ee ro ae Phe put |). ML ey - QJ. Sala 7 fi rl [gg oF we JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY eM, \ rin . Ll qe THIRD YEAR FIRST SEMESTER BACHELOR OF SCIENCE IN MECHANICAL \ “ ENGINEERING/MARINE AND MARITIME OPERATIONS ENGINEERING aML[Tl 11™ August 2021 __EMG 2301: FLUID MECHANICS Il_CAT2__ TIME: 30 MIN \ 2 aM TI "Byperience has shown that the polver required to driye a centrifugal pump, P, depends on the Fove= tet umetric flow rate of the liquid being pumped, ("the diameter of les, Dy th a tric flow rate of the lic , Othe diameter of the pump impeller, D, the = Myre auid being pumped, GF fe pump impeles, ea . . fA m¥sh ibiational speed of the impeller, Mf the viscosity of the fluid, f,'the density, pind the head > ML* | 7% developed per unit mass, {1¥? show by the Buckingham pi theorem that MLe/ T- P=pN'DO (NR Ee. at») 4 we oles ye Bee wi Che OND as the recurring set. N o\4. 10 , a ee recurring set . < o we (10 marks) We Face xc 4 4 wt “ghs wilt Por «We we ayWi2-60-1.6 JOMO KENYATTA UNIVERSITY oF AGRICULTURE AND TECHNOLOGY University Examinations 2020/2021 THIRD YEAR FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING/ BACHELOR OF SCIENCE IN MARINE, ENGINEERING AND MARITIME OPERATIONS EMG 2301. FLUID MECHANICS II ©) auGusr 2021 2HOURS INSTRUCTIONS s 1. This paper contains FIVE questions 2. Attempt any THREE questions 3. All questions carry EQUAL marks QUESTION ONE 20 MARKS ; fe a. Differentiate between the following ype of oa a (@ Steady uniform flow and steady non-uniform flow [marks] i) Unsteady uniform flow and unsteady non-uniform flow (2macks) b. Derive an expression forthe resultant force exerted by a moving fluid around a pipe bend of constant cross-section with inlet velocity, ui, and ouilet velocity uz making an angle 0 with horizontal axis atthe ext. [marks] ©. A 60? reducing pipe-bend (in horizontal plane) tapers from 800 mm diameter at inlet to 400 mm diameter at the outlet. The pressure at inlet is 160 kPa and the rate of flow of, ‘water through the bend is 0.675 mY. Neglecting friction and gravitational forces, calculate the net resultant force exerted by water on the bend and its direction Fe toga veloely. fF. a (Tacks) eae 1¢ \ u wetrel eau fe AP Cs FryeION TWO GoMARKs ' Derive an expression for the head lost in a pipe due to auelden enlayyement of exoss Sectional area, Explain the meaning ofall syrnbols an notations wed and comment om ‘any assumptions made. [Smatks) Show that the maximum hydraulic power transite by a given pipe of uniform eros section occurs when the frictional hea! lost ina pipe ix one thi of the total available ‘ea. qd [Smarks} © A pipeline of length 198m is used for power transmission, If 108 KW power isto he transmitted through the pipe in which water having a presure of 448.5 Nien at ile fs flowing. Find the diameter of the pipe and effcieney of transmission ithe pressure drop. over the length of pipe is 97.1 Niem. Take the fietionl eeticien, fs 0.0065 {Sucks} bother line of 4. A pipeline of 0.6 m diameter is 1.5 km Jong. To increase the discharge, the same diameter is introduced parallel to the fist in the secon hall of the length ‘Neglecting minor losses, find the increase in discharge i frictional coefcien, fi 0.01, the head at inlet is 300 mm, QUESTION THREE 20MARKS) ‘Explain the meaning of the following rms: on (Dimensionless quantities -» ue que hw (Geometric similarity 7» Vor dir : G1) Kiematesiity toon 6 rons ecw i) © Dynamic similarity yanks Me freer tebe papas, med (owen 0, Diss Rey's Number giving xan py mening an isan Dec ful csiiien Al estir ty to Sear] fis significance. ae The thrust force, F, generafed by &propeller is found to depend on the following parameters: diameter, D, forward velocity, u, density, , viscosity, and rotational speed, IN. Determine the dimensionless parameters to corelte the phenomenon. [13 marks} UD & areca set QUESTION FOUR‘@0 MARKS) a. A conveyor belt in rining company discharges titanium ore ino a barge 0s ‘downs Figs aterme of 0¢3n Ihe si ort doy of 24g, Stic teion ne woe teste he bgt he doc? ws]Fig HO) horizontal so ast reach the fir located at 10m ‘A fireman directs a waterjet at 60°10 the shove the level of he nozleas shown in Fig. Q4(), What should be the power of he pump assuming an overall ficiency of 6% Take, f = 0.003 [12.masks) ——-- Fire aN Qo 10m Nasal d= 20m 2m Rubber