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- Fluid Mechanics And Hydraulic Machines
- Fluid mechanics and hydraulic machines Dr. R. K. Bansal

scanned by Fahid PDF created by AAZSwapnil A TextBook of Fluid Mechanics and Hydraulic Machines -Dr. R. K. Bansal Scanned by Fahid Converted to PDF. Basic Fluid Mechanics sieflowiqroweb.gqlic Machines Zoeb Husain Principal Hi-Point College of Engineering and Technology Hyderabad. Mohd. Zulkifly Abdullah. *Sweepstakes not currently available in all countries; visit sieflowiqroweb.gq for official rules. Get More and Do More.. Ho FLUID MECHANICS AND HYDRAULIC.

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Fluid Mechanics and Hydraulic Machines. Book ยท September with 4, Reads. Publisher: Publisher: PHI Learning. A TextBook of Fluid Mechanics and Hydraulic Machines - Dr. R. K. sieflowiqroweb.gq - Ebook download as PDF File .pdf), Text File .txt) or read book online. A TextBook of Fluid Mechanics and Hydraulic Machines - Ebook download as PDF File .pdf), Text File .txt) or read book online. Dr. R. K. Bansal.

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Shear Str 'sses till Shear stress is g iven by. T heir va lues are dctc nnincd from boundary cond ition s as: Veloc ity grad ient. Solu t ion. Speed of sleeve. If " torqut' of J Let speed of sleeve is "2 when force. I-l x. Wh en the thin plate is in the middle of the tw o plane surfaces 1Re fer to Fig. Viscosity of g lyce rine. Distan ce Iwtw". Thl' Spllcr b. Let th e viscusit y. ISN 0. When the thin plalc is at 11 distanceofQ.

CaSt' II. I Lei Ihe lltil1 plate is al a distance 0. Width of gap " 2. Ulem 2. IOx 10 x. Jl" 2. Ihrough Ihe gap. Ihe shear force on Ihe Tight side of the metallic plale. Bul gas. When plale is in the m iddle of the gap. K For air If Ihe c hange in de nsity occu rs a1 co nstanl temp erature. The gas constant. T he rel ati onship be twee n press ure absolut e.

One kilogram mole is defined as the product of One kilogrlllll mass oflhe gas and its molecular weight. IlImi"8 i. Weight den s ity. Find i prl'. Dnfr- Problem 1.!!.

Using equation 1. A ssuml'. For temperature. For Iso thermal Proces! Equation Increase uf pn: LeI 'V" Volume of a g as cnclo. K which is defined as Ih".

Usi ng equat ion 1. Solu llon. Final vol ume. Pina l press ure " Nlc m 2. K is given by cqu31io n 1. Il '" Constant Differentiating II" liqllid durNlus by O. It is denoted by Greek Idlef 0 calkd sigma.: Let the droplet is cut into two halves. But the molecule IJ. In M KS units. The I1wgnitudc of this force per uni t icngth of Ih.: On the enlire surface oflhe droplel.

Thus the free surfa.. Thus a net result. Consider 11 small spherical droplet of a liquid of radi us. All the molecules on the free surface experience a downward force.

The phenomenon of surface tension is explained by Fig.: Th us the resultant force actirlg on the molecule A is zero. The molecule C. C of a liquid in a mass of liquid. Solut ion. Su rface tensioll. COil sider a liquid jet of diameter "tf and lenglh 'L' as shown in Fig.. I' in exc ess of outside pressure is. III suc h cao. Lli e. A llOliow bubble like a soap bubble in air has 1WO surfaces in co ntact wilh air.

Thus two surfaces arc subjected to surface lensioll. E IJress ion fur Cljllillary Risc.

Under a state ofeq uilihrium. Consider a glass lube of small diameter 'd' opened at ooth ends and is inserted in a liquid. Its val ue depends upon the specific weight of the liquid. Surface tension. But the force at he surface of the liquid in Ihe tube is due to surface Tensioll. The liquid wi ll rise in the tube aoove the level of the liquid. Capillarity is defined as a phenomenon of rise or fall of a liquid surface in a small!

The rise of liquid surface is known as capi lla ry rise while the fall o f the liquid surface is known as capillary depression. IF '" pg h. Iflhe g lass lube is dipped in mercury. SCl"Ond force is due to hydrostatic fo rce acting upward and is equal 10 inlensity of pressure al a deplh '11' x Area 1. P '" pgll 4 4 Equal ing the IWO. Take surfllce lellsiollS 0'" Theil in equilibrium. The negalive sign ind icmcs the capill: Tllia' drllsity of.

Ail S. Capi lI ary rise IOOOx 9. Tile IIIirk1l1'S. J m II x 05 x Tangc mi a l veloc ity of shan. J III: These vapour molecules ge t accumulated in Ihe space between th e free liquid s urface and top of the vessel.

