1.
Fluid dynamics
–
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids. It has several subdisciplines, including aerodynamics and hydrodynamics, before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, the foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum, and conservation of energy. These are based on mechanics and are modified in quantum mechanics. They are expressed using the Reynolds transport theorem, in addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects, however, the continuum assumption assumes that fluids are continuous, rather than discrete. The fact that the fluid is made up of molecules is ignored. The unsimplified equations do not have a general solution, so they are primarily of use in Computational Fluid Dynamics. The equations can be simplified in a number of ways, all of which make them easier to solve, some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. Three conservation laws are used to solve fluid dynamics problems, the conservation laws may be applied to a region of the flow called a control volume. A control volume is a volume in space through which fluid is assumed to flow. The integral formulations of the laws are used to describe the change of mass, momentum. Mass continuity, The rate of change of fluid mass inside a control volume must be equal to the net rate of flow into the volume. Mass flow into the system is accounted as positive, and since the vector to the surface is opposite the sense of flow into the system the term is negated. The first term on the right is the net rate at which momentum is convected into the volume, the second term on the right is the force due to pressure on the volumes surfaces. The first two terms on the right are negated since momentum entering the system is accounted as positive, the third term on the right is the net acceleration of the mass within the volume due to any body forces. Surface forces, such as forces, are represented by F surf. The following is the form of the momentum conservation equation

2.
Sediment
–
For sediment in beverages, see dregs. For example, sand and silt can be carried in suspension in water and on reaching the sea be deposited by sedimentation. Sediments are most often transported by water, but also wind, beach sands and river channel deposits are examples of fluvial transport and deposition, though sediment also often settles out of slow-moving or standing water in lakes and oceans. Desert sand dunes and loess are examples of transport and deposition. Glacial moraine deposits and till are ice-transported sediments, sediment can be classified based on its grain size and/or its composition. Sediment size is measured on a log base 2 scale, called the Phi scale, composition of sediment can be measured in terms of, parent rock lithology mineral composition chemical make-up. This leads to an ambiguity in which clay can be used as both a size-range and a composition, sediment is transported based on the strength of the flow that carries it and its own size, volume, density, and shape. Stronger flows will increase the lift and drag on the particle, causing it to rise, rivers and streams carry sediment in their flows. This sediment can be in a variety of locations within the flow and these relationships are shown in the following table for the Rouse number, which is a ratio of sediment fall velocity to upwards velocity. If the upwards velocity is less than the settling velocity, but still high enough for the sediment to move, it will move along the bed as bed load by rolling, sliding. If the upwards velocity is higher than the velocity, the sediment will be transported high in the flow as wash load. As there are generally a range of different particle sizes in the flow, sediment motion can create self-organized structures such as ripples, dunes, antidunes on the river or stream bed. These bedforms are often preserved in rocks and can be used to estimate the direction. Overland flow can erode soil particles and transport them downslope, the erosion associated with overland flow may occur through different methods depending on meteorological and flow conditions. If the initial impact of rain droplets dislodges soil, the phenomenon is called rainsplash erosion, if overland flow is directly responsible for sediment entrainment but does not form gullies, it is called sheet erosion. If the flow and the substrate permit channelization, gullies may form, glaciers carry a wide range of sediment sizes, and deposit it in moraines. The overall balance between sediment in transport and sediment being deposited on the bed is given by the Exner equation and this expression states that the rate of increase in bed elevation due to deposition is proportional to the amount of sediment that falls out of the flow. This can be localized, and simply due to obstacles, examples are scour holes behind boulders, where flow accelerates

