Tutorial: Viscosity Question 1

Tutorial: Viscosity Question 1 ii I I (a) What is meant by Newtonian fluid? {b) T.he viscosity of liquids can be measured through the use of a rotating cylinder viscorneter of the type illustrated in Figure Ql. In this device the outer cylinder is fixed and the inner rylinder is routed with an angular velocity ar. The torque 1" required to develop ar is moasured and the viscosity is calculated &om those two measurements. Derrelcp an eqution relating the dynamic viscosity p, rylinder dimlster D, angulr velocity er, torque I and lengh y. The gep betrren the rotating inner cylinder and its case is I mm. (c) Ifthe dynarnic viscosiy of test liquid is 0.6 N.s/m?, ar is I00 radls" {re depth y is 2A mm and the cylinder diameter is l4 mm, dctermine the torque Irequired to rotate the rylinder. fixed outer cvlinde r, --r It I i I I l *-t Figure Ql I ntm i-*

Tutorial: Viscosity Question 2 {a) What is mcent byncu*oriaq fluid? (2 ma*s) ft) A Newtonian fluid heviag a spwific gravityof 0-9 and kinernatics viseosity (v) of 4 * 10{ m% form a boudqty laycr mr a solid wall of cubic volocity profrle- The boundary layer thicknccs (d) is 6 mm, and &e maximum velocity is l0 ur/s. Detennine the shcarshess (r) in 6e bormdary laycr aty oqual ta (to (iil (iir) 3 mm,ad Dreg forca, FisQIb (8 marks) (c) Tho internal and txtemal diarnctan of a collar beariag ars 2Q0 mm and 250 mm respectively as sho$m in Fig Qt. An oil of viscosfy 1.5 N.s/mz is fill d between the surface of the collar and hearing which is t = 1.2 mm. Dctermine the povrer required to ov rcome the viscous resistaoae when the shaft is rotatss at 180 rpm. (10 ma*s) r? Fig. Qlc z

Tutorial: Viscosity Question 3 (a) What is meant by Newtonian fluid? (b) A circular disc immersed in oil is used in Fi gure r. ir, o* 1ha1 dre d"*p G1",i;,', llff 'J;i"i:LrJ accordance ffl,:: il::o'l,l* with reladon ; 4*piug = Cal /t r\ where C =0.Snplaa1la+ \l B ) Assume linear velocity profires on both sides of the disc and negrect the tip effects.

T Tutorial: Viscosity Question 4 (a) Explain what is meant by Ne*.tonian and Non-Nervtonian fluid (5 marks) (b) Figure Ql show's a shaft rotates at 2000 rpm. An oii rvith a viscosiry of p = 0.5 Pa.s fitls the O.2 mm gap befween rotating shaft and stationary housing. Determine the total power requirecl to overcome the viscous resistance. (20 marla) Figure Ql

Tutorial: Viscosity Question 5 a) Apakah lnng dimak;udlan dirrgan lxntlalir l'leu'toni* dan beldalir non*newtonian. lrl Rainlr I menunirrlikan aci bergaris pusat 1ti0 trm herarh di t*ngoh galas.r,ang bergtris pusat 360."16 mm. Jika aci hernu{rr dcrrgan halqiu 2ft(t rpm, krrakan nilai da1'a kilas pada sislern ini. Kelikata* minr'^ah pelirrcir ialah 0.?2Pa.s. n--*.**t :9. r,tl lt.i, ry Rtiah i 5

Tutorial: Viscosity Question 6 A circular disc immersed in oil is used as a damper in damping system shown as in Figure Ql. Show tbat the darnpiftg torqle is proportional to angular specd in accordance withrulation Tdanprng = Co rl where C=0.5np{:**)nn. AD Assume linear velocity profites on both sidcs of the disc sind nwlsst thc tipcffects. FigrrcQl 6

? Tutorial: Viscosity Question 7 (d Aeaesh yang dimalaudkrn dengun bendatir Newtonaa dan th*'newtonaa.eeri dua contoh eetiap jenis bendalir ini. (B markah) ft) $ekepiry catera berdiameter 30 cm dgn tebal 5 cm dibtalkon di dalam silinder tetap dengnn ruang kelegaan I mm,,&bi dengan glycerin (lelikatan /r = 0.6 N.dmg) seperti yang dituqiuklan dalam Rdah S1.'Ibntulal ttaya kilao dan kuesa yang dipertukln untut memut&rkan cahera pada kadal 20 p.p.m.ansgnp bakwa agihan hataju dalam ruang Lele gaan aebagai lirear. markau ''l l:r 'tr lmm 5 csr lmm Eajah 51 mm

