In fluid dynamics<\/a>, drag<\/strong> is a force acting opposite to the relative motion of any moving object. The force a flowing fluid exerts on a body in the flow direction. Unlike other resistive forces, such as dry friction, nearly independent of velocity, drag forces<\/strong> depend on velocity. Drag force<\/strong> is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow.<\/div><\/div>\n
Drag<\/strong> is generally caused by two phenomena:<\/p>\n
\n
\n
$\"Drag$ <\/a>
Source: wikipedia.org License: CC BY-SA 3.0<\/figcaption><\/figure>\n
Skin Friction<\/strong>. In general, when a fluid flows over a stationary surface<\/strong>, e.g., the flat plate, the bed of a river, or the pipe wall, the fluid touching the surface is brought to rest<\/strong> by the shear stress<\/strong> at the wall. The boundary layer<\/strong><\/a> is the region in which flow adjusts from zero velocity at the wall to a maximum in the mainstream of the flow. Therefore, a moving fluid exerts tangential shear forces on the surface because of the no-slip condition<\/strong> caused by viscous effects. This type of drag force<\/strong> depends especially on the geometry, the roughness of the solid surface, and the type of fluid flow.<\/li>\n
Form Drag<\/strong>. Form drag,<\/strong> also known as pressure drag,<\/strong> arises because of the shape and size of the object. This type of drag force is an interesting consequence the Bernoulli\u2019s effect<\/a>. <\/strong>According to Bernoulli\u2019s principle, faster-moving air exerts less pressure, and this causes that there can be a pressure difference between surfaces of the object. The general size and shape of the body are the most important factors in form drag<\/strong>. Generally, bodies with a larger presented geometric cross-section will have higher drag than thinner bodies.<\/li>\n<\/ul>\n
Both of these forces, in general, have components in the direction of flow, and thus the resulting drag force<\/strong> is due to the combined effects of pressure<\/strong> and skin friction<\/strong> forces in the flow direction.<\/p>\n
When the friction and pressure drag coefficients are available, the total drag coefficient is determined by simply adding them:<\/p>\n
$\"skin$ <\/a><\/p>\n
Most drag is due to friction drag at low Reynolds numbers<\/a><\/strong>, and this is especially the case for highly streamlined bodies such as airfoils. On the other hand, the pressure drop<\/a> is significant at a high Reynolds number<\/strong>, which increases form drag.<\/p>\n
The components of the pressure and skin friction forces in the normal direction<\/strong> to flow tend to move the body in that direction, and their sum is called lift<\/a><\/strong>.<\/p>\n
The lift<\/strong> is an upward-acting force on an aircraft wing or airfoil <\/strong>in aeronautics. Bernoulli\u2019s principle<\/strong> requires airfoil to be of an asymmetrical shape<\/strong>.<\/p>\n
<\/span>Bernoulli\u2019s Principle \u2013 Lift Force<\/div>See also:\u00a0 Bernoulli\u2019s Principle \u2013 Lift Force<\/a><\/p>\n
$\"Lift$ <\/a>The\u00a0lift<\/a><\/strong> is an upward-acting force on an aircraft wing or airfoil<\/strong> in aeronautics. Bernoulli\u2019s principle<\/a><\/strong> requires airfoil to be of an asymmetrical shape<\/strong>, and its\u00a0surface area must be greater on the top<\/strong> than on the bottom. As the air flows over the airfoil, it is displaced more by the top surface than the bottom. According to the continuity principle<\/a>, this displacement must lead to an increase in flow velocity <\/strong>(resulting in a decrease in pressure<\/a>). The flow velocity is increased by the bottom airfoil surface but considerably less than the flow on the top surface. The lift force of an airfoil, characterized by the lift coefficient<\/strong>, can be changed during the flight by changes in the shape of an airfoil. The lift coefficient can thus be even doubled with relatively simple devices (flaps and slats<\/strong>) if used on the full span of the wing.<\/p>\n