Watts or. This phenomenon is kno wn as ". The metallic surfaces. Consider a liquid say waler whic h is confined in a c losed vesse l.. The pressure developed by the collapsing bubbles is so high that the material from The adjoining boundaries geTS eroded and c aviTi es are formed on them. Thus a liquid may boil even at onlinary lcnlperature. If the pressur" above th e liquid surface is reduced by so me means.

Ihe boil in g of the liqu id wi ll stan.: When Ih e v. IS kW. These accumula ted vapou rs exen a pressure on Ihe liquid su rface. Ihe molecules escapes from Ihe free surface of Ihe liquid. When vaporization lakes place. If The pressure at any point in this flowing liqu id becomes equal to or less Ihan the vapour pressu re.

If Ihe pressure is reduced to such an exten t that it bccotnes equal to or less than the vapour pressure. The bubbles of these vapouT5 arc carr ied by the flowing liquid into th e region of high pressure where they collapse.

The vaporization whkl! Pa '" Pascal. For a perfect gas.. The shear stress is proponiOllal 10 the velocity gradient "" 4. For isolhcmlal process. It is also cqualto. Specific volume is the reciprocal of mass density.. Define the following fluid propenie.. To convert the unil of viscosity from poise to MKS units. What is the difference between dynamic viscosity and kinematic viscosity? State their units of mcasuremcnlS. Differentiate between: Define compressibility.

An oil film of thickness 1. Explain the len". Newtonian and Non-Newtonian fluids. No8pur Unil'ersity [Ans. I kgls-m dynamic viscosity in poise.. Explain thc importance of compressibility in fluid flow. Why does the viscosity of a gas increases with the increase in temperature while that of a liquid decreases with increase in temperature? One litre of crude oil weigh' 9. Explain the importance of viscosity in n uid motion. The "elocity distribution for flow oVer a flat plate i. Calcu late ilS specific weight.

The cleamnec is 1.

W hat. EXplain the phenomenon of capillarity. Assume dynamic viscosity as 8 poise. A plate 0. Two plates arc placed at a distance of The weight of thc square is 3'n. Give their dimensions. Find the dynamic viscosity of the oil. Define surface tension. Obtain an expression for capillary rise of a liquid.

Detennine the fluid viscosity between the plates in the poise. Whal do you understand by tenns: I lsothennal process. Enunciale Newton's law of. Deflne and explain Newton 's law of viscosity. State the Newton's law of viscosity and Kjve examples of its application. The lower plate is fixed while the upper plate having surface area 1.

IAn s. Calculale the "clocity gradic and shear stress at distances of O. Calculate lhe shear StreSS al1he poin!. In 'luestion Calculale the power losl in Ihe oil for a sk'"CYe lenglh of nnn. The diametcr of shaft is 0. The pressure oUlside the droplel of water of diameter 0.

DClcmlinc 1he viscosily of a liquid having kincmalic ". If the velocity distribution of a fluid over a plate is gi. The surface tension of Waler in eont.. IXlO rn' or 8. In a stream of glycerine in 1Iion. Molccular weight of nitrogen is Ihe shear stress is 0.

Take dynall1ic "is: The weight of a gas is given as The pressure inside a droplet of waler is 10 be 0. The air is cornpres.

A cylinder of 0. Find Ihe surface Icnsion in a SD. An oil of viscosity 5 poise is used for lubrication belween a shaft and slecve. The surface lension of watcr in contact with air at 20"C is gh'cn as 0. The thickness of the oil fihn is 1.

DCle"nine Ihe bulk modulus of elaslicity of a fluid which is compressed in a cylinder from a volume of 0. The length of the t1c:. If the annular space i Assumi ng that the bu lk modulus of elasticity of water is SI LTnits. The inclined plane is laid on a slope of 5 venicalto 12 horizonlnl and has an oil film of 1 mm thickness. A shaft of diameter mm is rotating inside a journal bearing of diameter mm at a space of J60 r..

A I SO mm diameter vertical cylinder rotates concentrically inside another cylinder of diameter lSI mm.. Dctennin" ils minimum size. Spcdfic gravity for mercury is given as Take surface len.

Find the capillary risc of water in a wtlc 0.

Both the cylinders are of mm height. A Shaft of diameter nlln is rotating inside a journal bearing of diameter mm at a speed of r. The surface tension of water is 0. S7 Nml. A square plate of size 1 m x 1m and weighing N slides down an inelined plall e with a unifonn velocily of 1.

Calculate the specific weight.

Calculmc its specifIc weight. A piston mill diameter and nun IonS works in a cylinder of mill diameter. Find the power absorbed in oil if the length of bearing is mm..

S97 poisei A du 1. The ']XIce between the Shaft and the bearins is f. The space between the shafl and bearing is filled with a lubricating oil of viscosity 5 poisc. Find the power absortlcd in the lubricating oil.

Detennine the torque required to rotate thc inner cylinder at T. S [ ' [ Ihnl. One lilre of crude oil weighs 9. The weight of the piston and 3. SI "nits. Caiculutc the d l11amic viscosity of oil. Calculate the capillary risc in: Tile flu id clement is of very small dimensions i. Other common ly used units of pressure arc: Tllen the ratio of.