hose D = #0 mm Z=3010 Fig. Q40)QUESTION FIVE 20 MARKS) (@) Show that fora laminar flow ina pipe, velo 1, at any points given by Where 1 is the dynamic viscosity, & isthe pipe radius and (Pd) isthe piezometric pressure, [65 mans} (©) A laminar flow of lubricating oil having « dynamic viscosity of 0.1 Ne'n® and specific gravity of 0.92 takes place in a 38 ram diameter pipe. Ifthe pressure drop is 718 kPa for 29 m length, find; (_—_Aneexpression for discharge at any point in the pipe [4 masks} Gi) Local velocity at a point where radius is 12 mim [1.5 marks) (Gi) “Local discharge ata point where radi is 12-mm [2marks} Gv), Mean velocity of flow [Smarks) (©) Maximum shearstressin flow) Bmwks) ADDITIONAL INFORMATION 1, Darcy's equation, hr: Be eo 2, Bonoecqutin Ent Dimensionless groups “2 1. Reynolds amber, Re = 282 2. Froude number, Fr= Tse i 5. Weber number, We= 2Wi2.60-16 JOMO KENYATTA UNIVERSITY oF AGRICULTURE AND TECHNOLOGY ‘University Examinations 2020/2021 ‘THIRD YEAR FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING! BACHELOR OF SCIENCE IN MARINE [ENGINEERING AND MARITIME OPERATIONS EMG 2301 FLUID MECHANICS 11 augusr2g) OURS: INSTRUCTIONS 1. This paper contains FIVE questions 2. Attempt any THREE questions 3. All questions carry EQUAL marks QUESTION ONE 20 MARKS) ‘a. Differentiate between the following types of flows (@ Steady uniform flow and steady non-uniform flow (2mavks) Gi) Unsteady uniform flow and unsteady non-uniform flow [amacks) Derive an expression forthe resultant force exerted by a moving id around a pipe bend ‘of constant cross-section with inlet velocity, u, and outlet velocity uz making an angle © with horizontal axis atthe exit. {Pmacks] [A 60 reducing pipe-bend (in horizontal plane) tapers ftom 800.mm diameter t inlet to “AO sam diameter atthe out. The pressure a net is 169 KPa andthe rate of fow of| Water through the bend is 0.675 mi. Neglecting friction and gravitational frees, calculate the net resultant force exerted by water on the bend and is direction, (Tearks]IUESTION TWO @OMARK: '% Derive an expression for the head Jost in a pipe due to sudden enlargement of cross section are. Explain the menning ofall symbols nd notations used snd comment on ‘ny assumptions made (smarks) Show tha the maximum hydrauie power transite by a given pipe of uniform cross- seston occurs when the fictional head lot ina pipe it one thd of the total available head, [Bmars) ‘© A pipeine of length 1998m is used for power tansmision. If 108.4 kW power Ist be ‘ransmitted through the pipe in which water having a pessure of 488.5 Nem* at inlet is ‘owing. Find the diameter ofthe pipe and efficiency of transmission fhe pressure drop ‘over the length of pipe i 97.1 Nim, Take the fictional coefficient, fa 0.0065 ° FPO sent ghO shabotl = [Smarks) 2 = —_—=S=—sSEOL_—_—_'_ss th tne dances eucd ult eae waa he ke a =—r_:—=aetd rc —r_—ser——— ‘the head at inlet is 300 mm, (marks) a Ca ay ourstio Tune cowanin is 4 os 1. Exp ememingof te fon tems tuoi 0 maaan quate @) Gomariesmty lnm sty 0° Dynmie sia Sr r——_ ieigina mt) eee ec (E)geomatt by «pope is and den ote lowing rut: dancis{ Soren wots) slp (shod lon! spn Deals ae dgeaatn pment oc ocean Ts ah Choore UD, Par recuming set ee — ‘QUESTION FOUR (20 MARKS) be cae 1. A conveyor belt in titanium mining company discharges titanium ore into a barge as ‘shown in Fig,Qé (a) at arate of 0.63n/s. Ifthe titanium ore has a density of 1922kp/m?, eee ine OalnaceGebqpiedead (ata) ce Yet eo ort ve‘A fireman directs a waterjet at 60° tothe horizontal so as to reach the fire focated at 10m above the level of the nozzle as shown in Fig. Q 4(b). What should be the power ofthe ‘pump assuming an overall efficiency of 0% Take, f = 0.003 (2 marks} ire set pe Nozale d= 20mm Pump 2m Rubber hose D= 80 mm Z= 30m |<— Water Fig. Q4(0)JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY OP OF SCIENCE IN MECHANICAL ND MARITIME OPERATIONS ENGINEERING ID MECHANICS Il_CAT.2__TIME: 30 MIN Experience has shown that the power required to drive a centrifugal pump, P, depends on the volumetric flow rate of the liquid being pumped, Q, the diameter of the pump impeller, D, the rotational speed of the impeller, Ny the vi osity of the Muid, 1, the density, p, and the head 8, gl. Show by the Buckingham pi theorem that 09 Qo bi) yey Choose AND as the recurring set. (10 marks]