The use of Bernoulli\u2019s principle<\/strong> may not be correct. Bernoulli\u2019s principle assumes incompressibility<\/strong> of the air, but in reality, the air is easily compressible. But there are more limitations of explanations based on Bernoulli\u2019s principle. There are two main popular explanations of lift:<\/p>\n
\n
Explanation based on downward deflection of the flow \u2013 Newton\u2019s third law<\/strong><\/li>\n
Explanation based on changes in flow speed and pressure \u2013 Continuity principle and Bernoulli\u2019s principle<\/strong><\/li>\n<\/ul>\n
Both explanations correctly identify some aspects of the lift forces but leave other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both changes in flow speed and downward deflection and requires looking at the flow in more detail.<\/p>\n
See more: Doug McLean, Understanding Aerodynamics: Arguing from the Real Physics. <\/em>John Wiley & Sons Ltd. 2013. ISBN: \u00a0978-1119967514<\/div><\/div>
<\/span>What is Parasitic Drag<\/div>The term parasitic drag is mainly used in aerodynamics, since for lifting wings drag it is in general small compared to lift. Parasitic drag combines form drag, skin friction drag, and interference drag.<\/p>\n<\/div><\/div><\/div>\n
\n
Skin Friction – Friction Drag<\/h2>\n
As was written, when a fluid flows over a stationary surface<\/strong>, e.g., the flat plate, the bed of a river, or the pipe wall, the fluid touching the surface is brought to rest<\/strong> by the shear stress<\/strong> at the wall. The boundary layer<\/strong><\/a> is the region in which flow adjusts from zero velocity at the wall to a maximum in the mainstream of the flow. Therefore, a moving fluid exerts tangential shear forces on the surface because of the no-slip condition<\/strong> caused by viscous effects. This type of drag force<\/strong>\u00a0depends especially on the geometry, the roughness of the solid surface (only in turbulent flow<\/a>), and the type of fluid flow<\/a>. The friction drag<\/strong> is proportional to the surface area. Therefore, bodies with a larger surface area will experience a larger friction drag. This is why commercial airplanes reduce their total surface area to save fuel. Friction drag<\/strong> is a strong function of viscosity, and an \u201cidealized\u201d fluid with zero viscosity would produce zero friction drag since the wall shear stress would be zero.<\/p>\n
Skin friction<\/strong> is caused by viscous drag in the boundary layer around the object. Basic characteristics of all laminar and turbulent boundary layers<\/strong> are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:<\/p>\n
$\"Boundary$ <\/a><\/p>\n
Boundary layers<\/strong> may be either laminar<\/strong>\u00a0or turbulent,<\/strong> depending on the value of the Reynolds number<\/a><\/strong>.<\/p>\n
The boundary layer is laminar for lower Reynolds numbers<\/strong>, and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. As the Reynolds number increases<\/strong> (with x), the flow becomes unstable<\/strong>. Finally, the boundary layer is turbulent for higher Reynolds numbers, and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer.<\/p>\n
The transition from laminar to turbulent<\/strong> boundary layer occurs when Reynolds number at x exceeds Re<\/strong>_{x<\/sub><\/strong> ~ 500,000<\/strong>. The transition may occur earlier, but it is dependent especially on the surface roughness<\/strong>. The turbulent boundary layer thickens more rapidly than the laminar boundary layer due to increased shear stress at the body surface.<\/p>\n}
There are two ways to decrease friction drag<\/strong>:<\/p>\n
\n
the first is to shape the moving body so that laminar flow is possible<\/li>\n
the second method is to increase the length and decrease the cross-section of the moving object as much as practicable.<\/li>\n<\/ul>\n
