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Tutorial: ViscosityQuestion 1

(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 devicethe outer cylinder is fixed and the inner rylinder is routEd with anangular velocity ar. The torque 1" required to develop ar is moasuredand the viscosity is calculated &om those two measurements. Derrelcpan eqution relating the dynamic viscosity p, rylinder dimlster D,angulr velocity er, torque I and lengh y. The gep betrren therotating 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" {redepth y is 2A mm and the cylinder diameter is l4 mm, dctermine thetorque Irequired to rotate the rylinder.

fixed outercvlinde r

,

*-t i-*I ntm

Figure Ql

--rItIIiIII

__l

Tutorial: ViscosityQuestion 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 bormdarylaycr aty oqual ta

( to(iil 3 mm,ad

(iir) Dreg forca,

FisQIb

(8 marks)

(c) Tho internal and txtemal diarnctan of a collar beariag ars 2Q0 mm and 250 mm respectively assho$m in Fig Qt. An oil of viscosfy 1.5 N.s/mz is fill€d between the surface of the collar andhearing which is t = 1.2 mm. Dctermine the povrer required to ov€rcome the viscous resistaoaewhen the shaft is rotatss at 180 rpm.

(10 ma*s)

Fig. Qlc

r?

z

Tutorial: ViscosityQuestion 3

(a) What is meant by Newtonian fluid ?

(b) A circular disc immersed in oil is usedin Fi gure r . ir, o* 1ha1 dre d"*p G1",i;,', llff 'J;i"i:LrJ ffl,:: il::o'l,l*accordance 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.

Tutorial: ViscosityQuestion 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.2mm gap befween rotating shaft and stationary housing. Determine the total power requirecl toovercome the viscous resistance.

(20 marla)

Figure Ql

T

Tutorial: ViscosityQuestion 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 ialah0.?2Pa.s.

n--*.**t

:9. r,tl lt.i,

Rt iah iry

5

Tutorial: ViscosityQuestion 6

A circular disc immersed in oil is used as adamper in damping system shown as inFigure Ql. Show tbat the darnpiftg torqle isproportional to angular specd in accordancewithrulation Tdanprng = Co

rlwhere C=0.5np{:**)nn.

ADAssume linear velocity profites on both sidcsof the disc sind nwlsst thc tipcffects.

FigrrcQl

6

Tutorial: ViscosityQuestion 7

(d Aeaesh yang dimalaudkrn dengun bendatir Newtonaa danth*'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 Imm,,&bi dengan glycerin (lelikatan /r = 0.6 N.dmg) sepertiyang dituqiuklan dalam Rdah S1.'Ibntulal ttaya kilao dankuesa yang dipertukln untut memut&rkan cahera padakadal 20 p.p.m.AnSgnp bakwa agihan hataju dalam ruangLele gaan aebagai lirear.

markaU

' ' ll:r'trmm

lmm

5 csrlmm

Eajah 51

?

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

gVdDh 2/)/)(09.0 to04.0( 24= 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.

Figure 1

QUESTION 3 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 m2/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, Ro, and Ri. 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/ft2. 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/m2). Acting in the direction of flow.

5. 1

312

RRRTorqueo −

=µωπ l

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, ωi, of the input disc and ωo of the output disc.

(c) Develop an expression for the slip ratio, s = ∆ω/ωi, in term of ωi 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)

2. (b) 2

)( 41 R

aoTorque ⋅⋅

−⋅= π

ωωµ

(c) 41

2R

aTSπµω

=