By Dr. Salah Salman. Problem (1)
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1 Chemical Eng. De. Problem ( Solved Problems Samles in Flid Flow 0 A late of size 60 cm x 60 cm slides over a lane inclined to the horizontal at an angle of 0. It is searated from the lane with a film of oil of thickness.5 mm. The late weighs 5kg and slides down with a velocity of 0.5 m/s. Calclate the dynamic viscosity of oil sed as lbricant. What wold be its kinematic viscosity if the secific gravity of oil is Comonent of W along the lane W cos(60 W sin(0 5 (0.5.5 kg F.5 kg (9.8 m/s.65 N τ F/A.65 N/(0.6 x0.6 m Pa τ Pa µ.044pa. s 0.44 oise ( d / dy (0.5 / s µ.044 Pa. s ν m / s.5 stoke 950 kg / m By Dr. Salah Salman 0 60 w 0.5m Problem ( By dimensional analysis, obtain an exression for the drag force (F on a artially sbmerged body moving with a relative velocity ( in a flid; the other variables being the linear dimension (, srface roghness (e, flid density (, and gravitational acceleration (g. Drag force (F N [MT - ] Relative velocity ( m/s [T - ] inear dimension ( m [] Srface roghness (e m [] Density ( kg/m [M - ] Acceleration of gravity (g m/s [ T - ] F k (,, e,, g f (F,,, e,, g 0 n 6, m, Π n m 6 No. of reeating variables m The selected reeating variables is (,, Π a b c F (
2 Solved Problems Samles in Flid Flow Chemical Eng. De. Π a b c e ( Π a b c g ( For Π eqation ( [M 0 0 T 0 ] [ T - ] a [] b [M - ] c [MT - ] Now alied dimensional homogeneity 0 For M 0 c + c For T 0 a a For 0 a + b c+ b Π F For Π eqation ( Π F [M 0 0 T 0 ] [ T - ] a [] b [M - ] c [] For M 0 c c 0 For T 0 a a 0 For 0 a + b c+ b Π - e For Π eqation ( Π [M 0 0 T 0 ] [ T - ] a [] b [M - ] c [ T - ] For M 0 c c 0 For T 0 a a For 0 a + b c+ b e g Π - g Π f (Π, Π, Π 0 f ( e g F f (, F e g,, 0
3 Chemical Eng. De. Solved Problems Samles in Flid Flow Problem ( A conical vessel is connected to a U-tbe having mercry and water as shown in the Figre. When the vessel is emty the manometer reads 0.5 m. find the reading in manometer, when the vessel is fll of water. 0 P P P (0.5 + H w g + P o P 0.5 m g +P o (0.5 + H w g + P o 0.5 m g +P o.5 m H 0.5 ( m w / w 0.5 (600 /000.5 m When the vessel is fll of water, let the mercry level in the left lim go down by (x meter and the mercry level in the right lim go to by the same amont (x meter. i.e. the reading manometer (0.5 + x P P P (0.5 + x +H +.5 w g + P o P (0.5 + x m g +P o m mercry H 5 cm P o P P (0.5 + x +H +.5 w g + P o (0.5 + x m g +P o x (0.5 + x ( m / w x 0.4 m The manometer reading ( m Problem (4 A m develoing a ressre of 800 kpa is sed to m water throgh a 50 mm ie, 00 m long to a reservoir 60 m higher. The flow rate obtained is 0.05 m /s. As a reslt of corrosion and scalling the effective absolte roghness of the ie srface increases by a factor of 0 by what ercentage is the flow rate redced. μ mpa.s. The total head of m develoing (ΔP/g 800,000/(000 x mh o The head of otential energy 60 m Neglecting the kinetic energy (same diameter P η W + z + s + h F 0 g αg g. 00 m Datm line 60 m