The skin friction coefficient<\/strong>, C_{D,friction<\/sub><\/strong>, is defined by<\/p>\n}
$\"skin$ <\/a><\/p>\n
It must be noted the skin friction coefficient<\/strong> is equal to the Fanning friction factor<\/a><\/strong>. The Fanning friction factor, named after John Thomas Fanning, is a dimensionless number that is one-fourth of the Darcy friction factor<\/strong><\/a>. As can be seen, there is a connection between skin friction forces<\/strong> and frictional head losses<\/strong><\/a>.<\/p>\n
See also: Darcy Friction Factor<\/strong><\/a><\/p>\n
For laminar flow<\/a> in a pipe, the Fanning friction factor<\/strong> (skin friction coefficient) is a consequence of Poiseuille\u2019s law<\/strong> that and it is given by the following equations:<\/p>\n
$\"drag$ <\/a><\/p>\n
However, things are more difficult in turbulent flows<\/a>, as the friction factor depends strongly on the pipe roughness<\/a>. The friction factor<\/strong><\/a> for fluid flow can be determined using a Moody chart<\/strong><\/a>. For example:<\/p>\n
$\"drag$ <\/a><\/p>\n
The frictional component of the drag force<\/strong> is given by:<\/p>\n
$\"drag$ <\/a><\/p>\n
Form Drag – Pressure Drag<\/h2>\n
$\"form$ <\/a>Form drag,<\/strong> also known as pressure drag,<\/strong> arises because of the shape<\/strong> and size<\/strong> of the object. The pressure drag<\/strong> is proportional to the difference between the pressures acting on the front and back of the immersed body and the frontal area. This type of drag force is also an interesting consequence the Bernoulli\u2019s effect<\/a>. <\/strong>According to Bernoulli\u2019s principle, faster-moving air exerts less pressure<\/a>, and this\u00a0causes that there can be a pressure difference<\/strong> between surfaces of the object. The general size and shape of the body are the most important factors in form drag<\/strong>. Generally, bodies with a larger presented geometric cross-section will have higher drag than thinner bodies.<\/p>\n
As can be seen from the figure, the drag force arises from the difference between the pressures acting on the front and back of the immersed body. For this force can be calculated (for this case) simply using the definition of pressure as:<\/p>\n
$\"form$ <\/a><\/p>\n
Since the head loss<\/a> is roughly proportional to the square of the flow rate<\/strong> in most engineering flows, the total drag coefficient<\/strong> can be determined by simply adding the friction and pressure drag coefficients:<\/p>\n
$\"skin$ <\/a><\/p>\n
Drag Force – Drag Equation<\/h2>\n
The drag force,<\/strong> F_{D<\/sub><\/strong>, depends on the}density<\/a> of the fluid, the upstream velocity, and the size, shape, and orientation of the body, among other things. One way to express this is by using the drag equation<\/strong>. The drag equation<\/strong> is a formula used to calculate the drag force<\/strong> experienced by an object due to movement through a fluid.<\/p>\n
$\"drag$ <\/a><\/p>\n
The reference area, A, is defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion. For hollow objects, the reference area may be significantly larger than the cross-sectional area, but for non-hollow objects, it is the same as a cross-sectional area.<\/p>\n
<\/p>\n
Drag Coefficient – Drag Characteristics<\/h2>\n
As was written, the drag characteristics<\/strong> of a body are represented by the dimensionless drag coefficient, C_{D<\/sub>,<\/strong> defined as:<\/p>\n}
$\"drag$ <\/a><\/p>\n
The reference area, A, is defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion. For hollow objects, the reference area may be significantly larger than the cross-sectional area, but for non-hollow objects, it is the same as a cross-sectional area. As can be seen, the drag coefficient is primarily a function of the shape of the body and takes into account both skin friction and form drag. It may also depend on the Reynolds number<\/a> and the surface roughness.<\/p>\n
