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For a fully filled duct or pipe whose cross-section is a convex regular polygon, the hydraulic diameter is equivalent to the diameter of a circle inscribed within the wetted perimeter. This can be seen as follows: The N {\displaystyle N} -sided regular polygon is a union of N {\displaystyle N} triangles, each of height D / 2 {\displaystyle D/2 ...
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. The pipe's relative roughness ε / D, where ε is the pipe's effective roughness height and D the pipe ...
For laminar flow in a circular pipe of diameter , the friction factor is inversely proportional to the Reynolds number alone (f D = 64 / Re ) which itself can be expressed in terms of easily measured or published physical quantities (see section below). Making this substitution the Darcy–Weisbach equation is rewritten as
Note that, in approximation, for a given value of flow volume, a step up in duct size (say from 100mm to 120mm) will reduce the friction loss by a factor of 3. Volumetric Flow Q of air at STP where friction loss per unit length Δ p / L (SI kg / m 2 / s 2 ) is, resp., 0.082, 0.245, and 0.816., for selected Nominal Duct Sizes [ 19 ] in smooth ...
is the air density in the duct (pounds per cubic foot), is the standard air density (0.075 pound per cubic foot), is the resistance (atkinsons), is the rate of flow of air (thousands of cubic feet per second).
d = equivalent depth, a function of L, (Di-Dd), and r; r = drain radius (m) Steady (equilibrium) state condition In steady state, the level of the water table remains constant and the discharge rate (Q) equals the rate of groundwater recharge (R), i.e. the amount of water entering the groundwater through the watertable per unit of time.