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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
In this example, the ratio (probability of living during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour −1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour −1.
In this article, the following conventions and definitions are to be understood: The Reynolds number Re is taken to be Re = V D / ν, where V is the mean velocity of fluid flow, D is the pipe diameter, and where ν is the kinematic viscosity μ / ρ, with μ the fluid's Dynamic viscosity, and ρ the fluid's density.
Copper(II) acetate, also referred to as cupric acetate, is the chemical compound with the formula Cu(OAc) 2 where AcO − is acetate (CH 3 CO − 2).The hydrated derivative, Cu 2 (OAc) 4 (H 2 O) 2, which contains one molecule of water for each copper atom, is available commercially.
Most charts or tables indicate the type of friction factor, or at least provide the formula for the friction factor with laminar flow. If the formula for laminar flow is f = 16 / Re , it is the Fanning factor f, and if the formula for laminar flow is f D = 64 / Re , it is the Darcy–Weisbach factor f D.
That is the case, for example, of the six pairs (1,2), (−2,3), (−3,1), (−1,−2), (2,−3), and (3,−1). In particular, the pairs ( k ,0) and (0, k ) describe the same nanotube geometry. These redundancies can be avoided by considering only pairs ( n , m ) such that n > 0 and m ≥ 0; that is, where the direction of the vector w lies ...
This formula can also be used to calculate μ s from empirical measurements of the friction angle. Friction at the atomic level Determining the forces required to move atoms past each other is a challenge in designing nanomachines .