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drag force F d. Using the algorithm of the Buckingham π theorem, these five variables can be reduced to two dimensionless groups: drag coefficient c d and; Reynolds number Re. That this is so becomes apparent when the drag force F d is expressed as part of a function of the other variables in the problem:
It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/(m 2 K)). The overall heat transfer rate for combined modes is usually expressed in terms of an overall conductance or heat transfer coefficient ...
f is the local Fanning friction factor (dimensionless); τ is the local shear stress (units of pascals (Pa) = kg/m 2, or pounds per square foot (psf) = lbm/ft 2); q is the bulk dynamic pressure (Pa or psf), given by: = ρ is the density of the fluid (kg/m 3 or lbm/ft 3) u is the bulk flow velocity (m/s or ft/s)
Alternative notations include C(n, k), n C k, n C k, C k n, [3] C n k, and C n,k, in all of which the C stands for combinations or choices; the C notation means the number of ways to choose k out of n objects. Many calculators use variants of the C notation because they can represent it on a single-line display.
The conversion factor k was chosen so that the values for C were the same as in the Chézy formula for the typical hydraulic slope of S=0.001. [9] The value of k is 0.001 −0.04. [10] Typical C factors used in design, which take into account some increase in roughness as pipe ages are as follows: [11]
Serghides's solution is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation. It was derived using Steffensen's method. [12] The solution involves calculating three intermediate values and then substituting those values into a final ...
where C is the heat capacity, it follows that: = The heat capacity depends on how the external variables of the system are changed when the heat is supplied. If the only external variable of the system is the volume, then we can write:
K v is the flow factor (expressed in m 3 /h), Q is the flowrate (expressed in m 3 /h), SG is the specific gravity of the fluid (for water = 1), ∆P is the differential pressure across the device (expressed in bar). K v can be calculated from C v using the equation [4] =.