When the friction<\/strong> and pressure drag coefficients<\/strong> are available, the total drag coefficient<\/strong> is determined by simply adding them:<\/p>\n
$\"skin$ <\/a><\/p>\n
Most drag is due to friction drag <\/strong>at low Reynolds numbers, and this is especially the case for highly streamlined bodies such as airfoils. On the other hand, the pressure drop is significant at a high Reynolds number, which increases form drag<\/strong>.<\/p>\n
<\/span>Drag Coefficient - Cars<\/div>
The drag coefficient<\/strong> is a common measure in automotive design<\/strong>. Drag coefficient, C_{D<\/sub><\/strong>, is a commonly published rating of a car\u2019s aerodynamic resistance<\/strong>\u00a0related to the shape of the car. Multiplying C_{D<\/sub> by the car\u2019s frontal area gives an index of total drag. The result is called drag area.<\/strong><\/p>\nSince aerodynamic drag and drag force increases with the square of velocity, this property becomes critically important at higher speeds. Reducing the drag coefficient in an automobile improves the vehicle\u2019s performance regarding speed and fuel efficiency. The average modern automobile achieves a drag coefficient of between C_{D<\/sub> = 0.30 and 0.35.<\/div><\/div><\/div>\n}}}Drag Force in Nuclear Engineering<\/h2>\n
Analysis of the hydraulic lift force<\/strong> is one of the most important analyses in designing a fuel assembly and analyzing the hydraulic compatibility of mixed cores. The vertical forces are induced by upward high-velocity flow through the reactor core<\/a>, and the\u00a0flow path for the reactor coolant through the reactor vessel <\/a>would be:<\/p>\n
\n
\n
$\"Continuity$ <\/a>
Example of flow rates in a reactor. It is an illustrative example, and the data do not represent any reactor design.<\/figcaption><\/figure>\n
The coolant enters the reactor vessel<\/strong> at the inlet nozzle and hits against the core barrel<\/a>.<\/li>\n
The core barrel forces the water to flow downward in the space between the reactor vessel wall and the core barrel<\/a>. This\u00a0space is usually known as the downcomer<\/strong>.<\/li>\n
The flow is reversed up through the core from the bottom of the pressure vessel to pass through the fuel assemblies<\/a>, where the coolant temperature increases as it passes through the fuel rods.<\/li>\n
Finally, the hotter reactor coolant enters the upper internals region, where it is routed out the outlet nozzle into the hot legs of the primary circuit and goes on to the steam generators<\/a>.<\/strong><\/li>\n<\/ul>\n
Fuel assemblies are held by the upper guide structure assembly<\/strong>, which defines the top of the core. This assembly is made of stainless steel and has many purposes. The upper guide structure assembly exerts an axial force<\/strong> on fuel assemblies (through springs in the top nozzle), thus defining the exact position of the fuel assembly in the core. The upper guide structure assembly<\/strong> flange is held in place and preloaded by the RPV closure head flange. The upper guide structure assembly also guides and protects control rod<\/a> assemblies and in-core instrumentation.<\/p>\n
Required downforce of the upper guide structure assembly <\/strong>on fuel assemblies must be carefully calculated. Insufficient downforce can result in the lift of the fuel assembly<\/strong>. On\u00a0the other hand, an excessive downforce can result in bowing of fuel assembly<\/strong>, which is also unacceptable.<\/p>\n
Example: Drag Force – Drag Coefficient – Fuel Bundle<\/h2>\n $\"Hydraulic$ <\/a>Calculate the friction drag<\/strong> of a single fuel rod<\/strong> inside a reactor core at normal operation (design flow rate). Assume that this fuel rod is part of a fuel bundle with the rectangular fuel lattice, and this fuel bundle does not contain spacing grids. Its height is h = 4m,<\/strong> and the core flow velocity is constant and equal to V<\/strong>_{core<\/sub><\/strong> = 5 m\/s.<\/strong><\/p>\n}
