Archimede forces

If we consider that pj2 / P2i- From a phenomenological point of view, it is easier to accept a difference between pj2 and p2i. This is typical for a case where a directional internal force acts on a marked particle. As an example, we can consider a particle displacement given by a difference between the weight and the Archimedes force. In this case, the model to be analyzed is described by relations (4.43) and (4.44). For v 1 u.c/s, Eq. (4.43) is written as below ... 

Three forces act on a gaseous bubble in free liquid (without a solid phase) gravitational force (G = mg = Vpog) Archimedes force (F = Vpg) and the resistant force of the medium defined by Stake s law (R = bTiqroVo), where, g = acceleration due to gravity, ro = radius of bubble, V = volume of bubble, po = density of gases in bubble, p = density of liquid, q = dynamic viscosity of liquid, Vq = speed of bubble at equilibrium of the three forces. 

Statement of the problem. Let us consider the motion of a viscous fluid in an infinite layer of constant thickness 2h. The force of gravity is directed normally to the layer. The lower plane is a hard surface on which a constant temperature gradient is maintained. The nonuniformity of the temperature field results in two effects that can bring about the motion of the fluid, namely, the thermogravitational effect related to the heat expansion of the fluid and the appearance of Archimedes forces, and the thermocapillary effect (if the second surface is free) produced by tangential stresses on the interface due to the temperature dependence of the surface tension coefficient. 

Taking the inertialess approximation and neglecting the Archimedes force, we see that the equations of motion for the drop reduce to... 

The sinking depth e is such that Archimedes force offsets the weight of the drop. It is possible to relate e and e by writing that the hydrostatic pressures on either side of the liquid/liquid interface (assumed planar) are equal ... 

The Stokes experiment consists in dropping a spherical particle of diameter D where Ps>Pf The ball rapidly reaches a constant fall velocity Wc parallel to the gravitational acceleration g. When steady-state velocity is reached, the equilibrium of the forces applied on the ball reduces to the equilibrium between the reduced weight Fg (difference between the weight and Archimedes force) and the hydrodynamic drag force Fr exerted by the fluid flow on the particle. 

Since, by using the reduced weight, Archimedes force has been subtracted from the weight of the particles, the pressures used hereafter for momentum balance over... 

Particles in suspension in a liqnid medium are subjected to three kinds of forces (a) gravitation forces the particles to faU down, (b) viscosity of the liquid decreases the speed of their displacement and (c) Archimedes force is opposed to gravitation forces in this case. By applying fundamental relation of dynamics, the expression of the steady state sedimentation speed... 

Solution Two vertical forces operate on the boat in the lake the gravitational (mg) and extruded Archimedes force F both of them equaUze each other, therefore we do not need to consider them. We shall connect the inertial system of reference with the earth. We shall direct the coordinate axes horizontal. The equation of the Newtonian second law in aprojection to an axis x will be written as... 

Solution. Choose an axis vertically and denote an origin (J = 0 at the areometer tube prior to its oscillation (Figure E2.7,a). In this state its gravity and Archimedes force are equalized. Oscillations will be accomplished by the periodically changing Archimedes force because the gravity remains constant. The value of areometer s... 

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