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Minor losses in pipe flow are a major part in calculating the flow, pressure, or energy reduction in piping systems. Liquid moving through pipes carries momentum and energy due to the forces acting upon it such as pressure and gravity.
In more practical terms, the flow coefficient C v is the volume (in US gallons) of water at 60 °F (16 °C) that will flow per minute through a valve with a pressure drop of 1 psi (6.9 kPa) across the valve. The use of the flow coefficient offers a standard method of comparing valve capacities and sizing valves for specific applications that is ...
The proportionality coefficient is the dimensionless "Darcy friction factor" or "flow coefficient". This dimensionless coefficient will be a combination of geometric factors such as π, the Reynolds number and (outside the laminar regime) the relative roughness of the pipe (the ratio of the roughness height to the hydraulic diameter).
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.
h f = head loss in meters (water) over the length of pipe; L = length of pipe in meters; Q = volumetric flow rate, m 3 /s (cubic meters per second) C = pipe roughness coefficient; d = inside pipe diameter, m (meters) Note: pressure drop can be computed from head loss as h f × the unit weight of water (e.g., 9810 N/m 3 at 4 deg C)
Moody's team used the available data (including that of Nikuradse) to show that fluid flow in rough pipes could be described by four dimensionless quantities: Reynolds number, pressure loss coefficient, diameter ratio of the pipe and the relative roughness of the pipe.
ΔE is the fluid's mechanical energy loss, ξ is an empirical loss coefficient, which is dimensionless and has a value between zero and one, 0 ≤ ξ ≤ 1, ρ is the fluid density, v 1 and v 2 are the mean flow velocities before and after the expansion. In case of an abrupt and wide expansion, the loss coefficient is equal to one. [1]
where h f is the head loss due to friction, calculated from: the ratio of the length to diameter of the pipe L/D, the velocity of the flow V, and two empirical factors a and b to account for friction. This equation has been supplanted in modern hydraulics by the Darcy–Weisbach equation, which used it as a starting point.