I. OBJECTIVE OF THE EXPERIMENT. Swissmero raels a high speeds hrough a unnel a low pressure. I will hereore undergo ricion ha can be due o: ) Viscosiy o gas (c. "Viscosiy o gas" eperimen) ) The air in ron o he objec being pushed ou o he way ("pison eec") 3) Drag orces Through calculaion only, i is diicul o esimae he oal resisance orces ha are applied o he objec, since hey depend on numerous geomerical parameers (aerodynamics o he objec, disance separaing objec rom wall, ) bu also physical parameers (gas pressure, elociy,...) The ollowing eperimen is a model ha will gie a global idea o he resisance orce acing on he objec in moion, and deermine how hese orces decrease wih air pressure. II. MOTION RESISTANCE Newon s equaion applied o a luid yields Bernoulli s equaion: P gh cons () where P is pressure, is densiy, is speed, h is heigh and g is graiaional acceleraion. Also, an objec raelling a a speed, in a moionless luid o pressure P and densiy, creaes an impac poin on he luid in he area where he pressure is P imp. and he densiy i. or a consan heigh, equaion () yields: Pimp P () The resisance orce opposing o he objec s moion in a unnel generally depends on he geomery o he ehicle. The pressure a he impac poin, epressed in (), should reduce he more we moe away rom ha poin.
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B5- We can epress he orce a he ron o he ehicle by: where S is he cross secion o he objec and K a consan F S Pimp S( P K ) (3) On he back o he ehicle, he pressure is equal o he aerage pressure acing on he wake, and can be epressed as: F S( P K ' ) (4) In hese condiions, he oal resisance orce acing on he ehicle behaes like: F F F S( K K ') (5) This orce hereore depends on he cross secion o he ehicle, is geomery ( C ), is speed, and he gas densiy.howeer, densiy depends on pressure. A zero pressure, here is no more gas, and hereore he orce mus anish. For an adiabaic compression: PV cons (6) And aer diereniaion: since d dv V dp dv d P V (7) and hus, rom (7): d P P dp wih d cons dp (8) and inally: F SC P wih C ( K K ') (9) Viscous orces The Reynolds number Re deermines he limi beween laminar and urbulen low. Re D () where is luid speed, D is disance beween wo walls where he luid lows and is dynamic iscosiy coeicien.
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B5-3 In general, when he Reynolds number reaches approimaely ', he low becomes urbulen, i.e. he elociies become random. Please noe ha Re decreases wih pressure and disance beween he walls. In a acuum o 665 Pa and a disance o 4 cm, Re is equal o '4. We could hereore suppose a laminar low beween Swissmero and he walls, as long as P 665 Pa and he rain-wall disance is inerior o 4 cm. I he rain-wall disance is o he order o a ew cenimeers, he low is laminar (see below). In hese condiions, he ricion is gien by: Fis d () wih is ehicle speed, is cross secion o he ehicle, d is rain-wall disance, is dynamic iscosiy coeicien. The iscosiy o a gas is relaiely independen o he pressure down o Pa and depends on he ype o gas, and he emperaure. 5 For air a C.84 Pa s. We can eriy ha he iscous ricion is negligible wih respec o he oher resisance orces. This era acuum is due o a poor space beween he walls. C o he rain raelling hrough a ube wih a small amoun o III. EXPERIMENTAL SETUP The eperimenal seup allows us o sudy he global orces acing on he objec when he ube is illed a dieren pressures. In order o simulae a ube o ininie lengh, we will use a looped ube (Fig. and Fig. ). We can also limi he lengh o he ube (pison eec) by closing a ale on he circui. In one o he ube s branches, here is a weigh o mass m ha can all reely in he ube. The equaion o moion is: mg F m where F is he ricion o he air on he weigh (we will neglec he ricion o he walls o he ube). I we can measure he acceleraion as a uncion o speed, (), we can deermine he uncion F F () and decide which o he epressions (9) or () is more suiable. In he een o a orce like in (9), we can ry o ind he mobile s C coeicien. Eamples: - Disk moing perpendicularly o is surace C = ~.3 - Sphere C = ~.5 - Hal sphere and cone (rain drop) C = ~.4
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B5-4 Wih he aailable seup, we can deermine ie dieren speeds along he pah: P m -> (, ) -> (, ) pos. pos. pos. pos. 3 3 3 4 pos. 4 4 The speeds are deermined rom he dwell ime o he mobile hrough an opical gae. I is hereore necessary o know he lengh o he weigh -> (, ) 3 3 3 -> (, ) 4 4 4 From hese alues, we can deermine 4 mean acceleraion alues or a : a a ec. These alues gie us an idea o insance, we can eriy wheher F supposing consan. F F () ; or F or ale Fig : Eperimenal diagram. acuum pump Supposing he equaion is o he ype we can sole he equaion below Soluion: ( m ) g mg ( e ) F, where m is a relaaion ime.
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B5-5 V. SUGGESTED EXPERIMENTS: ) Measure he speeds o he mobile m as a uncion o he pressure in he ube, or boh he inie and ininie ube. ) Calculae he acceleraion and deermine he ariaion o ricion: - wih pressure wih speed. 3) Under wha condiions is F alid (laminar low)? 4) Discuss he resuls o he inie and ininie ube according o is applicaion or Swissmero. (Can Swissmero push he air in ron o i as i i were and ininie ube? Operaing insrucions Turn on he main power, and measure he sysem a amospheric pressure, beore saring he pumping process. Make sure he leak ale is closed, and open boh ales beore saring he pump. Regularly close ale, and perorm a measure. Beore coninuing he pumping process, make sure ha ale is open. Take o 3 measuremens beween amospheric pressure and approimaely Torr. Perorming a measuremen: In order o ake a measuremen, li up he weigh using he coil around he ube, and place i on he wedge owards he op o he ube. The curren lowing hrough he coil can be adjused using he curren source (make sure he curren is no oo high). Then, rese he sopwach. Press and hold he Measure buon o le go o he weigh, and sar he sopwach. Repea he measuremen by swiching he posiion o he ale. The pressure is irs measured using a bourdon gauge (in mbar) and hen by a Pirani gauge (in orr) Useul quaniies: Mass o objec:.7 g Lengh o objec: 76 mm Diameer o objec:.4 mm Inernal diameer o ube: 4. mm Fig :Eperimenal seup