona care 5! Vein 11 cross dg 51 is a Min area F ra do / / / / we section Glarea(1559 cross issizis Jigs 1515 & A areaa cross sectiofidiS iss Q = Ay gi15950 5 Elgiso P> P2> P3 %1 Yslja & : d osbeis30e - 9. Dis & - 1 disti 5 Cartrei) S 11 149-15. & I Y 1/ g / & vein 51 venules 9/1 P At G -jisgs I P6 ↑ Veins1bvenules pil. Ejj: · sibisini es · S, j, /18 - &* I Pi Sylgi 2 JISIA - , 35 Sipisvenules sign wils &v Ps veins i venulei i + 1 pas ② regis -18 & * ② Vareas : Digs1/50s il, ↑ & ↑ [ Veins Venules Vains Vana cava Jehad Ahmed ALSHANTY 39  > - not constant nejiganji ~ K G - & - - - - geos " 6 - 95 Fina 294159 - I · 11 E is o & jedls.T S z Jehad Ahmed ALSHANTY 40  & 's endlies sys j461 & & 1s/joins dissid gissi 5 urasi , abidi Sin sli S ei V > - 0-352 4 hypoxia S -51 - a 8 - illet sit &5 ① · 519: & 3lydjsi ③ in is as # Jehad Ahmed ALSHANTY 41  Est - B best ·d is iii n Si - · 20- 1 & >. i [ 3 5451 % & Seli -- ~ 6 & 95 is - 93 Jehad Ahmed ALSHANTY is 3 , 42  normal 55 4 isj8. - L 's - (1!5- 4) E - - C ⑤ C > - ↓ - 55- - ~ C W G O Good O C - Op & Jehad Ahmed ALSHANTY 43  S & & Sis int i O C je'jis & jaji systolision su Diastolic - > - Jehad Ahmed ALSHANTY 44  S - jaj - I -S ↑ -- Ig : · I jo. -59 - j · I · -2 1595 is. x. · % sid first Fr 3559 sound · 5 95 1 : systolic pressure · · 95 % a.. 259y areus's ~ Jehad Ahmed ALSHANTY is 45 - Diastolic S %  pl 618 ventric S 21 % · g _. 9. 162 & 3 E11y619 S · si od's hi n - - & & Jehad Ahmed ALSHANTY 46  ‫ﻺﻧﺴﺎِن إِﻻّ ﻣﺎ َﺳﻌﻰ ۝ َوأَﱠن َﺳﻌﯿَﮫُ َﺳﻮ َ‬ ‫ف ﯾُﺮى ﴾‬ ‫﴿ َوأَن ﻟَﯿ َ‬ ‫ﺲ ﻟِ ِ‬