Assume that:<\/p>\n
\n
the outer diameter of the cladding is: d = 2 x r<\/strong>_{Zr,1<\/sub><\/strong> = 9,3 mm<\/strong><\/li>\n}
the pitch of fuel pins is: p = 13 mm<\/strong><\/li>\n
the relative roughness<\/a> is \u03b5\/D = 5×10<\/strong>^{-4<\/sup><\/strong><\/li>\n}
the fluid density<\/a> is: \u03c1 = 714 kg\/m<\/strong>^{3<\/sup><\/strong><\/li>\n}
the core flow velocity is constant and equal to V<\/strong>_{core<\/sub><\/strong> = 5 m\/s<\/strong><\/li>\n}
the average temperature<\/a> of reactor coolant is: T<\/strong>_{bulk<\/sub><\/strong> = 296\u00b0C<\/strong><\/li>\n<\/ul>\n}Calculation of the Reynolds number<\/h2>\n
To calculate the Reynolds number<\/a>, we have to know:<\/p>\n
\n
the outer diameter of the cladding is: d = 2 x r<\/strong>_{Zr,1<\/sub><\/strong> = 9,3 mm<\/strong> (to calculate the hydraulic diameter)<\/li>\n}
the pitch of fuel pins is: p = 13 mm<\/strong> \u00a0(to calculate the hydraulic diameter)<\/li>\n
the dynamic viscosity of saturated water at 300\u00b0C is: \u03bc = 0.0000859 N.s\/m<\/strong>^{2<\/sup><\/strong><\/li>\n}
the fluid density is: \u03c1 = 714 kg\/m<\/strong>^{3<\/sup><\/strong><\/li>\n<\/ul>\nThe hydraulic diameter, D<\/strong>_{h<\/sub><\/strong>, is a commonly used term when handling flow in non-circular tubes and channels<\/strong>. The hydraulic diameter of the fuel channel<\/strong>, D<\/em>_{h<\/sub><\/em>, is equal to 13,85 mm<\/strong>.<\/p>\n}}}
See also: Hydraulic Diameter<\/a><\/p>\n
The Reynolds number <\/strong>inside the fuel channel is then equal to:<\/p>\n
$\"reynolds$ <\/a><\/p>\n
This fully satisfies the turbulent conditions<\/strong><\/a>.<\/p>\n
Calculation of the Skin Friction Coefficient<\/h2>\nThe friction factor<\/strong> for turbulent flow depends strongly on the relative roughness. <\/strong>It is determined by the Colebrook equation or can be determined using the Moody chart<\/strong><\/a>. The Moody chart <\/strong>for Re = 575 600 <\/strong>and \u03b5\/D = 5 x 10<\/strong>^{-4<\/sup><\/strong> returns following values:<\/p>\n}
\n
the Darcy friction factor<\/strong><\/a> is equal to f<\/strong>_{D<\/sub><\/strong> = 0.017<\/strong><\/li>\n}
the Fanning friction factor<\/strong><\/a> is equal to f<\/strong>_{F<\/sub><\/strong> = f<\/strong>_{D<\/sub><\/strong>\/4 = 0.00425<\/strong><\/li>\n<\/ul>\nTherefore the skin friction coefficient is equal to:<\/p>\n}} $\"skin$ <\/a><\/p>\n
Calculation of the Drag Force<\/h2>\n
To calculate the drag force<\/strong>, we have to know:<\/p>\n
\n
the skin friction coefficient, which is: C<\/strong>_{D,friction<\/sub><\/strong> = 0.00425<\/strong><\/li>\n}
the area of pin surface, which is: A = \u03c0.d.h = 0.1169 m<\/strong>^{2<\/sup><\/strong><\/li>\n}
the fluid density<\/a>, which is: \u03c1 = 714 kg\/m<\/strong>^{3<\/sup><\/strong><\/li>\n}
the core flow velocity, which is constant and equal to V<\/strong>_{core<\/sub><\/strong> = 5 m\/s<\/strong><\/li>\n<\/ul>\n}From the skin friction coefficient, <\/strong>which is equal to the Fanning friction factor<\/strong><\/a>, we can calculate the frictional component of the drag force. <\/strong>The drag force is given by:<\/p>\n
$\"drag$ <\/a><\/p>\n
Assuming that a fuel assembly can have, for example, 289 fuel pins (17×17 fuel assembly), the frictional component<\/strong> of the drag force <\/strong>is then of the order of kilonewtons<\/strong>. Moreover, this drag force originates purely from the skin friction on the fuel bundle. But typical PWR fuel assembly contains other components which influence the fuel assembly hydraulics:<\/p>\n
\n
Fuel rods<\/strong>. Fuel rods contain fuel and burnable poisons.<\/li>\n
Top nozzle<\/strong>. Provides the mechanical support for the fuel assembly structure.<\/li>\n
Bottom nozzle<\/strong>. Provides the mechanical support for the fuel assembly structure.<\/li>\n
Spacing grid<\/strong>. Ensures an exact guiding of the fuel rods.<\/li>\n
