a fireman) must be strong enough to withstand these forces. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. write as mentioned here. The momentum equation is a mathematical formulation of the law of conservation of momentum. It has no own shape, but confirms to the shape of the containing vessels. The equations for the conservation of momentum, mass, and energy can also be used for fluid flow that involves multiple phases; for example, a gas and a liquid phase or two different liquid phases, such as oil and water. Force acting on a fluid mass (m) will be given by Newton's second law of motion and we will have following equation as mentioned here. p is the pressure at depth h in a fluid of uniform density. The vector sum of the momenta (momentum is equal to the mass of an object multiplied by its velocity) of all the objects of a system cannot be changed by interactions within the system. It states that the rate of change in linear momentum of a volume moving with a fluid is equal to the surface forces and the body forces acting on a fluid. 0000001607 00000 n Therefore vv + P = f. There is no local source of momentum, but the gravitational force from outside where g denotes the . We are thus in a position to use (2.14), where the sources and sinks of momentum are forces. Manage Settings But here it is not clear what mass of moving fluid we should use and therefore it is necessary to use a different form of the equation. The lift force on an aircraft is exerted by the air movingover the wing. 0000008853 00000 n Concept of spring in strength of material, Difference between positive and non positive displacement This chapter will study the forces generated by fluids in motion. Answer: It can be a bit tricky to appreciate this, so I'll try to break it down into a few steps. Relation of System Derivatives to the Control Volume Formulation 3. FLUID MECHANICS 1. the flow per second based on average velocity across a section. Conservation of energy. principle. Solve for different variables related to force, area, bulk modulus, compressibility . Thermal Engineering. What is momentum equation in fluid mechanics? The Cookies Statement is part of our Privacy Policy. 13.82 KN. Force The piping diameter is equal to 700 mm. F = m x a. In many situations we are interested in the moment or torque on the volume. This means the more mass an object has, the more force you need to accelerate it. of change of linear momentum. The momentum flux vector is defined simply as the momentum flow per area. Calculate the force on the wall of a deflector elbow (i.e. equation is based on the law of conservation of momentum or on the momentum In symbols, linear momentum p is defined to be p = mv, where m is the mass of the system and v is its velocity. wt@-LA% ZFPDL R(X f`| R`13sqXmefqx``pZ pyzU] \tCA@A2VY&&*`QY$~@ld`&Q` endstream endobj 718 0 obj 441 endobj 683 0 obj << /Type /Page /Parent 677 0 R /Resources << /ColorSpace << /CS2 691 0 R /CS3 690 0 R >> /ExtGState << /GS2 710 0 R /GS3 712 0 R >> /Font << /TT4 688 0 R /TT5 684 0 R /TT6 689 0 R /TT7 695 0 R >> /ProcSet [ /PDF /Text ] >> /Contents [ 693 0 R 697 0 R 699 0 R 701 0 R 703 0 R 705 0 R 707 0 R 709 0 R ] /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Rotate 0 /StructParents 0 >> endobj 684 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 146 /Widths [ 250 0 0 0 0 0 778 0 333 333 0 0 250 333 250 0 500 500 500 500 500 500 500 500 500 500 278 0 0 564 0 444 0 722 667 667 722 611 556 0 0 333 389 0 611 0 722 0 0 0 667 556 611 0 722 944 0 722 0 0 0 0 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 ] /Encoding /WinAnsiEncoding /BaseFont /KMEKFA+TimesNewRoman /FontDescriptor 686 0 R >> endobj 685 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -558 -307 2034 1026 ] /FontName /KMEKHA+TimesNewRoman,Bold /ItalicAngle 0 /StemV 160 /XHeight 0 /FontFile2 715 0 R >> endobj 686 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2028 1007 ] /FontName /KMEKFA+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 713 0 R >> endobj 687 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 98 /FontBBox [ -498 -307 1120 1023 ] /FontName /KMEKBM+TimesNewRoman,Italic /ItalicAngle -15 /StemV 0 /XHeight 0 /FontFile2 711 0 R >> endobj 688 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 121 /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 250 333 250 0 0 0 0 0 0 0 0 0 0 0 0 0 0 675 0 0 0 611 611 667 0 611 611 0 0 0 0 0 0 833 0 0 611 722 611 500 556 0 611 0 0 0 0 0 0 0 0 0 0 500 500 444 500 444 278 500 500 278 0 444 278 722 500 500 500 500 389 389 278 500 0 0 444 444 ] /Encoding /WinAnsiEncoding /BaseFont /KMEKBM+TimesNewRoman,Italic /FontDescriptor 687 0 R >> endobj 689 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 121 /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 0 0 250 0 0 500 500 500 500 0 500 0 0 0 333 0 0 0 0 0 0 722 0 0 722 667 611 0 0 389 500 0 0 944 0 0 611 0 0 0 667 0 722 0 0 0 0 0 0 0 0 0 0 500 556 444 556 444 333 0 556 278 333 0 278 833 556 500 556 556 444 389 333 556 500 722 500 500 ] /Encoding /WinAnsiEncoding /BaseFont /KMEKHA+TimesNewRoman,Bold /FontDescriptor 685 0 R >> endobj 690 0 obj /DeviceGray endobj 691 0 obj [ /ICCBased 714 0 R ] endobj 692 0 obj 507 endobj 693 0 obj << /Filter /FlateDecode /Length 692 0 R >> stream An elbow (let say of primary piping) is used to deflect water flow at a velocity of 17 m/s. For example, a power washer produces a high velocity jet of water which produces a force large enough to remove debris. If you want to get in touch with us, please do not hesitate to contact us via e-mail: In fluid dynamics, the law of conservation of momentum or principle of momentum conservation states that the momentum of an isolated system is a constant. