Fluid Kinematics. by Dr. Nor Azlina binti Alias Faculty of Civil and Earth Resources Engineering

Transcription

1 Flui Kinematics by Nor A Alias For upate ersion, please click on Flui Kinematics by Dr. Nor Azlina binti Alias Faculty of Ciil an Earth Resources Enineerin azlina@ump.eu.my

2 Flui Kinematics by Nor A Alias Chapter Description Aims Apply an analyze Flui Mechanics theories such as Bernoulli s Theorem, Continuity Equation in Flui Mechanics system. Expecte Outcomes Define olume flow rate, weiht flow rate, an mass flow rate an their units. Define steay flow an the principle of continuity. Write the continuity equation, an use it to relate the olume flow rate, area, an elocity of flow between two points in a flui flow system. References Doulas F.J., Gasiorek J.M., Swaffiel J.A. Flui Mechanics. rentice Hall 4th Eition. Bruce R. M., Donal F.Y an Theoore H.O. Funamentals of Flui Mechanics. Wiley. Nakayama Y an Broucher R.F. Introuction to Flui Mechanics. Reise. Butterworth Heinmann.

3 Flui Kinematics by Nor A Alias SYNOSIS Detail objecties: Define olume flow rate, weiht flow rate, an mass flow rate an their units. Define steay flow an the principle of continuity. Write the continuity equation, an use it to relate the olume flow rate, area, an elocity of flow between two points in a flui flow system. WEEK CHATER TOIC 6 3 Flui Kinematics 3. Flow attern 3. The Continuity Equation The Bernoulli s Theorem 3.4 Application Of Bernoulli An Continuity Equations 3.4. Venturi Meter 3.4. ipe Orifice

4 Flui Kinematics by Nor A Alias Reise Flui Static ressure Flui pressure an epth ascal s principle Buoyancy Archimees principle Flui Kinematics Flui flow Reynols number Continuity Equation Bernoulli s principle

5 Flui Kinematics by Nor A Alias Ieal Flui Consier an IDEAL FLUID Flui motion is ery complicate. Howeer, by makin some assumptions, we can eelop a useful moel of flui behaiour. An ieal flui is : Incompressible the ensity is constant Irrotational the flow is smooth, no turbulence Noniscous flui has no internal friction Steay flow the elocity of the flui at each point is constant in time.

6 Flui Kinematics by Nor A Alias Ieal flui Consier the aerae motion of the flui at a particular point in space an time. Streamlines - in steay flow, a bunle of streamlines makes a flow tube. An iniiual flui element will follow a path calle a flow line Steay flow is when the pattern of flow lines oes not chane with time

7 Flui Kinematics by Nor A Alias Flow attern Laminar : flui particles moin in an orerly manner an retainin the same positions in successie cross-sections. Turbulent : flui particle occupie ifferent relatie position in successie cross sections. There are small fluctuation in manitue an irection of elocity, accompanie by small fluctuation of pressure.

8 Flui Kinematics by Nor A Alias Flow attern The Reynol s Number Criterion etermines whether the flow is laminar or turbulent is the ratio of inertial force to iscous force actin on the particle, known as Reynol s Number. Re = Re l l Where : ensity; : ynamic iscosity; : elocity; l : lenth; : kinematic iscosity In pipes; l is replace by iameter of pipe;. Re inertia force [promotes turbulent flow] iscous force [promotes laminar flow]

9 Flui Kinematics by Nor A Alias Flow attern The flow is classifie base on the calculate alue of Reynols number ass follow : Re < 000 Laminar 4000 < Re > 000 transitional Re > 4000 Turbulent by Lucho we Source :

10 Flui Kinematics by Nor A Alias Flui Flow Rate The quantity of flui flowin in a system per unit time can be expresse by the followin three ifferent terms: Q : The olume flow rate is the olume of flui flowin past a section per unit time. W : The weiht flow rate is the weiht of flui flowin past a section per unit time. m : The mass flow rate is the mass of flui flowin past a section per unit time.

11 Flui Kinematics by Nor A Alias Flui Flow Rate The most funamental of these terms is the olume flow rate Q, which is calculate from Q A The weiht W is relate to Q by, W Q Where is the specific weiht of the flui. The unit of W is then W Q N m m s 3 3 N s The mass flow rate, is relate to Q by; m m Q

12 Flui Kinematics by Nor A Alias Conseration of mass, m The principle of conseration of mass : Matter can neither be create nor estroye mass flowin in = mass flowin out m = m ρ = ρ ρa t = ρa t A = A = Q = t = constant Application of the conseration of mass to steay flow in the streamtube results in the Equation of Continuity

13 Flui Kinematics by Nor A Alias 3. The Continuity Equation The conseration of mass principle for a control olume can be expresse as: The net mass transfer to or from a control olume (CV) urin a time interal t is equal to the net chane (increase or ecrease) in the total mass within the control olume urin t. Total mass enterin Total mass leain - = the CV urin t the CV urin t Net chane in mass within the CV urin t For steay flow in a stream; m in m out m CV For steay incompressible flow (= ) in a stream; Q Q A A m m A A

