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1 FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom DE FINITION OF FLU ID The term fuid refers to substnce tht cn fow nd does not hve shpe of its own For exmpe iquid nd gses Fuid incudes property () Density (B) Viscosity (C) Buk moduus of esticity (D) pressure (E) specific grvity PRE SSURE IN FL UID The pressure p is defined s the mgnitude of the norm force cting on unit surfce re P F F norm force on surfce re The pressure is scr quntity This is becuse hydrosttic pressure is trnsmitted equy in directions when force is ppied, which shows tht definite direction is not ssocited with pressure Thrust The tot force exerted by iquid on ny surfce in contct with it is ced thrust of the iquid CONSEQUENCES OF PRESSURE (i) Riwy trcks re id on rge sized wooden or iron seepers This is becuse the weight (force) of the trin is spred over rge re of the seeper This reduces the pressure cting on the ground nd hence prevents the yieding of ground under the weight of the trin (ii) shrp knife is more effective in cutting the objects thn bunt knife The pressure exerted Force/re The shrp knife trnsmits force over sm re s compred to the bunt knife Hence the pressure exerted in cse of shrp knife is more thn in cse of bunt knife (iii) cme wks esiy on snd but mn cnnot inspite of the fct tht cme is much hevier thn mn This is becuse the re of cme s feet is rge s compred to mn s feet So the pressure exerted by cme on the snd is very sm s compred to the pressure exerted by mn Due to rge pressure, snd under the feet of mn yieds nd hence he cnnot wk esiy on snd VRITION OF P RE SS URE WITH HEIGHT dp Weight of the sm eement dh is bnced by the excess pressure It mens ρg dh P dp ρg P FLUID MECHNICS h dh P P ρgh PSCL L S LW if the pressure in iquid is chnged t prticur, point the chnge is trnsmitted to the entire iquid without being diminished in mgnitude In the bove cse if P is incresed by some mount thn P must increse to mintined the difference (P P ) hρg This is Psc s Lw which sttes tht Hydruic ift is common ppiction of Psc s Lw Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

2 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Hydruic press Ex So p f W or f W s >> then f << W This cn be used to ift hevy od pced on the ptform of rger piston or to press the things pced between the piston nd the hevy ptform The work done by ppied force is equ to chnge in potenti energy of the weight in hydruic press The re of cross-section of the two rms of hydruic press re cm nd cm respectivey (figure) force of 5 N is ppied on the wter in the thinner rm Wht force shoud be ppied on the wter i n t he thick er rm s so tht the wter m y rem i n in equiibrium? In equiibrium, the pressures t the two surfces shoud be equ s they ie in the sme horizont eve If the tmospheric pressure is P nd force F is ppied to mintin the equiibrium, the pressures re 5 N F P nd P cm respectivey cm This givens F 5 N Hydruic Brke Hydruic brke system is used in uto-mobies to retrd the motion HYDROST OSTTIC TIC PRDOX Pressure is directy proportion to depth nd by ppying psc s w it cn be seen tht pressure is independent of the size nd shpe of the contining vesse P P B P C TMOSPHERIC PRESSU RE Definition The tmospheric pressure t ny point is numericy equ to the weight of coumn of ir of unit cross-section re extending from tht point to the top of the tmosphere t ºC, density of mercury 595 g cm, nd t se eve, g 9866 cm s Now P hρg tmospheric pressure dyne cm 5 N-m (p ) Height of tmosphere The stndrd tmospheric pressure is 5 P (N m ) If the tmosphere of erth hs uniform density ρ kg m, then the height h of the ir coumn which exert the stndrd tmospheric pressure is given by hρg 5 h ρg m 795 m 8 km In fct, density of ir is not constnt but decreses with height The density becomes hf t bout 6 km high, th t bout km nd so on Therefore, we cn not drw cer cut ine bove Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