This is proved as: Nfm 2 is known as Pascal and is represented by Pa. Conside r an arbitrary fluid clement of wedge shaP'C in a fluid mass al rest as show n in Fig. If tile fluid is stationary. Let the width of tile p. L Pressure forces nonnallo the surfaces.

The forces acting on tile fluid clement are: The forces the faces arc: Force on the face All '" fI. Xdxx l-p. BUl from Fig.. This is prt l'ed as: Since the choice of fluid element was co mple tely arbitrary..

Weight of c lemen t in Ihe vcnical direction. AC and Be respectively. Let LABe". Resol ving Ihe forces in J Distance of fluid elemellt from free surface.

For equilibriu m o f nuid c le men!. Find Ihe! From equation 2. Here Z is called ]Irl'ssurl' hl'ad.. Problem 2. This is Hydrostatil: Elj uati on Are a of plunger. Give n: By integrating tile above equation 2. See Fig. Height o f liq uid co lumn. Fo rce F Pressure int ensi ty develo ped due 10 p lun ge r ". Area " By Pasca l" s La w. II ld c Ilwrcur ' of sp. From eq uation 1. Density of oil.

Density of oil Po" 0. Po xg x9. N Pressure imensity. A liS. IA we know that tile den s ity of J fluid is eq ua l to specific g ravi ty of fluid multiplied by densit y o f water Densi1y of mercury. The 1I'usil.

Pl'" Sp. Z2'" 1m Sp Corresponding liclght of water'" -. So'" 0. Hciglll of water. In one system. Mano meters are defi ned as [he dev ices used for measuri ng th e pressure at a point in a fluid by ba lancin g th e co lu mn of fl uid by tile sa me o r anothe r co lumn of the fl uid.

Mec han ic al Gau ges. Vacuum IIrl'ss un' is defin ed as the pres. T il ey are d assified as: Man o me[e rs 2. In case of M KS units. Absol ute pressure. Not e. Mathe mati call y: III sure be low the atmos phe ric pressure. Co mm on types of simple ma - nometers arc: It cons ists o f g lass tube bent in U-shape.

It is Ihe s implest form of mano meter used fOf measurin g gauge pressures. One end of this mano meter is cu nn ected to T the point where pressure is to he measured and ot her end is open to the atmusph erc as shown in Fig. The commonly used mcc hani -. Single Column Man ometer. The datum line is A-A. The ri se of liquid g ivcs th e pressure head at that point. Mechan ic al ga uges arc defmed as th e dev ices used for me as urin g Ih e press ure by balanc in g llie nuid co lumn by Ih e spring or dead we ig ht.

T he tuhe gene rall y contains mercury u r any oth er liquid whose specific gravity is grea te r than th e specific gravity uf the liquid whu se press ure is to he me asured. If at a point A. P2 '" G ivcn: SS UI'f'. Height of liquid in Idl limb. Equat ing pressure above datum. Find IIII' pre. T hen Pressure above A-A in the left co lumn "P! Pressure h"ad in Ihe ri ght column arovc A-A " 0 P!

Hence pressure above th e horizontal datum line A -A in the Ieli co luilln and in the right co lumn of U-Iube manometer shou ld be same.

S1 xO. PI '" SOO. Hence equating th e two prc! The OIher em f of lhe mllltollieler is open 10 almosphere. G ive n: Diffe rence o f merc ury'" 10 em '" Bu t pressure at B '" PreSl. In this case the pressure at A i 0 Nlm '"w hie h is Jess lhanlh e He nce merc ury in Je fllimb will ri se.

The ri se o f merc ury i n Jeft lim b will be equ a l 10 l he fall o f mercury in righl lim b as lhe tOlal vo lu me of merc ury re mai ns sam e.

Sketch Ihe arrangements ill bOlh ea. The arrangemcnt is shown in Fig. Hence pressure. Hence equat ing the equa- ti ons il and ii. Delermine Ihe pressure of. Solu tion. The mercury wi ll rise in the left hy a d ist an ce of ' Clll. Vcssd is elllll' '. Indy filled.. When ves. Pressure in left lim b"" Pressure in righ t limb Now the datum line is Z-z. I Density of nU'rcury. Let the distance throu gh which mercury goes down in the right limb be. Now fall in surfac" IeI'd of C mul tip lied by cross.

Th en Y. FI NAL. Lei X-X bc the datum line in the reservoir. When the manom eter is I I Ii. IUOC manometer in wllich a r. Due to Jarge cross-sectional are a o f the reservoir. The other limb ma y be vcnical or inclined. Inclined Single Column Manom eter. J Single Column Manometer.

QI 40 40 4! Z 39 --"-x. Thus thcre are two types of single column manometer as: Single colulnn manometer is a 1I1odificd form of a U. Vertical Single Column Manometer rig. Ven icaJ Sin. IS s hows tile vertical single column manometer. This manometer is more sensitive. Inclined Single Column Manometer Fig.

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