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page. In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. the linear momentum equations can be rearranged to yield the reaction forces as. we will have following equation as mentioned here. 0000029794 00000 n For example, the vector equation can be rewritten in terms of x-, y- and z-components for a Cartesian coordinate system. In classical mechanics, this law is implied by Newtons laws. CM4650 Newtonian Fluid Mechanics 5 Chapter 3: Newtonian Fluid Mechanics Faith A. Morrison, Michigan Tech U. Polymer Rheology Consider an arbitrary We were discussing the Elongation of uniformly tapering circular rod and Elongation of uniformly tapering rectangular rod and also We were discussing various basic concepts of thermodynamics such as thermal energy reservoir in thermodynamics in our recent post. According to the principle of conservation of mass. momentum or just the momentum of the body. Newtons second law is often stated as F=ma, which means the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a). When researching a derivation of the angular momentum balance equations, I came across these excellent online notes from a course on continuum mechanics. The Reynolds Transport theorem and its derivation is presented. We hav We will discuss here the difference between positive and non-positive displacement pump with the help of this post. In fluid dynamics, the analysis of motion is performed in the same way as in solid mechanics by use of Newtons laws of motion. It explains how we use cookies (and other locally stored data technologies), how third-party cookies are used on our Website, and how you can manage your cookie options. The creation process is more interesting than in a reaction-diffusion equation. Moment of momentum equation According to the concept of moment of momentum equation, Resulting torque acting on a rotating fluid will be equal to the rate of change of moment of momentum. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion. Momentum flux is the transport of momentum that acts in a direction perpendicular to the direction of fluid flow. where . Above Newtons second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes. Therefore, the direction of an exposed reaction force depends on the body taken as the system. In addition to this, in one of these three directions a fluid particle can be moving in a positive or negative direction. 0000003834 00000 n To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. The boundary layer equations for an incompressible fluid are conceptually similar to a reaction diffusion equation. We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development. m . Glasstone, Sesonske. Conservation of momentum for an inviscid fluid. Also assume a pressure, p, at each end (can be different). 1-(844)-Need-Mud. 0000062456 00000 n According What does Enterococcus faecalis look like? The momentum of a fluid is defined to be u, per unit volume. Springer; 2015, ISBN:978-3-319-13419-2, Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,John Wiley & Sons, 2006, ISBN:978-0-470-03037-0. In general, the law of conservation of momentum or principle of momentum conservation states that the momentum of an isolated system is a constant. The resulting force on the vane being struck by the fluid is an impulsive force. Fluid is of constant density ~ 720 kg/m3 (at 290C). The pressure force per meter length on one side of tank when the acceleration is upward is. Mass flowing per second through the elemental strip = udy . Assuming simple inlets and outlets from the control volume, i.e. 0000001131 00000 n Control volume is an imaginary surface enclosing a volume of interest. It states that the rate of change in linear momentum of a volume moving with a fluid is equal to the surface forces and the body forces acting on a fluid. of flow at any point in the pipe or channel in the subject of fluid mechanics, The different terms correspond to the inertial forces (1), pressure forces (2), viscous forces (3), and the external forces applied to the fluid (4). Linear Momentum is Directional. 0000059778 00000 n Choosing I as its symbol would lead to confusion with moment of inertia and inertia. will see here the concept of the momentum equation, in the subject of fluid 2. 0000007695 00000 n that acceleration could be defined as the rate of change of velocity or we can 57:020 Mechanics of Fluids and Transport Processes Chapter 5 Professor Fred Stern Fall 2006 1 Chapter 5 Mass, Momentum, and Energy Equations Flow Rate and Conservation of Mass 1. cross-sectional area oriented normal to velocity vector (simple case where V A) 2. calculate vector F3). Momentum Drilling Fluids LLC. What is the momentum of a 1.5 103 kilogram van that is moving at a velocity of 32 meters/second? 