3 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom which there is no tmosphere nyhow the tmosphere extends upto km This imit is considered for prctic purposes FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom MESUREMENT OF TMOSPHERIC PRESSURE Mercury Brometer To mesure the tmospheric pressure experimenty, torricei invented mercury brometer in 6 p hρg The pressure exerted by mercury coumn of mm high is ced Torr Torr mm of mercury coumn Open tube Mnometer Open-tube mnometer is used to mesure the pressure guge W hen equiibrium is reched, the pressure t the bottom of eft imb is equ to the pressure t the bottom of right imb ie p y ρg p y ρg p p ρg (y y ) ρgy p p ρg (y y ) ρgy p bsoute pressure, p p guge pressure Thus, knowing y nd ρ (density of iquid), we cn mesure the guge pressure Ex ns So The mnometer shown beow is used to mesure the difference in wter eve between the two tnks Ccute this difference for the conditions indicted cm p h ρg ρ g ρg p h ρg h ρg h ρg ρg ρ g s ρ 9ρ (h h ) ρg ρg 6ρg h h cm Wter Brometer Let us suppose wter is used in the brometer insted of mercury hρg 5 or h ρg The height of the wter coumn in the tube wi be m Such ong tube cnnot be mnged esiy, thus wter brometer is not fesibe Ex In given U-tube (open t one-end) find out retion between p nd p Given d 6 gm/cm d 6 gm/cm So Pressure in iquid t sme eve is sme ie t, In CGS p dyg xd g p 5 Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

4 FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom Ex p 6 5 g 6 6 g p p 6 g [5 6] p p p [p 6 g 76] Find out pressure t points nd B so find nge θ So Pressure t P P tm ρ g sin θ Pressure t B P B P tm ρ gh θ But P B is so equ to P B P ρ g sin θ Hence - P tm ρ gh P ρ g sin θ P tm ρ gh P tm ρ g sin θ ρ g sin θ Ex 5 So sin θ ρh ( ρ ρ ) In the given figure, the continer sides down with cceertion on n incine of nge θ Liquid is sttionry with respect to continer Find out - (i) nge mde by surfce of iquid with horizont pne (ii) nge if g sin θ Consider fuid prtice on surfce The forces cting on it re shown in figure Resutnt force cting on iquid surfce, wi wys norm to it tn α mcosθ mg msinθ cos θ (g sinθ) Thus nge of iquid surfce with the horizont is equ to α tn (ii) If g sin θ, then α tn cosθ tn g gsin θ tn (tn θ) α θ gsinθcosθ gcos θ Ex 6 Wter nd iquid is fied up behind squre w of side Find out () Pressures t, B nd C (b) Forces in prt B nd BC (c) Tot force nd point of ppiction of force (negect tmosphere pressure in every ccution) So () s there is no iquid bove, So pressure t, p Pressure t B, p B ρgh Pressure t C, p C ρgh ρgh (b) Force t Tke strip of width dx t depth x in prt B cos θ (g sinθ) Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

5 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Pressure is equ to ρgx Force on strip pressure re df ρgx dx Tot force upto B h F ρ gx dx ρgxh N In prt BC for force tke eementry strip of width dx in portion BC Pressure is equ to ρgh ρg(x h ) Force on eementry strip pressure re df [ρgh ρg(x h )] dx Tot force on prt BC F h ρgh [ ρgh ρg(x h)] dx x x ρg hx ρgh h ρg h h h h ρg ρgh h [ h h ] ρgh h ρg ( h ) ρgh [h h ] ρgh N (c) Tot force N Tking torque bout Tot torque of force in B ρgx h ρgh df x Tot torque of force in BC df x On soving we get ρgh h [h 5 h ρ gxdxx h ] ρgh [h 5 h ] 7 N - m 5 5 [5 5] 5 [5 ] Tot torque Tot torque tot force distnce of point of ppiction of force from top F x p 65 6 x p x p 7m Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge 5

