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In addition to other physical phenomena, this equation describes the flow of heat in a homogeneous and isotropic medium, with u(x, y, z, t) being the temperature at the point (x, y, z) and time t. If the medium is not homogeneous and isotropic, then α would not be a fixed coefficient, and would instead depend on ( x , y , z ) ; the equation ...
The model describes how dissolved oxygen (DO) decreases in a river or stream along a certain distance by degradation of biochemical oxygen demand (BOD). The equation was derived by H. W. Streeter, a sanitary engineer, and Earle B. Phelps, a consultant for the U.S. Public Health Service, in 1925, based on field data from the Ohio River. The ...
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where = = = = Then the only non-trivial equation is the -equation, which now reads + = Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.
All non-relativistic balance equations, such as the Navier–Stokes equations, can be derived by beginning with the Cauchy equations and specifying the stress tensor through a constitutive relation. By expressing the deviatoric (shear) stress tensor in terms of viscosity and the fluid velocity gradient, and assuming constant viscosity, the ...
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
The simplified form of Bernoulli's equation can be summarized in the following memorable word equation: [1]: § 3.5 Static pressure + Dynamic pressure = Total pressure. Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q .
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.