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  2. List of equations in fluid mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_fluid...

    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.

  3. Darcy's law - Wikipedia

    en.wikipedia.org/wiki/Darcy's_law

    Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell.The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.

  4. Lagrangian and Eulerian specification of the flow field

    en.wikipedia.org/wiki/Lagrangian_and_Eulerian...

    In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. [1] [2] Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat ...

  5. Euler equations (fluid dynamics) - Wikipedia

    en.wikipedia.org/wiki/Euler_equations_(fluid...

    Flow around a wing. This incompressible flow satisfies the Euler equations. In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal ...

  6. Flow (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Flow_(mathematics)

    In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of ordinary differential equations. Informally, a flow may be viewed as a continuous motion of points over time.

  7. Numerical methods in fluid mechanics - Wikipedia

    en.wikipedia.org/wiki/Numerical_Methods_in_Fluid...

    This is an example of an implicit method since the unknown u(n + 1) has been used in evaluating the slope of the solution on the right hand side; this is not a problem to solve for u(n + 1) in this scalar and linear case. For more complicated situations like a nonlinear right hand side or a system of equations, a nonlinear system of equations ...

  8. Derivation of the Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the_Navier...

    The assumptions for the stream function equation are: The flow is incompressible and Newtonian. Coordinates are orthogonal. Flow is 2D: u 3 = ⁠ ∂u 1 / ∂x 3 ⁠ = ⁠ ∂u 2 / ∂x 3 ⁠ = 0; The first two scale factors of the coordinate system are independent of the last coordinate: ⁠ ∂h 1 / ∂x 3 ⁠ = ⁠ ∂h 2 / ∂x 3 ⁠ = 0 ...

  9. Pipe network analysis - Wikipedia

    en.wikipedia.org/wiki/Pipe_network_analysis

    In fluid dynamics, pipe network analysis is the analysis of the fluid flow through a hydraulics network, containing several or many interconnected branches. The aim is to determine the flow rates and pressure drops in the individual sections of the network. This is a common problem in hydraulic design.