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Stokes problem in a viscous fluid due to the harmonic oscillation of a plane rigid plate (bottom black edge). Velocity (blue line) and particle excursion (red dots) as a function of the distance to the wall.
If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A ...
As the fluid flows outward, the area of flow increases. As a result, to satisfy continuity equation, the velocity decreases and the streamlines spread out. The velocity at all points at a given distance from the source is the same. Fig 2 - Streamlines and potential lines for source flow. The velocity of fluid flow can be given as -
A fluid is flowing between and in contact with two horizontal surfaces of contact area A. A differential shell of height Δy is utilized (see diagram below). Diagram of the shell balance process in fluid mechanics. The top surface is moving at velocity U and the bottom surface is stationary. Density of fluid = ρ; Viscosity of fluid = μ
The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The vector area is a combination of the magnitude of the area through which the volume passes through, A , and a unit vector normal to the area, n ^ {\displaystyle {\hat {\mathbf {n} }}} .
where is the fluid density and the fluid velocity. To obtain the equations of motion for incompressible flow , it is assumed that the density, ρ {\displaystyle \rho } , is a constant. Furthermore, occasionally one might consider the unsteady Stokes equations, in which the term ρ ∂ u ∂ t {\displaystyle \rho {\frac {\partial \mathbf {u ...
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. Right: The reduction in flux passing through a surface can be visualized by reduction in F or dS equivalently (resolved into components, θ is angle to ...
The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil (and any two-dimensional body including circular cylinders) translating in a uniform fluid at a constant speed so large that the flow seen in the body-fixed frame is steady and unseparated.