0000004777 00000 n HKO@+,CBH$$Uba91JlGi}c'B+K]s$7u[y!K2mml!Dcri8(!P fRTs)IKYPQd%aP Im+V.vy[IKO xx/_9@$k9P4\W8#`):AUUWm*wXD)XL` In general, the law of conservation of momentum or principle of momentum conservation states that the momentum of an isolated system is a constant.The vector sum of the momenta (momentum is equal to the mass of an object multiplied by its velocity) of all the objects of a system cannot be changed by interactions within the system. p0 is the pressure at the fluid's surface. n as before. n3 is positive (V3). Generally the component momentum equation is as. Equation (9) can be written in a vector form which combined all three components into one equation. 0000083977 00000 n p = p0 + gh. force exerted by a flowing fluid on a pipe bend. Newton's 2nd Law can be written: The Rate of change of momentum of a body is equal to the resultant force acting on the body, and takes place in the direction of the force. We take the elbow as the control volume. Momentum Thickness *: Again consider the flow through an elemental strip of area (1.dy) distance y from the boundary. In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluidsliquids and gases.It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). The most detailed way of modeling multiphase flow is with surface tracking methods, such as the level set or phase field methods. The example shows only the momentum balance in the x direction. As can be seen from the picture the control volume method can be used to analyze the law of conservation of momentum in fluid. principle. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER,AND FLUID FLOW. the walls due to the fluid? e. u = internal energy associated with fluid temperature = u e. p = potential energy per unit mass = gh. ). 0000006570 00000 n 1.0 Introduction. A units check gives area x length/time x time = area x length = volume. ), m = p/v (Mass equals momentum divided by velocity. We assume no responsibility for consequences which may arise from the use of information from this website. 1) A rectangular tank is moving horizontally in the direction of its length with a constant acceleration of 4.8 m/s2. The momentum equation is a vector equation so it has three components. Introductory Momentum Equations, Definition. Lecture 11 F. Morrison CM3110 10/10/2019 2 . The momentum theorem developed in Chapter 10 gives the force acting on a fixed volume in terms of linear momentum flux through the surface of the volume. The gauge pressure inside the pipe is about 16 MPa at the temperature of 290C. Newtons second law of motion states that momentum is conserved by a mechanical system of masses if no forces act on the system. Where i is the balance direction and j and k are two other coordinates. With the application of Newton's Second Law, the product rule gives a form more appropriate for the analysis of fluid flow: F = d ( m v) d t = m d v d t + v d m d t = m a + m v. where. 1) You may use almost everything for non-commercial and educational use. The vector form of the linear momentum equation can be written in scalar form once a coordinate system is established. Is there an easy explanation for how it "works"? . Skip to content Hence it will be considered a negative or a positive quantity. Conservation of momentum. The energy equation (Eq. 0000007110 00000 n In mechanics of fluids flow in a porous medium, the momentum equation is expressed as Darcy . When you are solving a linear momentum problem, there can be as many as three orthogonal coordinate direction. The control volume is shown at the picture. Our Website follows all legal requirements to protect your privacy. Derivation of the equation for conservation of momentum in an ideal fluid info@momentumfluids.com . Do you n will be positive when the flow is out of the control volume while it is negative when the flow is into the control volume (see another section . 0000004289 00000 n The analysis takes the following procedure: 1) Draw a control volume 2) Decide on co-ordinate axis system 3) Calculate the total force 4) Calculate the . At section (2), the velocity profile is axisymmetric and parabolic, with zero velocity at the pipe wall . To further illustrate the use of the linear momentum equation, consider a pipe elbow as shown in the figure on the right with steady fluid flowing from one end to the other. 4,940 3 3 gold badges 26 26 silver badges 41 41 bronze badges. To determine the mass flow rate mdot, we divide the mass by the time. equation will be termed as the impulse-momentum equation. Fluid mechanics assumes that every fluid obeys the following: Conservation of mass. In mechanics of fluids flow in a porous medium, the momentum equation is expressed as Darcys law. So, what we have is a fluid coming in at 2 m/s at 200 kPa. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417; See above: Fluid Dynamics. What is momentum equation in fluid mechanics? This section focuses on the "MCQ with answers on Momentum Principle". is the acceleration of the fluid flow acting in the same direction as force F. As we know Momentum and forces in fluid flow. Conservation of momentum for an incompressible flow. Recall the conservation of linear momentum law for a system: In order to convert this for use in a control volume, use RTT with B = m V, beta = V. we get: NOTE: Recall that at any instant of time t, the system & CV occupy the SAME physical space. This form of the momentum equation is useful when the mass flow rate is involved, just as water jets or rocket exhaust. The consent submitted will only be used for data processing originating from this website. 0000010006 00000 n 0000002149 00000 n From this information we can get the mass flow. The mass m contained in this volume is simply density r times the volume. the rate at which mass comes in or leaves a control volume). Newton's first law states that a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight momentum flux = Vn V. A. Viscosity is a measure of a fluids resistance to flow. Gravity and pressure forces influence the problem of fluid statics. 0000006094 00000 n Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering. While this is helpful, I would appreciate a fuller derivation, with clarification as to where each term in the expression in the first yellow box . Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft . to the law of conservation of momentum, net force acting on a fluid mass will 0000007088 00000 n 0000002171 00000 n DUi Dt = ii i + ji j + ki j + fGi. flat and uniform flow, the momentum equation becomes, Using the continuity condition, dm/dt = AV, the momentum equation simplifies to. fluid-dynamics; continuum-mechanics; Share. The size of the tank is 7 m, and the depth is 1.5 m. mv = Momentum. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1. Compare this result with the linear momentum of the fluid using the average velocity of flow. The left side represents the rate of change of internal energy of a fluid element. It is the expression describing the relationship of the force applied onto the fluid unit and the mass of the fluid in the unit and velocity of fluid movement. Momentum thickness is the distance that, when multiplied by the square of the free stream velocity, equals the integral of the momentum defect. Today we Above Momentum of this quantity in the absence of the boundary layer . In free-surface flows momentum flux can also be generated by gravity waves. considering above equation we can say that impulse of a force F acting on a Further, it is often useful (at subsonic conditions) to assume a fluid is incompressible - that is, the density of the fluid does not change. Linear momentum equation for fluids can be developed using Newton's 2nd Law which states that sum of all forces must equal the time rate of change of the momentum, F = d(mV)/dt.This easy to apply in particle mechanics, but for fluids, it gets more complex due to the control volume (and not individual particles). u2(u2)A2 0000009447 00000 n Why was cos40 the only one chosen? Some of our partners may process your data as a part of their legitimate business interest without asking for consent. 4 Linear momentum or just the momentum of the body: The product of the mass and the velocity of a body. Since we have the exit area: 0.0125 (0.00672 x 2), we can get the exit velocity. 0000006592 00000 n 0000010085 00000 n It states that the rate of change in linear momentum of a volume moving with a fluid is equal to the surface forces and the body forces acting on a fluid. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1. Now apply the linear momentum equation to find the reaction forces (Rx, Ry and Rz) applied on the selected control volume. mentioned here. x [ u ( u e u ) ] + y [ ( u e u ) ] + d u e d x ( e u e u ) = y ( u y u ) . Angular Momentum Balance in Fluid Mechanics. Ch 4. Take $\rho=800 \mathrm{~kg} / \mathrm{m}^{3}$. 2) You may not distribute or commercially exploit the content, especially on another website. Copyright 2022 Thermal Engineering | All Rights Reserved |, The second conservation equation we have to consider in the control volume is the, What is Law of Conservation of Matter - Definition, What is Bernoullis Principle Examples Definition. The Navier-Stokes equations were derived by Navier, Poisson, Saint-Venant, and Stokes between 1827 and 1845. An example of data being processed may be a unique identifier stored in a cookie. The first conservation equation we have to consider in the control volume is the continuity equation (the law of conservation of matter). For one-way motion in one dimension, this is expressed in equation form as W = Fd cos , where W is work, F is the magnitude of the force on the system, d is the magnitude of the displacement of the system, and is the angle between the force vector F and the displacement vector d. It is expressed mathematically as p = m * v and has units of kg m/s. Mathematical and scientific backgrounds that helps sprint well into studies on fluid mechanics is provided. Pumps are basically We were discussing meaning and importance of shear force and bending moment and types of beams in strength of materials and also some bas We were discussing the various basic concept of thin