4 Chemical Eng. De. Solved Problems Samles in Flid Flow 0 ΔP/g + Δz +h F 0 h F ΔP/g Δz m Q/A (0.05 m /s/( π/ m/s h Fs ( ΔP fs /g 4f (/d ( /g f h Fs d g/(4 (.55 (0.5(9.8/( x 00 x Φ 0.00, Re (000 x.8 x 0.5/ x0 5 From Figre (.7 e/d 0.00 De to corrosion and scalling the roghness increase by factor 0 i.e. (e/d new 0 (e/d old 0.0 The m head that slied is the same ( ΔP fs h Fs g.55 ( kpa ΦRe (-ΔP fs /(d /4μ [(40/( 00][(000(0.5 /(4(0.0 ] 6 x 0 8 From Figre (.8 Re.95 x0 5.97m/s The ercentage redced in flow rate ( /.8 x 00 % 0. %. Problem (5 It is reqired to m cooling water from storage ond to a condenser in a rocess lant sitated 0 m above the level of the ond. 00 m of 74. mm i.d. ie is available and the m has the characteristics given below. The head loss in the condenser is eqivalent to 6 velocity heads based on the flow in the 74. mm ie. If the friction factor Φ 0.00, estimate the rate of flow and the ower to be slied to the m assming η 0.5 Q (m /s Δh (m [Usally the m done its exact dty and retrn the liqid at the sction ressre i.e the m give the minimm limit of energy reqired to arrive the liqid to oint or d] [( h + ( h ( h ] P h z F d F + s g g α ( h ( h F F condenser d + s 4 f 4(0.006(00/0.074( /g. d g F condenser g Q/A.6 Q 4
5 Chemical Eng. De. Solved Problems Samles in Flid Flow 0 Δh 0 + ( (.6 Q 0 +. x 0 5 Q To draw the system crve Q (m /s Δh (m From Figre Q m /s Δh 6.4 m Δh (m 0 8 Pm 6 4 System Power reqired for m Q (m /s Q h g η (0.0054(6.4(000(9.8/ kw.5 m/s g 0.08 m ; Δz 0 m; h f 6.45 m Problem (6 A Power-law liqid of density 96 kg/m flows in steady state with an average velocity of.5 m/s throgh a tbe.67 m length with an inside diameter of m. For a ie consistency coefficient of 4.46 Pa.s n [or 4.46 (kg / m.s s n ], calclate the vales of the aarent viscosity for ie flow (μap in Pa.s, the Reynolds nmber Re, and the ressre dro across the tbe for ower-law indices n 0., 0.7,.0, and.5 resectively. Aarent viscosity ( µ a P 8 K( d n 4.46 (kg/m s n- [8 (.5/0.076] n- s n- 5
6 Chemical Eng. De. Solved Problems Samles in Flid Flow 0 (μ a P 4.46 (59.9 n- (Pa.s ( d d Re n- 96 (.5(0.076 / 4.46 (59.9 n- ( µ 4.46 (59.9 a ΔP fs 4f (/d ( / Problem (7 P Re 5.006/ (59.9 n ( 4(6/Re (.67 / 0.076[96(.5 /] for laminar ΔP fs (59.9 n- (Pa ( n (μ a P Eq.( Re Eq.( ΔP fs Eq.( ( ΔP fs non-new / ( ΔP fs New ( η 0.6 Power , , , ,6, A (0cm x 5cm Ventri meter is rovided in a vertical ie-line carrying oil of s.gr The flow being wards and the difference in elevations of throat section and entrance section of the ventre meter is 0 cm. The differential U-tbe mercry manometer shows a gage deflection of 5 cm. Take Cd 0.98 and calclate: - i- The discharge of oil ii- The ressre difference between the entrance and throat sections. (W i- Q A 0.98 C d R( m g A A A A (0.5( [ π / 4( ] m /s ii- Alying Bernolli s eqation at oints and P P + + z + + z g g g g P P z + g g 0.488/(π/4 0.. m/s, 0.488/(π/ m/s 0cm 5cm 6
7 Chemical Eng. De. Solved Problems Samles in Flid Flow 0 P P 900 (9.8 [0. + (8.4. /(9.8].5675 kpa bt P P 0.5 ( ( kpa % error 4.6 % Problem (8 A vacm distillation lant oerating at 7 kpa ressre at to has a boil- rate of 0.5 kg/s of xylene. Calclate the ressre dro along a 50 mm bore vaor ie sed to connect the colmn to the condenser. And also calclate the maximm flow rate if 6 m, e m, Mwt 06 kg/kmol, T 8 K, μ 0.0 mpa.s. P ( P P G ln + + 4φ G 0 P P υ d G 0.5 / [π/4 (0.5 ] kg/m.s P 7 kpa, P Pressre at condenser RT 84 (Pa.m /kmol.k 8K P υ Mwt 06 kg/kmol ( J / kg m / s Re G d / μ 7.074(0.5/0.0 x x 0 5, e/d 0.00 Φ 0.00 (Figre ln [ P (7 0 ] + 4( P 0.5 ln(7 0 / P P by trial and error ln(7 0 / P ( 0 ( 7 P P Assmed 5 x x x x 0 P Calclated x x x x 0 V V D P x 0 Pa ΔP P P ( x 0 94.Pa [(P P / P ] % % we can neglect the K.E. term in this roblem For maximm flow rate calclations m A P / P υ G P P υ max w max w / P P To estimate P w ln + + 8φ 0 et X (P /P w w P P w d 7