6 FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom terntivey We cn sove this probem by pressure digrm so Force on B prt is re of tringe BC h ρgh F B ρgh Torque of force of B prt bout - τ B ρgh h ρgh ρg Force on BC prt is re of trpezium - h F BC ρgh h ρgh Torque of force of BC prt bout - h τ BC ρgh h (h ) ρgh (h Tot force Tot torque But F x p ρg ρg ρgh ρg 8 9ρg 8 ρg 8 ρg ρg 9 8 ρgh h ρgh ρg ρg ρg ρgh h ρgh h ) ρg 8 5ρg 8 x p 7 m Thus tot force is cting t 7m beow point p ρg 8 RCHIMEDES PRINCIPLE ccording to this principe, when body is immersed whoy or prtiy in fuid, it oses its weight which is equ to the weight of the fuid dispced by the body Up thrust buoyncy Vρ g V voume submerged ρ density of iquid Retion between density of soid nd iquid weight of the foting soid weight of the iquid dispced or V ρ g V ρ g ρ ρ V V 5ρg 8 Density of soid Voume of the immeresed portion of the soid Density of iquid Tot Voume of the soid This retionship is vid in cceerting fuid so Thus, the force cting on the body re : (i) its weight Mg which cts downwrd nd (ii) net upwrd thrust on the body or the buoynt force (mg) Hence the pprent weight of the body Mg mg weight of the body weight of the dispced iquid Or ctu Weight of body pprent weight of body weight of the iquid dispced The point through which the upwrd thrust or the buoynt force cts when the body is immersed Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge 6

7 FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom Ex 7 So Ex 8 So Ex 9 So in the iquid is ced its centre of buoyncy This wi coincide with the centre of grvity if the soid body is homogeneous On the other hnd if the body is not homogeneous, then the centre of grvity my not ie on the ine of the upwrd thrust nd hence there my be torque tht cuses rottion in the body If the centre of grvity of the body nd the centre of buoyncy ie on the sme stright ine, the body is in equiibrium If the centre of grvity of the body does not coincide with the centre of buoyncy (ie, the ine of upthrust), then torque cts on the body This torque cuses the rottion motion of the body copper piece of mss g is suspended by vertic spring The spring eongtes cm over its ntur ength to keep the piece in equiibrium beker contining wter is now pced beow the piece so s to immerse the piece competey in wter Find the eongtion of the spring Density of copper 9 kg/m Tke g m/s Let the spring constnt be k When the piece is hnging in ir, the equiibrium condition gives k ( cm) ( kg) ( m/s) or k ( cm) N (i) The voume of the copper piece kg 9kg/m 9 5 m This is so the voume of wter dispced when the piece is immersed in wter The force of buoyncy weight of the iquid dispced 9 5 m ( kg/m ) ( m/s ) N If the eongtion of the spring is x when the piece is immersed in wter, the equiibrium condition of the piece gives, kx N N 89 N (ii) By (i) nd (ii), x 89 cm 89 cm cubic bock of wood of edge cm fots in wter The ower surfce of the cube just touches the free end of vertic spring fixed t the bottom of the pot Find the mximum weight tht cn be put on the bock without wetting it Density of wood 8 kg/m nd spring constnt of the spring 5 N/m Tke g m/s The specific grvity of the bock 8 Hence the height inside wter cm 8 cm The height outside ter cm 6 cm Suppose the mximum weight tht cn be put without wetting it is W The bock in this cse is competey immersed in the wter The voume of the dispced wter voume of the bock 7 6 m Hence, the force of buoyncy (7 6 m ) ( kg/m) ( m/s ) 7 N The spring is compressed by 6 cm nd hence the upwrd force exerted by the spring 5 N/m 6 cm N The force of buoyncy nd the spring force tken together bnce the weight of the bock pus the weight W put on the bock The weight of the bock is W (7 6 m) (8 kg/m ) ( m/s ) N Thus, W 7 N N N 5 N wooden pnk of ength m nd uniform cross-section is hinged t one end to the bottom of tnk s shown in figure The tnk is fied with wter up to height of 5 m The specific grvity of the pnk is 5 Find the nge θ tht the pnk mkes with the vertic in the equiibrium position (Excude the cse θ ) The forces cting on the pnk re shown in the figure The height of wter ev e is 5 m The ength of the pnk is m The weight of the pnk cts through the centre B of the pnk We hve OB The buoynt force F cts through the point which is the midde point of the dipped prt OC of the pnk Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge 7