PROBLEMS FOR CHAPTER 1 FLUID PROPERTIES QUESTION 1 According to information found in an old hydraulics book, the energy loss per unit weight of fluid flowing through a nozzle connected to a hose can be estimated by the formula 4 2 h = (0.04 to 0.09)( D / d) V / 2g where h is the energy loss per unit weight, D the hose diameter, d the nozzle tip diameter, V the fluid velocity in the hose, and g the acceleration of gravity. Do you think this equation is valid in any system of units? Explain. QUESTION 2 The no-slip condition means that a fluid sticks to a solid surface. This is true for both fixed and moving surfaces. Let two layers of fluid be dragged along by the motion of an upper plate as shown in Figure 1. The bottom plate is stationary. The top fluid puts a shear stress on the upper plate, and the lower fluid puts a shear stress on the bottom plate. Determine the ratio of these two shear stresses. QUESTION 3 Figure 1 A 25-mm-diameter shaft is pulled through a cylindrical bearing as shown in Figure 2. The lubricant that fills the 0.3-mm gap between the shaft and bearing is an oil having a kinematic viscosity of 8.0 10 4 m 2 /s and a specific gravity of 0.91. Determine the force P required to pull the shaft at a velocity of 3 m/s. Assume the velocity distribution in the gap is linear. Figure 2 1

QUESTION 4 A layer of water flows down an inclined fixed surface with the velocity profile shown in Figure 3. Determine the magnitude and direction of the shearing stress that the water exerts on the fixed surface for U = 2 m/s and h = 0.1 m. Figure 3 QUESTION 5 The viscosity of liquids can be measured through the use of a rotating cylinder viscometer of the type illustrated in Figure 4. In this device the outer cylinder is fixed and the inner cylinder is rotated with an angular velocity, ω. The torque T required to develop ω is measured and the viscosity is calculated from these two measurements. Develop an equation relating µ, ω, T, l, R o, and R i. Neglect end effects and assume the velocity distribution in the gap is linear. Figure 4 2

QUESTION 6 A conical body rotates at a constant angular velocity of 600 rpm in a container as shown in Figure 5. A uniform 0.001-ft gap between the cone and the container is filled with oil that has a viscosity of 0.01 lb s/ft 2. Determine the torque required to rotate the cone. Figure 5 QUESTION 7 A 12-in.-diameter circular plate is placed over a fixed bottom plate with a 0.1-in. gap between the two plates filled with glycerin as shown in Figure 6. Determine the torque required to rotate the circular plate slowly at 2 rpm. Assume that the velocity distribution in the gap is linear and that the shear stress on the edge of the rotating plate is negligible. Figure 6 3

QUESTION 8 Surface tension forces can be strong enough to allow a double-edge steel razor blade to float on water, but a single-edge blade will sink. Assume that the surface tension forces act at an angle θ relative to the water surface as shown in Figure 7. (a) The mass of the double-edge blade is 0.64 10 3 kg, and the total length of its sides is 206 mm. Determine the value of θ required to maintain equilibrium between the blade weight and the resultant surface tension force. (b) The mass of the single-edge blade is 2.61 10 3 kg, and the total length of its sides is 154 mm. Explain why this blade sinks. Support your answer with the necessary calculations. Figure 7 Answer : 1. Valid. Similarity in units 2. 1 3. P = 286 (N) 4. τ = 4.48 10-2 (N/m 2 ). Acting in the direction of flow. 3 2πR1 lµω 5. Torque = R o R1 6. Torque = 0.197 ft.lb 7. Torque = 0.0772 ft.lb 8. (a) sinθ = 0.415 (float) (b) sinθ = 2.265 (impossible, sink) 4

PAST YEAR QUESTION QUESTION 1 Rajah S1 (a) Sebuah cakera berdiameter 75mm berputar pada kelajuan ω = 4 rad/s dalam sebuah bekas yang berputar pada kelajuan ω = 2 rad/s seperti dalam rajah S1. Bekas dipenuhi minyak berkelikatan 8 10-3 Ns/m2. Dengan mengabaikan kesan kelikatan dihujung cakera, buktikan bahawa daya kilas yang diperlukan untuk memutarkan satu permukaan cakera ialah : T = 4.97 10-8 / h dengan h ialah kelegaan antara cakera dengan bekas. (b) Jika kelegaan dibahagian atas cakera dalam soalan 1(a) ialah 3m dan dibahagian bawah ialah 2mm, tentukan daya kilas yang diperlukan untuk memutar cakera tersebut.

QUESTION 2 Figure Q1 (a) State and explain the Newton s law of viscosity. (b) A viscous clutch is to be made from a pair of closely spaced parallel discs enclosing a thin layer of viscous liquid a shown in Figure Q1. Develop algebraic expression for the torque and the power transmitted by the disc pair, in term of liquid viscosity, µ, disc radius, R, disc spacing, a, and the angular speed, ω i, of the input disc and ω o of the output disc. (c) Develop an expression for the slip ratio, s = ω/ω i, in term of ω i and the torque transmitted. ω is the difference of angular speed between the disc pair. Answer : 1. (b) Total Torque = 4.1 10-5 (N.m) ( ω ωo) 2. (b) Torque = µ π a 2aT (c) S = 4 ω πµ R 1 4 1 R 2