ME Homework Set-4

ME Homework Set-4 - ME 3720 HOMEWORK SET-4 1. A 1/4—m...

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Unformatted text preview: ME 3720 HOMEWORK SET-4 1. A 1/4—m diameter pipe carries an oil (SG=0.8) at the rate of 120 liters per second and the pressure at a point “ ‘A’ is 19.62 kPa (gage). If the point ‘A’ is 3.5-rn above the datum line, calculate the total energy at point ‘A’ in meters of oil. I ,. 6 3/ ,1! I r— .5 TE at A: LA 4%+i/¥, VA: ERR": “‘2 :zwrm a; I ,. i—— I S V ‘ t (E) G c) TE wt A 1': 6.33%“ of 01') QY 44'4‘4 “‘94) 2. An Eulerian velocity vector field is given as (y2+z2) i + (x2+22) j + (x2+y2) k. Determine total acceleration of a particle in the flow field. Also find the acceleration of a particle at (x, y,z,t) = (-l,0,l,10). CHL: U 2’“ +v 91‘ Avail 414 ; ZN, (“2+ia2_f 2% (flzrxzz 3" 39" Mr 7" 2 ~21 42%(u2+2 3:0 300 C i p 2&0 w (0/ :M 0;: “git—l “by F} 37*“ ,_ a :0 4.}: ‘9’ :: ’li0;l1’9/ OX’Q7 J ) ¢i\’}ilt)’L / H C n m '0’ 401‘770 3 5”"1J4 3. Water flows through a small hole in the bottom of a large, open tank with a speed of 8-rn/s. Determine the depth of water in the tank if viscous effects are negligible. I ’- z. PMEPV; +32, =f2+§§f3Vz +3432 wifbfl:fi:zzsl/,:fll 5'2: :ZPV; J W/YE/E’ andfl‘h sot/mi z I Pfih‘IFV‘ Of“ .. Ki (8%? W n 29 ’ 20.81%.) gig—- 1/3 4. Air flows steadily through a horizontal, 4-in diameter pipe and exits into the atmosphere through a 3-in diameter nozzle. The velocity at the nozzle exit is 150-m/s. Determine the pressure in the pipe if viscous effects are negligible. A fl =ZI-P(V:‘Vlt) fl 1 z . 1. But s/lzl/z.’ or l4 = Vz (Iggy) sggygfl ’7‘!!! 7th) 4‘ 7- A at =%(0'W’—;%->{w£t> We)? SI. or lb fl = /6’.3 a; 3 0.31735 5. Water flows steadily with a speed of 10-ft/s from a large tank as shown. Determine the depth H of the layer of liquid (Specific Weight = 50-lb/ft3) that covers the water in the tank assuming an inviscid, incompressible flow. From Hue Bernoul/i equal/’0”, 2 2. €1 +72%- +z,=_ +3? +32 w/Ierefl: 6M, 1&0, 102:0! z,="7‘f/J 417012; “SH 3 Thus) ’1 50 mm A énl +2, = 35’; _+ z: 50 find my; 14: mag 50/5/1913 00 {xi/sf (“ails/r43)” + 4‘ H “ W *5 1’ 1’ Therefore} H = 3.“? 6. If water flows from a garden hose nozzle with a velocity of 15-m/s. What is the maximum height that it can reach above the nozzle? é+g+zzée+g+zz 7711/51 3 v2: (rs-21f , h 5?— 2(22/gn1)”éé_.§_£ 2/3 7. A circular stream of water from a faucet is observed to taper from a diameter of 20-mrn to 10-mm in a distance of 50-cm. Determine the flow rate assuming steady, incompressible, frictionless flow. h~ V1 ’- V2. $+§é~+zfié+§j +2!2 Q where f), .392 = 0 J 21:0, 2, = 0. 50;» m and DI=O.02.0fl7 0.50m } 1 2 2&2, 1 i . =(%1) 0!“ :4 M (1)DZ:O,O/pm . 2 fl,‘ 7/ 4141/4? Q or smce A 2. 75' “ WE abhm 1 Q = z __L__._ V5?! = 120) 0/0 a. 2(£€/%)(o,50m) E lI-(Dz/m‘ “ ' ”’) W'— 3 = 2 51; x/o 43’”— 8. In relation to the venturimeter discussed in class, draw the sketch and (a) Derive an expression for the volume low rate (Q) in terms of areas (A1 and A2), gravity g, and h. —. __.————-"fi ‘ \ldlLf“ 6’2 3/3 2. 3.48 @‘d2 W in $1 walk: a .m_.~__ ...
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ME Homework Set-4 - ME 3720 HOMEWORK SET-4 1. A 1/4—m...

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