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The second equation is the incompressible constraint, stating the flow velocity is a solenoidal field (the order of the equations is not causal, but underlines the fact that the incompressible constraint is not a degenerate form of the continuity equation, but rather of the energy equation, as it will become clear in the following).
In order to find the weak form of the Navier–Stokes equations, firstly, consider the momentum equation [20] + + = multiply it for a test function , defined in a suitable space , and integrate both members with respect to the domain : [20] + + = Counter-integrating by parts the diffusive and the pressure terms and by using the Gauss' theorem ...
It is also used to prevent cytomegalovirus following a kidney transplant in high risk cases. [2] It is taken by mouth. [2] Common side effects include headache and vomiting. [2] Severe side effects may include kidney problems. [2] Use in pregnancy appears to be safe. [2] It is a prodrug, which works after being converted to aciclovir in a ...
The equation is a nonlinear integro-differential equation, and the unknown function in the equation is a probability density function in six-dimensional space of a particle position and momentum. The problem of existence and uniqueness of solutions is still not fully resolved, but some recent results are quite promising.
The Euler–Lagrange equation was developed in connection with their studies of the tautochrone problem. The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in ...
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
When the fluid is moving relative to the reference system, for example, a car driving into headwind, the power required to overcome the aerodynamic drag is given by the following formula: = = (+) Where v w {\displaystyle v_{w}} is the wind speed and v o {\displaystyle v_{o}} is the object speed (both relative to ground).
The following alternate analyses of motion before the stone is released consider only forces acting in the radial direction. Both analyses predict that string tension T = mv 2 / r . For example, if the radius of the sling is r = 1 metre, the velocity of the stone in the map frame is v = 25 metres per second, and the stone's mass m = 0.2 ...