8 Chemical Eng. De. Solved Problems Samles in Flid Flow 0 ln(x + X + 8 Φ /d 0 X.96 + ln(x by trial and error X Assmed X Calclated X.087 (P /P w P w P /( Pa This system did not reached maximm velocity (H.W. exlain G max 984 / ( kg/m.s Problem (9 Calclate the theoretical ower in Watt for a 0. m diameter, 6-blade flat blade trbine agitator rnning at 6 rev/s in a tank system withot baffles and conforming to the standard tank configration. The liqid in the tank has a dynamic viscosity of 0.08 Pa.s, and a liqid density of 900 kg/m. (Re m N D A / μ (900 (6 (0. / (0.08,800 From Power crve Figre ( Φ. The theoretical ower for mixing P A Φ [(Fr m ] y N D A 5 α log(re m log(800 y y β 40 (Fr m N D A / g (6 (0. / [(Fr m ] y [.6] P A. ( (900 (6 ( W Problem (0 In contact slhric acid lant the secondary converter is a tray tye converter. m I.D. with the catalyst arranged in three layers, each 0.45 m thickness. The catalyst is in form of cylindrical ellets 9.5 mm I.D. and 9.5 mm long. The void fraction is 0.5. The gas enters the converter at 675 K and leaves at 70 K. Its inlet and otlet comositions are:- Gas SO SO O N mol % In mol % Ot The gas flow rate is 0.68 kg/m.s. Calclate the ressre dro throgh the converter. Taken that the dynamic viscosity 0.0 mpa.s. 8
9 Chemical Eng. De. Solved Problems Samles in Flid Flow 0 ( P e Φ J f + 0. and S( e Re Re Re µ s( e A S V P P Srface area of article Volme of article ( π / 4 d π / 4 d + ( πd P π / d π / 4 d + π d 6 d d Gd Re 6( e µ 6( e µ gas ( ot Mwt avg P Tin + Tot Mwt in + Mwt, Tavg, ( Mwt avg RT avg,( Mwt x i Mwt i n i (Mwt in 0.066( ( ( (8 (Mwt ot 0.08( ( ( + 0.8(8 (Mwt ag.58 kg/kmol; T avg K.58( ( gas 0.569kg / m.44 kg/kmol.7 kg/kmol Gd 0.68( e 5.76 Φ ( e µ 6( (5.76 R S( e P Φ e Φ 6( e G d e 0.66( 0.456( 0.5( ( Pa Problem ( What will be the settling velocity of a sherical steel article, 0.4 mm diameter, in an oil of s.gr 0.8 and viscosity 0 mpa.s? The sgr. of steel is For a shere C D 4 ( (Re gd Ga, Ga 6.9 µ C D C (Re D 48.4 (Re 4. C D From Figre at (Re 4., (Re.667 (Re µ.667( m d 80( / s 9
10 Chemical Eng. De. Solved Problems Samles in Flid Flow Problem ( A mixtre of gas and liqid flows throgh a tbe of ID 0.0m at a steady total flow rate of 0. kg/s. Calclate the ressre gradient in the ie sing the ockhart-martinelli correlation. Given that e mm, µg 0.0 and µ mpa.s, G 60 and 000 kg/m, and the qality w G 0./(π/ kg/m s Re [66.6 (-0.49 x 0.0/ x x0 trblent Re G [66.6 (0.49 x 0.0/ 0.0 x x0 5 trblent X tt 0.9 w µ w µ G C + + X X 0. G Φ, for tt C 0 Ф.7 Re 5.47 x0, e/d f dp G ( w 66.6 ( f 4( Pa/m d d 0.0 (000 dp dp Φ.7( Pa/m d T d Problem ( A cylindrical tank 0.9 m ID and m high oen at to is filled with water to a deth of.5 m. it is rotated abot its vertical axis at N rm. Determine the vale of N which will raise water level even with the brim. 0 The water level even with brim P P o, z m The rise of liqid at wall y r m The fall of liqid at wall y f y r 0.5 m z o H - y f m, z m at r R ω z z g r o + ω (9.8 ω 9.84 rad/s π N 60(9.84 ω N 94 rm 60 π ω R y r y f z o H 0
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