3.
Terminal velocity
–
Terminal velocity is the highest velocity attainable by an object as it falls through a fluid. It occurs when the sum of the force and the buoyancy is equal to the downward force of gravity acting on the object. Since the net force on the object is zero, the object has zero acceleration, in fluid dynamics, an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving. As the speed of an object increases, so does the drag force acting on it, at some speed, the drag or force of resistance will equal the gravitational pull on the object. At this point the object ceases to accelerate and continues falling at a constant speed called the terminal velocity, an object moving downward faster than the terminal velocity will slow down until it reaches the terminal velocity. Drag depends on the area, here, the objects cross-section or silhouette in a horizontal plane. An object with a projected area relative to its mass, such as a parachute, has a lower terminal velocity than one with a small projected area relative to its mass. Based on wind resistance, for example, the velocity of a skydiver in a belly-to-earth free-fall position is about 195 km/h. This velocity is the limiting value of the velocity. In this example, a speed of 50% of terminal velocity is reached only about 3 seconds, while it takes 8 seconds to reach 90%,15 seconds to reach 99%. Higher speeds can be attained if the skydiver pulls in his or her limbs, in this case, the terminal velocity increases to about 320 km/h, which is almost the terminal velocity of the peregrine falcon diving down on its prey. In reality, an object approaches its terminal velocity asymptotically, so instead of m use the reduced mass m r = m − ρ V in this and subsequent formulas. The terminal velocity of an object due to the properties of the fluid. Air density increases with decreasing altitude, at about 1% per 80 metres, for objects falling through the atmosphere, for every 160 metres of fall, the terminal velocity decreases 1%. After reaching the terminal velocity, while continuing the fall. Such flows are called creeping flows and the condition to be satisfied for the flows to be creeping flows is the Reynolds number, R e ≪1. From Stokes solution, the force acting on the sphere can be obtained as D =3 π μ d V or C d =24 R e where the Reynolds number. The expression for the force given by equation is called Stokes law

4.
United States
–
Forty-eight of the fifty states and the federal district are contiguous and located in North America between Canada and Mexico. The state of Alaska is in the northwest corner of North America, bordered by Canada to the east, the state of Hawaii is an archipelago in the mid-Pacific Ocean. The U. S. territories are scattered about the Pacific Ocean, the geography, climate and wildlife of the country are extremely diverse. At 3.8 million square miles and with over 324 million people, the United States is the worlds third- or fourth-largest country by area, third-largest by land area. It is one of the worlds most ethnically diverse and multicultural nations, paleo-Indians migrated from Asia to the North American mainland at least 15,000 years ago. European colonization began in the 16th century, the United States emerged from 13 British colonies along the East Coast. Numerous disputes between Great Britain and the following the Seven Years War led to the American Revolution. On July 4,1776, during the course of the American Revolutionary War, the war ended in 1783 with recognition of the independence of the United States by Great Britain, representing the first successful war of independence against a European power. The current constitution was adopted in 1788, after the Articles of Confederation, the first ten amendments, collectively named the Bill of Rights, were ratified in 1791 and designed to guarantee many fundamental civil liberties. During the second half of the 19th century, the American Civil War led to the end of slavery in the country. By the end of century, the United States extended into the Pacific Ocean. The Spanish–American War and World War I confirmed the status as a global military power. The end of the Cold War and the dissolution of the Soviet Union in 1991 left the United States as the sole superpower. The U. S. is a member of the United Nations, World Bank, International Monetary Fund, Organization of American States. The United States is a developed country, with the worlds largest economy by nominal GDP. It ranks highly in several measures of performance, including average wage, human development, per capita GDP. While the U. S. economy is considered post-industrial, characterized by the dominance of services and knowledge economy, the United States is a prominent political and cultural force internationally, and a leader in scientific research and technological innovations. In 1507, the German cartographer Martin Waldseemüller produced a map on which he named the lands of the Western Hemisphere America after the Italian explorer and cartographer Amerigo Vespucci

5.
Bed load
–
The term bed load or bedload describes particles in a flowing fluid that are transported along the bed. Bed load is complementary to suspended load and wash load, bed load moves by rolling, sliding, and/or saltating. Generally, bed load downstream will be smaller and more rounded than bed load upstream. This quantity reads as, τ ∗ = u ∗2 g d, where u ∗ is the velocity, s is the relative particle density, d is an effective particle diameter which is entrained by the flow. Specifically, q s is a monotonically increasing nonlinear function of the excess Shields stress ϕ, typically expressed in the form of a power law

