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Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
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]
In fluid mechanics, pipe flow is a type of fluid flow within a closed conduit, such as a pipe, duct or tube. It is also called as Internal flow. [1] The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important aspect.
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 fluid dynamics, total dynamic head (TDH) is the work to be done by a pump, per unit weight, per unit volume of fluid.TDH is the total amount of system pressure, measured in feet, where water can flow through a system before gravity takes over, and is essential for pump specification.
The equation for head loss in pipes, also referred to as slope, S, expressed in "feet per foot of length" vs. in 'psi per foot of length' as described above, with the inside pipe diameter, d, being entered in feet vs. inches, and the flow rate, Q, being entered in cubic feet per second, cfs, vs. gallons per minute, gpm, appears very similar.
The Euler number (Eu) is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by a restriction and the kinetic energy per volume of the flow, and is used to characterize energy losses in the flow, where a perfect frictionless flow corresponds to an Euler number of 0.
In order to derive Torricelli's formula the first point with no index is taken at the liquid's surface, and the second just outside the opening. Since the liquid is assumed to be incompressible, ρ 1 {\displaystyle \rho _{1}} is equal to ρ 2 {\displaystyle \rho _{2}} and; both can be represented by one symbol ρ {\displaystyle \rho } .