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where is the density of the fluid, is the average velocity in the pipe, is the friction factor from the Moody chart, is the length of the pipe and is the pipe diameter. The chart plots Darcy–Weisbach friction factor f D {\displaystyle f_{D}} against Reynolds number Re for a variety of relative roughnesses, the ratio of the mean height of ...
Even in the case of laminar flow, where all the flow lines are parallel to the length of the pipe, the velocity of the fluid on the inner surface of the pipe is zero due to viscosity, and the velocity in the center of the pipe must therefore be larger than the average velocity obtained by dividing the volumetric flow rate by the wet area.
In fluid dynamics, dynamic pressure (denoted by q or Q and sometimes called velocity pressure) is the quantity defined by: [1] = where (in SI units): q is the dynamic pressure in pascals (i.e., N/m 2, ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s.
Pressure head is a component of hydraulic head, in which it is combined with elevation head. When considering dynamic (flowing) systems, there is a third term needed: velocity head. Thus, the three terms of velocity head, elevation head, and pressure head appear in the head equation derived from the Bernoulli equation for incompressible fluids:
In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity ¯ (with the usual dimension of length per time), defined as the quotient between the volume flow rate ˙ (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):
(Common) symbol/s Defining equation SI units Dimension Flow velocity vector field u = (,) m s −1 [L][T] −1: Velocity pseudovector field ω = s −1 [T] −1: Volume velocity, volume flux φ V (no standard symbol)
where is the Darcy friction factor (from the above equation or the Moody Chart), is the sublayer thickness, is the pipe diameter, is the density, is the friction velocity (not an actual velocity of the fluid), is the average velocity of the plug (in the pipe), is the shear on the wall, and is the pressure loss down the length of the pipe.
Sonar flowmeters have the capacity of measuring the velocity of liquids or gases non-intrusively within the pipe and then leverage this velocity measurement into a flow rate by using the cross-sectional area of the pipe and the line pressure and temperature. The principle behind this flow measurement is the use of underwater acoustics.