6.
Sediment transport
–
Sediment transport is the movement of solid particles, typically due to a combination of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained. Sediment transport due to fluid motion occurs in rivers, oceans, lakes, seas, Transport is also caused by glaciers as they flow, and on terrestrial surfaces under the influence of wind. Sediment transport due only to gravity can occur on sloping surfaces in general, including hillslopes, scarps, cliffs, sediment transport is important in the fields of sedimentary geology, geomorphology, civil engineering and environmental engineering. Aeolian or eolian is the term for sediment transport by wind and this process results in the formation of ripples and sand dunes. Typically, the size of the sediment is fine sand and smaller, because air is a fluid with low density and viscosity. Bedforms are generated by aeolian sediment transport in the terrestrial near-surface environment, ripples and dunes form as a natural self-organizing response to sediment transport. Aeolian sediment transport is common on beaches and in the regions of the world, because it is in these environments that vegetation does not prevent the presence. Wind-blown very fine-grained dust is capable of entering the upper atmosphere, dust from the Sahara deposits on the Canary Islands and islands in the Caribbean, and dust from the Gobi desert has deposited on the western United States. This sediment is important to the budget and ecology of several islands. Deposits of fine-grained wind-blown glacial sediment are called loess, in geology, physical geography, and sediment transport, fluvial processes relate to flowing water in natural systems. This encompasses rivers, streams, periglacial flows, flash floods, sediment moved by water can be larger than sediment moved by air because water has both a higher density and viscosity. In typical rivers the largest carried sediment is of sand and gravel size, coastal sediment transport takes place in near-shore environments due to the motions of waves and currents. At the mouths of rivers, coastal sediment and fluvial sediment transport processes mesh to create river deltas, coastal sediment transport results in the formation of characteristic coastal landforms such as beaches, barrier islands, and capes. As glaciers move over their beds, they entrain and move material of all sizes, glaciers can carry the largest sediment, and areas of glacial deposition often contain a large number of glacial erratics, many of which are several metres in diameter. Glaciers also pulverize rock into glacial flour, which is so fine that it is carried away by winds to create loess deposits thousands of kilometres afield. Sediment entrained in glaciers often moves approximately along the glacial flowlines, in hillslope sediment transport, a variety of processes move regolith downslope. For this reason, the tops of hills generally have a parabolic concave-up profile, as hillslopes steepen, however, they become more prone to episodic landslides and other mass wasting events. Large masses of material are moved in debris flows, hyperconcentrated mixtures of mud, clasts that range up to boulder-size, debris flows move as granular flows down steep mountain valleys and washes

7.
Froude number
–
In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field. The Froude number has some analogy with the Mach number, for example homogeneous Euler equations are conservation equations. However, in architecture the Froude number is a very significant figure used to determine the resistance of a partially submerged object moving through water. Dynamics of vessels that have the same Froude number are easily compared as they produce a similar wake, the Denny Ship Model Experiment tank in Dumbarton, Scotland, has a bust of Froude near the front door. In open channel flows, Bélanger introduced first the ratio of the velocity to the square root of the gravity acceleration times the flow depth. When the ratio was less than unity, the flow behaved like a fluvial motion, quantifying resistance of floating objects is generally credited to William Froude, who used a series of scale models to measure the resistance each model offered when towed at a given speed. The naval constructor Ferdinand Reech had put forward the concept in 1852 for testing ships, in France, it is sometimes called Reech–Froude number after Ferdinand Reech. To show how the Froude number is linked to general continuum mechanics, in order to make the equations dimensionless, a characteristic length r0, and a characteristic velocity u0, need to be defined. These should be such that the dimensionless variables are all of order one. The limit of high Froude numbers is thus notable and can be studied with perturbation theory and it is an important parameter with respect to the ships drag, or resistance, especially in terms of wave making resistance. For rectangular cross-sections with uniform depth d, the Froude number can be simplified to, for Fr <1 the flow is called a subcritical flow, further for Fr >1 the flow is characterised as supercritical flow. When Fr ≈1 the flow is denoted as critical flow, in such cases, the Froude number should be respected. Similarly, when simulating hot smoke plumes combined with natural wind, geophysical mass flows such as avalanches and debris flows take place on inclined slopes which then merge into gentle and flat run-out zones. So, these flows are associated with the elevation of the slopes that induce the gravity potential energy together with the pressure potential energy during the flow. Therefore, the classical Froude number should include this additional effect, for such a situation, Froude number needs to be re-defined. In the classical definition of the shallow-water or granular flow Froude number, the extended Froude number differs substantially from the classical Froude number for higher surface elevations. The term β h emerges from the change of the geometry of the mass along the slope. Dimensional analysis suggests that for shallow flows β h is of order ≪1, if the mass is shallow with a virtually bed-parallel free-surface, then β h can be disregarded

