Examples of Reynolds Number in the following topics:
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- It occurs when the Reynolds number is above a certain critical threshold while mixed turbulent–laminar flow occurs within a range of Reynolds number below this threshold value.
- At the lower limit of this mixed turbulent–laminar flow Reynolds number region there is another critical threshold value, below which only laminar flow is possible.
- Laminar flow is often encountered in common hydraulic systems, such as where fluid flow is through an enclosed, rigid pipe; the fluid is incompressible, has constant viscosity, and the Reynolds number is below this lower critical threshold value.
- Considering laminar flow of a constant density, incompressible fluid such as for a Newtonian fluid traveling in a pipe, with a Reynolds number below the upper limit level for fully laminar flow, the pressure difference between two points along the pipe can be found from the volumetric flow rate, or vice versa.
- This equation is valid for laminar flow of incompressible fluids only, and may be used to determine a number of properties in the hydraulic system, if the others are known or can be measured.
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- We use another form of the Reynolds number N′R, defined for an object moving in a fluid to be
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- A round-off error is the difference between the calculated approximation of a number and its exact mathematical value.
- Calculations rarely lead to whole numbers.
- The number $\pi$ (pi) has infinitely many digits, but can be truncated to a rounded representation of as 3.14159265359.
- However, when doing a series of calculations, numbers are rounded off at each subsequent step.
- Rounding these numbers off to one decimal place or to the nearest whole number would change the answer to 5.7 and 6, respectively.
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- Scientific notation is a way of writing numbers that are too big or too small in a convenient and standard form.
- In scientific notation all numbers are written in the form of $a\cdot 10^{b}$ ($a$ multiplied by ten raised to the power of $b$), where the exponent $b$ is an integer, and the coefficient $a$ is any real number.
- Each number is ten times bigger than the previous one.
- Continuing on, we can write $10^{-1}$ to stand for 0.1, the number ten times smaller than $10^{0}$.
- Negative exponents are used for small numbers:
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- The number of molecules in a mole is called Avogadro's number (NA)—defined as 6.02x 1023 mol-1.
- When measuring the amount of substance, it is sometimes easier to work with a unit other than the number of molecules.
- The actual number of atoms or molecules in one mole is called Avogadro's constant (NA), in recognition of Italian scientist Amedeo Avogadro .
- Avogadro's number (N) refers to the number of molecules in one gram-molecule of oxygen.
- In 1811 Amedeo Avogadro first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules, regardless of the nature of the gas (i.e., this number is universal and independent of the type of gas).
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- Through radioactive decay, nuclear fusion and nuclear fission, the number of nucleons (sum of protons and neutrons) is always held constant.
- In physics and chemistry there are many conservation laws—among them, the Law of Conservation of Nucleon Number, which states that the total number of nucleons (nuclear particles, specifically protons and neutrons) cannot change by any nuclear reaction.
- Electron capture has the same effect on the number of protons and neutrons in a nucleus as positron emission.
- Finally, nuclear fusion follows the Law of Conservation of Nucleon Number.
- Thus, the number of nucleons before and after fission and fusion is always constant.
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- The stability of an atom depends on the ratio and number of protons and neutrons, which may represent closed and filled quantum shells.
- The stability of an atom depends on the ratio of its protons to its neutrons, as well as on whether it contains a "magic number" of neutrons or protons that would represent closed and filled quantum shells.
- Of the 254 known stable nuclides, only four have both an odd number of protons and an odd number of neutrons:
- All elements form a number of radionuclides, although the half-lives of many are so short that they are not observed in nature.
- An atomic nucleus emits an alpha particle and thereby transforms ("decays") into an atom with a mass number smaller by four and an atomic number smaller by two.
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- In alpha decay an atomic nucleus emits an alpha particle and transforms into an atom with smaller mass (by four) and atomic number (by two).
- As the result of this process, the parent atom transforms ("decays") into a new atom with a mass number smaller by four and an atomic number smaller by two.
- Because an alpha particle is the same as a helium-4 nucleus, which has mass number 4 and atomic number 2, this can also be written as:
- The lightest known alpha emitters are the lightest isotopes (mass numbers 106-110) of tellurium (element 52).
- An atomic nucleus emits an alpha particle and thereby transforms ("decays") into an atom with a mass number smaller by four and an atomic number smaller by two.
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- Scalars are physical quantities represented by a single number, and vectors are represented by both a number and a direction.
- Scalars can be thought of as numbers, whereas vectors must be thought of more like arrows pointing in a specific direction.
- The magnitude of a vector is a number for comparing one vector to another.
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- It is impossible to reduce the temperature of any system to zero temperature in a finite number of finite operations.
- Assuming an entropy difference at absolute zero, T=0 could be reached in a finite number of steps.
- However, going back to the third law, at T=0 there is no entropy difference, and therefore an infinite number of stepswould be needed for this process (illustrated in ).
- Left side: Absolute zero can be reached in a finite number of steps if S(T=0,X1)≠S(T=0, X2).
- Right: An infinite number of steps is needed since S(0,X1)= S(0,X2).