8 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom We hve O OC cosθ Let the mss per unit ength of the pnk be ρ Its weight mg ρg The mss of the prt OC of the pnk The mss of wter dispced 5 cosθ cosθ ρ ρ ρ cos θ ρg The buoynt force F is, therefore, F cosθ Now, for equiibrium, the torque of mg bout O shoud bnce the torque of F bout O So, mg (OB) sinθ F(O) sinθ ρ or, (ρ) cosθ or, cos θ cosθ or, cosθ, or, θ 5 Ex cyindric bock of wood of mss M is foting in wter with its xis vertic It is depressed itte nd then reesed Show tht the motion of the bock is simpe hrmonic nd find its frequency So Suppose height h of the bock is dipped in the wter in equiibrium position If r be the rdius of the cyindric bock, the voume of the wter dipced πr h For foting in equiibrium, π r hρg W (i) where ρ is the density of wter nd W the weight of the bock Now suppose during the v ertic motion, the bock is further dipped through distnce x t some instnt The voume of the dispced wter is π r (h x) The forces cting on the bock re, the weight W verticy downwrd nd the buoyncy π r (h x) ρg verticy upwrd Net force on the bock t dispcement x from the equiibrium position is F W πr (h x)ρg W πr hρg πr ρxg Using (i) F πr ρgx kx, where k πr ρg Thus, the bock executes SHM with frequency v π k M π πr ρg M Ex cyindric bucket with one end open is observed to be foting on wter (ρ kg/m ) with open nd down It is of N weight nd is supported by ir tht is trpped inside it s shown beow The bucket fots with height cm bove the iquid surfce If the ir trpped is ssumed to foow isotherm w, then determine the force F necessry just to submerge the bucket The intern re of cross-section of bucket is cm The thickness of the w is ssumed to negigibe nd the tmospheric pressure m ust be negected (g m/sec ) So W eight of bucket W x ρ g () pressure t iquid - ir interfce pressure of ir ρg x From () p ρ gx ρg W ρg W W v [h x ] h ρg Let force F is ppied Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge 8

9 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom downwrd force F W Buoynt x ρg() from () W F W ρg F p x ρg, v x p v p v W W W h ρg x ρ g x x h ρg ρg Wρgh W W W h ρg ρg substituting vues - W N, ρ kg/m, m W F F W W ρgh W - N Ex rge bock of ice cuboid of height nd density ρ ice 9 ρ w, hs rge vertic hoe ong its xis This bock is foting in ke Find out the ength of the rope required to rise bucket of wter through the hoe So Let re of ice-cuboid excuding hoe weight of ice bock weight of iquid dispced ρ ice g ρ w ( h) g 9 9 h h PRESSURE SU IN CSE OF CCELERCEL ERTING FLU UID (i) Liquid Pced in eevtor : When eevtor cceertes upwrd with cceertion then pressure in the fuid, t depth h my be given by, p hρ [g ] nd force of buoyncy, B m (g ) (ii) Free surfce of iquid in horizont cceertion : tn θ g p p ρ where p nd p re pressures t point & Then h h Ex n open rectngur tnk 5 m wide m deep nd m ong is hf fied with wter It is cceerted horizonty t 7 m/sec in the direction of its ength Determine the depth of wter t ech end of tnk [g 98 m/sec ] g Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge 9