14 Flui Kinematics by Nor A Alias 3.3 The Bernoulli s theorem Bernoulli's principle can be erie from the principle of conseration of enery. ressure enery when flui flowin uner pressure ressure enery ; F istance ressure enery per unit weiht; ρ Kinetic enery ue to its elocity Kinetic enery ; m Kinetic enery per unit weiht; = kinetic enery correction factor otential enery ue to heiht aboe atum, z otential enery; mz otential enery per unit weiht; z In practice flows encountere turbulent thus inore an is set equal to..04 < <. for fully eelope turbulent flow in roun pipe Howeer, some situation is sinificant especially for laminar flow. =.0 for fully eelope laminar pipe flow The total enery; H H ρ ρ z z

15 Flui Kinematics by Nor A Alias The Bernoulli s Theorem In a steay flow, the sum of all forms of enery in a flui alon a streamline is the same at all points on that streamline. Enery before = enery after Bernoulli s equation accounts for the chanes in eleation hea, pressure hea, an elocity hea between two points in a flui flow system. It is assume that there are no enery losses or aitions between the two points, so the total hea remains constant. Total hea before ( H ) Total hea after ( H ) ρ z z ρ ρ ρ z z ressure enery per unit weiht Kinetic enery otential enery Total enery per + per unit weiht + per unit weiht = unit weiht (H) = Constant

16 Flui Kinematics by Nor A Alias Bernuolli s Equation - Restriction Vali only for incompressible fluis because the specific weiht of the flui is assume to be the same at the two sections of interest. There can be no mechanical eices between the two sections that woul a enery to or remoe enery from the system, because the equation states that the total enery in the flui is constant.

17 Flui Kinematics by Nor A Alias 3.4 Application of Bernoulli an Continuity Equations Flow measurement Differential pressure eices : orifice meter enturi meter pitot static tube Make use of the pressure ifference between two points in the flow to ie an inication of the flow rate. Bernoulli s equation is applie to obtain expressions for flow rate

18 Flui Kinematics by Nor A Alias Consists of a section of pipe which coneres to a throat section an then ieres back to the oriinal pipe iameter iezometers at sections () an () recor the pressure heas h an h. The ifference in the pressure heas h aries with the rate of flow Venturi Meter If the flui is an incompressible liqui, then the ensity will be constant an ρ = ρ, thus : A A Q or 4 4 A A

19 Flui Kinematics by Nor A Alias Applyin Bernoulli s equation to sections () an () ies: As Thus, the pressure ifference between () an (), z z h Δ h h thus, an h h rearrane ies : h

20 Flui Kinematics by Nor A Alias Substitutin into ies : thus, h h h h h A Q The Q actual is always slihtly lesser than Q theory ue to iscous ra an turbulence. The actual flowrate is obtaine by : The ischare coefficient C for enturi meter normally rane between theory act Q C Q This is the theoretical olume-flow rate (Q theory ).

21 Flui Kinematics by Nor A Alias Venturi meter Venturi meter (incline) with the erie equations to calculate the elocity an ischare at the throat section. A h A A man A A Q h A A man The ischare formula ien aboe is the theoretical ischare. Thus in orer to et the actual ischare, the ischare coefficient C must be known. Q act C Q theory

22 Flui Kinematics by Nor A Alias 3.4. ipe orifice An orifice meter operates exactly the same as the enturi meter. Cheap compare to the enturi meter, howeer there is substantial enery losses. Consists of a sharp-ee orifice plate which is inserte between the connectin flanes of a pipeline. The arranement : consists of flat circular plate which has a circular hole. Diameter of orifice is enerally 0.5 times the iameter of the pipe (D), althouh it may ary from 0.4 to 0.8 times the pipe iameter by Mbeychok

23 Flui Kinematics by Nor A Alias The section at C is calle Vena Contracta, an C c is the coefficient of contraction. Actual area of jet at C is, C c x A. a sharp ee orifice has coefficient of contraction C c = The alue of coefficient C, C, C c are etermine experimentally an normally the C ranes from 0.6 to 0.65 for most orifice meters. C actual measure ischare theoretical ischare Q Q act theory C elocity at ena contracta theoretical elocity c theory C c area of jet at ena contracta area of the orifice Ac A o by Boalbo

24 Flui Kinematics by Nor A Alias Assumin no enery loss, thus As A is open to atmosphere, an water is still, h= za zb, thus: Rearranin ies; this theory is known as Torricelli s theorem. the elocity of the issuin jet is proportional to h, where h is the hea proucin flow. As with the enturi meter, the actual flow rate Q is ien by: or Aain, the actual ischare flowin throuh the pipe orifice is : B B B A A A z z h B h h A Q H A Q H A C Q act