Fluid Properties (three types)

Transcription

1 Fluid Prperties (three types) Kinematic prperties - prperties related t fluid mtin, like velcity and acceleratin. Thermdynamic prperties - prperties which describe the thermdynamic state f a fluid. These include temperature, pressure, density, internal energy, specific entrpy, specific enthalpy, etc. Miscellaneus prperties - prperties which d nt fall int either f the abve categries. Viscsity - a measure f the imprtance f frictin in fluid flw. Cnsider, fr example, simple shear between tw plates: Cnsider a fluid in 2-D steady shear between tw infinite plates, as shwn in the sketch. The bttm plate is fixed, while the upper plate is mving at a steady speed f V. It turns ut (we will prve this at a later date) that the velcity prfile, u(y) is linear, i.e. u(y) = Vy/h. Als ntice that the velcity f the fluid matches that f the wall at bth the tp and bttm walls. This is knwn as the n slip cnditin. The tp plate will experience a frictin frce t the left, since it is ding wrk trying t drag the fluid alng with it t the right. The fluid at the tp f the channel will experience an equal and ppsite frce (i.e. t the right). Similarly the bttm plate will experience a frictin frce t the right, since the fluid is trying t pull the plate alng with it t the right. The fluid at the bttm f the channel will feel an equal and ppsite frce, i.e. t the left. In fluid mechanics, shear stress, defined as a

2 tangential frce per unit area, is used rather than frce itself. Define (Greek letter "tau") as the frictin frce per unit area acting n the fluid, as illustrated belw: In a simple 2-D shear flw such as this, the shear stress is directly prprtinal t the slpe f the velcity prfile. In fact, the cnstant f prprtinality is the cefficient f viscsity itself! Mathematically, This little equatin turns ut t be quite useful fr a lt f practical engineering prblems. Fr example, cnsider a blck sliding dwn an incline: Given: A blck f weight W is sliding dwn an incline at cnstant speed V n a thin film f il f thickness h, as sketched. Find: Speed V as a functin f the ther variables in the prblem

3 Slutin: Draw a free bdy diagram f the blck. The frces acting n the blck are its weight, W, a nrmal frce, N, due t pressure f the il n the bttm surface f the blck, and a viscus frce, F viscus, due t frictin n the bttm f the blck. Frm simple trig, we can sum the frces in bth x and y and set the net frce t zer (this is a statics prblem since the blck is mving at cnstant speed). Thus,

4 A magnified view f the il film reveals that it is lcally the same as ur simple shear between plates prblem. Thus, the x cmpnent f velcity, u is given by u(y) = Vy/h. We als knw that fr simple 2-D shear, Finally, the ttal viscus frce is equal t the shear stress times the surface area, A, in cntact between the fluid and the bttm surface f the plate. Therefre, Kinematic viscsity is simply defined as the viscsity divided by density, i.e. Surface tensin is a prperty f liquids which is felt at the interface between the liquid and anther fluid (typically a gas). Surface tensin has dimensins f frce per unit length, and always acts parallel t the interface. Surface tensin causes the mlecules at the interface t repel each ther, frming a kind f "skin" under tensin at the interface. A gd example f surface tensin is fund in a cmmn sap bubble. A sap bubble is a gd example t illustrate the effects f surface tensin. Hw des a sap bubble remain spherical in shape? The answer is that there is a higher pressure inside the bubble than utside, much like a balln. In fact, surface tensin in the sap film acts much the same as the tensin in the skin f a balln. Cnsider a sap bubble f radius R with internal pressure p in and external (atmspheric) pressure p ut. If the area shwn is magnified, a free bdy diagram f the sap film can be drawn.

5 On the free bdy diagram, the sum f all frces must be zer, since the sap film segment is nt accelerating. Surface tensin frces act parallel t any interface. On the free-bdy diagram f the sap bubble segment, there are fur lcatins where surface tensin acts, as shwn. Analysis f a sap bubble yields the fllwing, Surface tensin (cntinued) Surface tensin is als imprtant at the interface between a liquid, a gas, and a slid. Fr example, a meniscus ccurs when the surface f a liquid tuches a slid wall, as mst readily nticed when a capillary tube is placed in a liquid. Cnsider a glass capillary tube inserted int a liquid, such as water. The water will rise up the tube t a height, h, because surface tensin pulls the surface f the water twards the glass, as shwn. The meniscus is the curved surface at the tp f the water clumn.

6 The cntact angle is defined as the angle between the liquid and slid surface, as shwn in the sketch. Cntact angle depends n bth the liquid and the slid. If theta is less than 90, the liquid is said t "wet" the slid. Hwever, if theta is greater than 90, the liquid is repelled by the slid, and tries nt t "wet" it. Fr example, water wets glass, but nt wax. Mercury des nt wet glass. Water wets glass Mercury des nt wet glass Cnsider a small glass capillary tube inserted int water. The height f the water clumn can be fund by summing all frces acting n the water clumn as a free bdy diagram. (This is a statics prblem since there is n acceleratin.) The dwnward frce is due t gravity, i.e. the weight f the water clumn. The nly upward frce available t balance the weight is that caused by surface tensin (pressure frces all cancel ut, as will be

7 explained in a later lecture). Clumn height h can be predicted as fllws: Vapr pressure is defined as the pressure at which a liquid will bil (vaprize). Vapr pressure rises as temperature rises. Fr example, suppse yu are camping n a high muntain (10,000 ft. r rughly 3,000 m in altitude). Frm Table A.6 the atmspheric pressure at this elevatin is abut 70. kpa. Frm Table A.5 it is seen that at a temperature f arund 90. C, the vapr pressure f water is als arund 70. kpa. Frm this it can be stated that at 10,000 ft. f elevatin, water bils at arund 90 C, rather than the cmmn 100 C at standard sea level pressure. This has cnsequences fr cking. Fr example, eggs have t be cked lnger at elevatin t becme hard-biled since they ck at a lwer temperature. A pressure cker has the ppsite effect. Namely, the tight lid n a pressure cker causes the pressure t increase abve the nrmal atmspheric value. This causes water t bil at a temperature even greater than 100 C; eggs can be cked a lt faster in a pressure cker! Vapr pressure is imprtant t fluid flws because, in general, pressure in a flw decreases as velcity increases. This can lead t cavitatin, which is generally destructive and undesirable. In particular, at high speeds the lcal pressure f a liquid smetimes drps belw the vapr pressure f the liquid. In such a case, cavitatin ccurs. In ther wrds, a "cavity" r bubble f vapr appears because the liquid vaprizes r bils at the lcatin where the pressure dips belw the lcal vapr pressure. Cavitatin is nt desirable fr several reasns. First, it causes nise (as the cavitatin bubbles cllapse as they migrate int regins f higher pressure). Secnd, it can lead t inefficiencies and reductin f heat transfer in pumps and turbines (turbmachines). Finally, the cllapse f these cavitatin bubbles causes pitting and crrsin f blades and ther surfaces nearby.

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