8.
Mach number
–
In fluid dynamics, the Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound. M = u c, where, M is the Mach number, u is the flow velocity with respect to the boundaries. By definition, Mach 1 is equal to the speed of sound, Mach 0.65 is 65% of the speed of sound, and Mach 1.35 is 35% faster than the speed of sound. The local speed of sound, and thereby the Mach number, depends on the condition of the surrounding medium, the Mach number is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. The medium can be a gas or a liquid, the boundary can be the boundary of an object immersed in the medium, or of a channel such as a nozzle, diffusers or wind tunnels channeling the medium. As the Mach number is defined as the ratio of two speeds, it is a dimensionless number, if M <0. 2–0.3 and the flow is quasi-steady and isothermal, compressibility effects will be small and simplified incompressible flow equations can be used. The Mach number is named after Austrian physicist and philosopher Ernst Mach, as the Mach number is a dimensionless quantity rather than a unit of measure, with Mach, the number comes after the unit, the second Mach number is Mach 2 instead of 2 Mach. This is somewhat reminiscent of the modern ocean sounding unit mark, which was also unit-first. In the decade preceding faster-than-sound human flight, aeronautical engineers referred to the speed of sound as Machs number, never Mach 1, Mach number is useful because the fluid behaves in a similar manner at a given Mach number, regardless of other variables. As modeled in the International Standard Atmosphere, dry air at sea level, standard temperature of 15 °C. For example, the atmosphere model lapses temperature to −56.5 °C at 11,000 meters altitude. In the following table, the regimes or ranges of Mach values are referred to, generally, NASA defines high hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Aircraft operating in this include the Space Shuttle and various space planes in development. Flight can be classified in six categories, For comparison. At transonic speeds, the field around the object includes both sub- and supersonic parts. The transonic period begins when first zones of M >1 flow appear around the object, in case of an airfoil, this typically happens above the wing. Supersonic flow can decelerate back to only in a normal shock. As the speed increases, the zone of M >1 flow increases towards both leading and trailing edges

9.
Nusselt number
–
In heat transfer at a boundary within a fluid, the Nusselt number is the ratio of convective to conductive heat transfer across the boundary. In this context, convection includes both advection and diffusion, named after Wilhelm Nusselt, it is a dimensionless number. The conductive component is measured under the conditions as the heat convection. A similar non-dimensional parameter is Biot Number, with the difference that the conductivity is of the solid body. A Nusselt number close to one, namely convection and conduction of similar magnitude, is characteristic of slug flow or laminar flow, a larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. The convection and conduction heat flows are parallel to other and to the surface normal of the boundary surface. For complex shapes, the length may be defined as the volume of the body divided by the surface area. An understanding of boundary layers is necessary to understanding convective heat transfer between a surface and a fluid flowing past it. A thermal boundary layer develops if the free stream temperature. A temperature profile exists due to the energy exchange resulting from this temperature difference, while the left hand side is similar to the Biot modulus. This becomes the ratio of thermal resistance to the convective thermal resistance of the fluid, otherwise known as the Nusselt number. It is easy to solve but is accurate when there is a large temperature difference across the fluid. It is tailored to smooth tubes, so use for rough tubes is cautioned, the Dittus-Boelter equation is valid for 0. This increases to 3.57 with a heat transfer surface temperature of 100 °C, making a significant difference to the Nusselt number, the Sieder-Tate correlation for turbulent flow is an implicit function, as it analyzes the system as a nonlinear boundary value problem. The Sieder-Tate correlation is normally solved by a process, as the viscosity factor will change as the Nusselt number changes. The values depend on the hydraulic diameter

10.
Reynolds number
–
The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. It has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds, who popularized its use in 1883. A similar effect is created by the introduction of a stream of higher velocity fluid and this relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, the Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed, the Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. These definitions generally include the properties of density and viscosity, plus a velocity. This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, for aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is used today. Other shapes such as pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as gases or fluids of variable viscosity such as non-Newtonian fluids. The velocity may also be a matter of convention in some circumstances, in practice, matching the Reynolds number is not on its own sufficient to guarantee similitude. Fluid flow is chaotic, and very small changes to shape. Nevertheless, Reynolds numbers are an important guide and are widely used. Osborne Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow, when the velocity was low, the dyed layer remained distinct through the entire length of the large tube. When the velocity was increased, the broke up at a given point. The point at which this happened was the point from laminar to turbulent flow. From these experiments came the dimensionless Reynolds number for dynamic similarity—the ratio of forces to viscous forces