Guide thimble tube<\/strong>. Vacant tube for control rods or in-core instrumentation.<\/li>\n<\/ul>\n
As was written, the second component of the drag force is the form drag. Form drag,<\/strong> also known as pressure drag,<\/strong> arises because of the shape<\/strong> and size<\/strong> of the object. The pressure drag<\/strong> is proportional to the difference between the pressures acting on the front and back of the immersed body and the frontal area.<\/p>\n
Pressure Drop – Fuel Assembly<\/h2>\nIn general, total fuel assembly <\/strong>pressure drop<\/strong> is formed by fuel bundle frictional drop (dependent on relative roughness<\/a> of fuel rods, Reynolds number<\/a>, hydraulic diameter<\/a>, etc.) and other pressure drops of structural elements (top and bottom nozzle, spacing grids, or mixing grids).<\/p>\n
In general, it is not so simple to calculate pressure drops in fuel assemblies (especially the spacing grids), and it belongs to the key know-how<\/strong> of certain fuel manufacturers. Mostly, pressure drops are measured in experimental hydraulic loops<\/strong>\u00a0rather than calculated.<\/p>\n
Engineers use the pressure loss coefficient<\/strong><\/a>, PLC<\/strong>. It is noted K or \u03be<\/strong> \u00a0(pronounced \u201cxi\u201d). This coefficient characterizes pressure loss<\/a> of a certain hydraulic system or a part of a hydraulic system, and it can be easily measured in hydraulic loops. The pressure loss coefficient can be defined or measured for both straight pipes and especially for local (minor) losses<\/strong><\/a>.<\/p>\n
$\"PLC$ <\/a><\/p>\n
Using data from the example mentioned above, the pressure loss coefficient<\/strong> (only frictional from the straight pipe) is equal to \u03be = f_{D<\/sub>L\/D_{H<\/sub> = 4.9<\/strong>. But the overall pressure loss coefficient (including spacing grids, top, and bottom nozzles, etc.) is usually about three times higher. This PLC (\u03be = 4.9<\/strong>) causes the pressure drop to be of the order of (using the previous inputs) \u0394p_{friction<\/sub><\/strong> = \u00a04.9 x 714 x 5^{2<\/sup>\/ 2 = 43.7 kPa<\/strong> (without spacing grids, top, and bottom nozzles). About three times higher real PLC means about three times higher \u0394p_{fuel\u00a0<\/sub><\/strong>will be.<\/p>\n}}}}}
The overall reactor pressure loss, \u0394p_{reactor<\/sub><\/strong>, must include:<\/p>\n}
\n
downcomer and reactor bottom<\/li>\n
lower support plate<\/li>\n
fuel assembly including spacing grids, top and bottom nozzles, and other structural components – \u0394p_{fuel<\/sub><\/strong><\/li>\n}
upper guide structure assembly<\/li>\n<\/ul>\n
As a result, the overall reactor pressure loss – \u0394p_{reactor<\/sub><\/strong> is usually of the order of hundreds kPa (let say 300 – 400 kPa) for design parameters.<\/p>\n<\/div>\n}
<\/div>\n\u00a0
<\/span>References:<\/div>
Reactor Physics and Thermal Hydraulics:<\/strong>\n
\n
J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n
J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n
W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n
Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n
Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871<\/li>\n
Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2<\/li>\n
Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,\u00a0John Wiley & Sons, 2006, ISBN:\u00a0978-0-470-03037-0<\/li>\n
Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010,\u00a0ISBN 978-1-4020-8670-0.<\/li>\n
U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2, and 3. June 1992.<\/li>\n
White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN:\u00a0978-0077422417<\/li>\n<\/ol>\n<\/div><\/div><\/div>
<\/div><\/div><\/div>
<\/div>
<\/div><\/div>
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See above:<\/h2>\n
Fluid Dynamics<\/i> <\/span><\/a><\/p><\/div><\/div>
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