10 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom So tn θ g FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom (iii) Depth t corner 5 tnθ 5 m ns Depth t corner B 5 tn θ 5 m ns Free surfce of iquid in cse of rotting cyinder h v g STREMLINE FLOW ω r g The pth tken by prtice in fowing fuid is ced its ine of fow In the cse of stedy fow the prtices pssing through given point foow the sme pth nd hence we hve unique ine of fow pssing through given point which is so ced stremine CHRCTERISTICS OF STREMLINE tngent t ny point on the strem ine gives the direction of the veocity of the fuid prtice t tht point Two stemines never intersect ech other Lminr fow : If the iquid fows over horizont surfce in the form of yers of different veocities, then the fow of iquid is ced Lminr fow The prtice of one yer do not go to nother yer In gener, Lminr fow is stremine fow Turbuent Fow : The fow of fuid in which veocity of prtices crossing given point is not sme nd the motion of the fuid becomes disordery or irregur is ced turbuent fow REYNOLD S NUMBER ccording to Reynod, the critic veocity (v c ) of iquid fowing through ong nrrow tube is (i) directy proportion to the coefficient of viscosity (η) of the iquid (ii) inversey proportion to the density ρ of the iquid nd (iii) inversey proportion to the dimeter (D) of the tube Tht is v c η ρd or v c Rη ρd or v c ρd η () where R is the Reynod number If R <, the fow of iquid is stremine or minr If R >, the fow is turbuent If R ies between nd, the fow is unstbe nd my chnge from stremine fow to turbuent fow EQUTION OF C ONTIN UIT Y The eqution of continuity expresses the w of conservtion of mss in fuid dynmics v v In gener v constnt This is ced eqution of continuity nd sttes tht s the re of cross section of the tube of fow becomes rger, the iquid s (fuid) speed becomes smer nd vice-vers Iustrtions - (i) Veocity of iquid is greter in the nrrow tube s compred to the veocity of the iquid in broder tube (ii) Deep wters run sow cn be expined from the eqution of continuity ie, v constnt W here wter is deep the re of cross section increses hence veocity decreses ENERGY OF LIQUID iquid cn posses three types of energies : Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

11 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom (i) Kinetic energy : The energy possessed by iquid due to its motion is ced kinetic energy The kinetic energy of FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom iquid of mss m moving with speed v is mv KE per unit mss mv m v (ii) Potenti energy : The potenti energy of iquid of mss m t height h is m g h PE per unit mss mgh gh m (iii) Pressure energy : The energy possessed by iquid by v irtue of its pressure is ced pressure energy Consider vesse fitted with piston t one side (figure) Let this vesse is fied with iquid Let be the re of cross section of the piston nd P be the pressure experienced by the iquid The force cting on the piston P If dx be the distnce moved by the piston, then work done by the force P dx PdV where dv dx, voume of the iquid swept This work done is equ to the pressure energy of the iquid Pressure energy of iquid in voume dv PdV The mss of the iquid hving voume dv ρdv, ρ is the density of the iquid Pressure energy per unit mss of the iquid PdV ρdv ρ P BERN OULLI S THEOREM It sttes tht the sum of pressure energy, kinetic energy nd potenti energy per unit mss or per unit voume or per unit weight is wys constnt for n ide (ie incompressibe nd non-viscous) fuid hving strem-ine fow ie ρ P v gh constnt Ex circur cyinder of height h cm nd rdius r cm is opened t the top nd fied with iquid It is rotted bout its vertic xis Determine the speed of rottion so tht hf the re of the bottom gets exposed (g m/sec ) So re of bottom πr If r is rdius of the exposed bottom, then π r πr r ppying Bernouis eqution between points () nd () - r P tm ρv ρgh P tm ρv ρg(h h ) ρgh ρ(v v ) gh [v v ] [w r w r ] r m gh w [r r ] w r gh rdin / sec Ex 5 Wter fows in horizont tube s shown in figure The pressure of wter chnges by 6 N/m between nd B where the res of cross-section re cm nd 5 cm respectivey Find the rte of fow of wter through the tube Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

