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SRS can be solved in polynomial time in the Real RAM model. [3] However, its run-time complexity in the Turing machine model is open, as of 1997. [1] The main difficulty is that, in order to solve the problem, the square-roots should be computed to a high accuracy, which may require a large number of bits.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
The viscous friction causes the flow properties to change along the duct. The frictional effect is modeled as a shear stress at the wall acting on the fluid with uniform properties over any cross section of the duct. For a flow with an upstream Mach number greater than 1.0 in a sufficiently long duct, deceleration occurs and the flow can become ...
For the limiting case of a very wide duct, i.e. a slot of width b, where b ≫ a, and a is the water depth, then D H = 4a. For a fully filled duct or pipe whose cross-section is a convex regular polygon , the hydraulic diameter is equivalent to the diameter D {\displaystyle D} of a circle inscribed within the wetted perimeter .
In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed. [1] Entrance length refers to the length of the entry region, the area following the pipe entrance where effects originating from the interior wall of the pipe propagate into the flow as an expanding boundary layer.
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.
Duct dead loads: are often simplified (in Cement plant usage) by using duct plate weight, multiplied by 1.15 as a stiffener allowance, as duct stiffeners usually weigh less than 15% times the duct plate weight. Duct stiffener allowance for rectangular power plants ductwork may be 50% to 100% of the duct plate weight.
There are two major systems to classify ductwork airtightness, one based on European standards, the other based on ASHRAE standard 90.1-2010.Both are based on the leakage airflow rate at a given ductwork pressure divided by the product of the ductwork surface area and the same ductwork pressure raised to the power 0.65.