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The Streeter–Phelps equation is also known as the DO sag equation. This is due to the shape of the graph of the DO over time. The biological oxygen demand (BOD) and dissolved oxygen (DO) curves in a river flowing right reaching equilibrium after a continuous input of high BOD influent is added into the river at x = 15 m and t = 0 s.
The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes' law can be used to calculate its fall velocity or settling velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the ...
so the flow velocity components in relation to the stream function must be =, =. Notice that the stream function is linear in the velocity. Consequently if two incompressible flow fields are superimposed, then the stream function of the resultant flow field is the algebraic sum of the stream functions of the two original fields.
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-line velocity) and the same Reynolds and Womersley numbers, then the fluid flows will be identical. This can be seen from inspection of the ...
A schematic diagram of the Blasius flow profile. The streamwise velocity component () / is shown, as a function of the similarity variable .. Using scaling arguments, Ludwig Prandtl [1] argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate).
In fluid dynamics, the Stokes stream function is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry. A surface with a constant value of the Stokes stream function encloses a streamtube, everywhere tangential to the flow velocity vectors. Further, the volume flux within this streamtube ...
Rayleigh's equation (fluid dynamics) Example of a parallel shear flow. In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow. The equation is: [1]
Contents. Moody chart. In engineering, the Moody chart or Moody diagram (also Stanton diagram) is a graph in non-dimensional form that relates the Darcy–Weisbach friction factor fD, Reynolds number Re, and surface roughness for fully developed flow in a circular pipe. It can be used to predict pressure drop or flow rate down such a pipe.