cylinders such as thin cylindrical and spherical shells , stresses in thin cylindric We were discussing Slope and deflection of beam , Rankines formula for columns , bending stress in beam and different types of load acti We were discussing the various basic concepts of bearings such as Basic concept of bearings , Main functions of bearings , Bearing operatin We were discussing in our previous post about the pump performance curve and we have also seen the difference between positive and non We were discussing theconcept of laminar and turbulent flow , Reynolds experiment , frictional loss in pipes , derivation of expressio We have discussed in our previous post about the basic of helical gears, where we have seen the various characteristics of helical gears, We were 0000030001 00000 n Basic Laws for a System 2. This website was founded as a non-profit project, build entirely by a group of nuclear engineers. Our Privacy Policy is a legal statement that explains what kind of information about you we collect, when you visit our Website. We and our partners use cookies to Store and/or access information on a device. Momentum of this quantity = (udy) u = u 2 dy . In the simplest form it is represented by following equation: Sum of mass flow rates entering per unit time = Sum of mass flow rates leaving per unit time. 3. The conservation of linear momentum equation becomes: Second, let us consider the component in the y-coordinate. 0000008875 00000 n After e = energy per unit mass = E. mass. The equation developed by Albert Einstein, which is usually given as E = mc2, showing that, when the energy of a body changes by an amount E (no matter what form the energy takes), the mass (m) of the body will change by an amount equal to E/c2. Note that BSL is an abbreviation often used for this classic textbook based on the initials of its authors. 0000008301 00000 n Note that while mass ow is a scalar, the momentum . , p = mv (Momentum equals mass times velocity. be equivalent to the change in momentum of flow per unit time in that direction. 0000002582 00000 n 0000005659 00000 n Where, a &!z79,~ ~v Z"9oBA*` R endstream endobj 694 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 98 /FontBBox [ -547 -307 1206 1032 ] /FontName /KMEKJK+TimesNewRoman,BoldItalic /ItalicAngle -15 /StemV 133 /FontFile2 716 0 R >> endobj 695 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 121 /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 250 0 0 0 500 0 0 500 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 611 0 0 0 611 0 0 0 611 0 0 0 0 0 0 333 0 333 0 0 0 500 0 0 500 444 0 0 556 278 0 0 278 778 556 500 500 0 389 389 278 556 0 0 0 444 ] /Encoding /WinAnsiEncoding /BaseFont /KMEKJK+TimesNewRoman,BoldItalic /FontDescriptor 694 0 R >> endobj 696 0 obj 374 endobj 697 0 obj << /Filter /FlateDecode /Length 696 0 R >> stream Let us consider the above quantity of the fluid. *1* E Incompressible, laminar water flow develops in a straight pipe having radius R as indicated in Figure. Continue with Recommended Cookies. where i represents each outlet and inlet (sign difference). The Impulse-Momentum Equation for fluid can be derived from Newton's second law of motion, Application of Impulse-Momentum Equation (a) To determine the resultant force acting on the boundary of a flow passage by a stream of fluid as the stream changes its direction or magnitude of both. How to write technical memorandum for a pumping system? Question 5: Momentum conservation (nozzle) Because the fluid is contracted at the nozzle forces are induced in the nozzle. trailer << /Size 719 /Info 675 0 R /Root 681 0 R /Prev 210163 /ID[<50bd547dc12dd4e062dbf629bce95e4c><32bae00fe746f1d38aad4b47fbce482b>] >> startxref 0 %%EOF 681 0 obj << /Type /Catalog /Pages 678 0 R /Metadata 676 0 R /OpenAction [ 683 0 R /XYZ null null null ] /PageMode /UseNone /PageLabels 674 0 R /StructTreeRoot 682 0 R /PieceInfo << /MarkedPDF << /LastModified (D:20020904174217)>> >> /LastModified (D:20020904174217) /MarkInfo << /Marked true /LetterspaceFlags 0 >> >> endobj 682 0 obj << /Type /StructTreeRoot /ClassMap 58 0 R /RoleMap 60 0 R /K 542 0 R /ParentTree 573 0 R /ParentTreeNextKey 12 >> endobj 717 0 obj << /S 390 /L 509 /C 525 /Filter /FlateDecode /Length 718 0 R >> stream Momentum For steady flow there is no change in momentum inside the pipe (control volume) and the linear momentum equation reduces to. 0000003130 00000 n e. q = kinetic . The linear momentum of a parcel of fluid is an extensive property. is the uniform density of the fluid. There is a time component and a spatial component because the fluid element under consideration is moving. And the greater the force, the greater the objects acceleration. The momentum equation is a mathematical formulation of the law of conservation of momentum. Springer, 2010,ISBN 978-1-4020-8670-0. For theory relevant to the fluid mechanics and momentum transfer problems below, please refer to the following books: Bird, R. B., Stewart, W. E., and Lightfoot, E. N., "Transport Phenomena", 2nd edition, John Wiley, New York (2002). We can determine the value of the mass flow rate from the flow conditions.
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