12 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom So Let the veocity t v nd tht t B v B FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom By the eqution of continuity, By Bernoui s eqution, v v P ρ v P B ρv B B cm 5cm or, P P B ρ(v ) ρv ρv N or, 6 m kg v m or, v m / s 6 m/s The rte of fow ( cm ) (6 m/s) 8 cm /s PPLICTION OF BERNOULLI S THEOREM (i) Busen burner (ii) Lift of n irfoi (iii) Spinning of b (Mgnus effect) (iv) The spryer (v) ping-pong b in n ir jet (vi) Torricei s theorem (speed of effux) t point, P P, v nd h h t point B, P P, v v (speed of effux) nd h P P Using Bernoui s theorem ρ gh v ρ gh v, we hve P P ρ gh ρ v Ex 6 cyindric continer of cross-section re, is fied up with wter upto height h Wter my exit through tp of cross section re in the bottom of continer Find out : () (b) Veocity of wter just fter opening of tp The re of cross-section of wter strem coming out of tpe t depth h beow tp in terms of just fter opening of tp v gh or v gh (c) Time in which continer becomes empty (Given :, h cm, h cm ) So ppying Bernoui s eqution between () nd () - P ρgh ρv P ρv Through continuity eqution : v v, v gh v ρgh ρv ρv on soving - v m/sec () (b) ppying Bernoui s eqution between () nd () ρv ρgh ρv Through continuity eqution - / Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

13 Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Ex7 (c) v v v gh ' v v ρv ' ρgh ρ ' ' ' 98 From () t ny height h of iquid eve in continer, the veocity through tp, v gh 98 h we know, voume of iquid coming out of tp decrese in voume of iquid in continer For ny sm time interv dt v dt dx t x dt dx dt h Given [ x ] t h / t h or Thus t 5 5 second h dx x 5 In given rrngement () Find out veocity of wter coming out of C (b) Find out pressure t, B nd C So () ppying Bernoui is eqution between iquids surfce nd point C (VII) p ρ v p ρgh ρ through continuity eqution v v, v v v gh, v v ρ v ρgh gh (b) Pressure t, p p tm ρgh Pressure t B, p B p tm ρ g h Pressure t C, p C p tm Venturimeter ρ v h v h B h C h v Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge

14 FREE Downod Study Pckge from website: wwwtekocssescom & wwwmthsbysuhgcom Get Soution of These Pckges & Lern by Video Tutoris on wwwmthsbysuhgcom (viii) (ix) It is guge put on fow pipe to mesure the fow of speed of iquid (Fig) Let the iquid of density ρ be fowing through pipe of re of cross section Let be the re of cross section t the throt nd mnometer is ttched s shown in the figure Let v nd P be the veocity of the fow nd pressure t point, v nd P be the corresponding quntities t point B Using Bernoui s theorem : P gh v ρ P gh v ρ P gh ρ v, we get P gh ρ v (Since h h h) or (P P ) ρ( v v ) () ccording to continuity eqution, v v or v v Substituting the vue of v in eqution () we hve (P P ) ρ v v Since >, therefore, P > P or v (P P ) ρ (P P ) ρ( ρ v where (P P ) ρ m gh nd h is the difference in heights of the iquid eves in the two tubes v ρ ρ m gh The fow rte (R) ie, the voume of the iquid fowing per second is given by R v ) During wind storm, The veocity of ir just bove the roof is rge so ccording to Bernoui s theorem, the pressure just bove the roof is ess thn pressure beow the roof Due to this pressure difference n upwrd force cts on the roof which is bown of without dmging other prts of the house When fst moving trin cross person stnding ner riwy trce, the person hs tendency to f towrds the trin This is becuse fst moving trin produces rge veocity in ir between person nd the trin nd hence pressure decreses ccording to Bernoui s theorem Thus the excess pressure on the other side pushes the person towrds the trin Teko Csses, Mths : Suhg R Kriy (S R K Sir), Bhop Phone : , pge