It follows that the flow on both sides of the interface between the two liquids, which extend above the plane can be irrotational only if one of the fluids is in a quiescent state, but for a different angle is 120 °. Otherwise, the liquid must have the same density and velocity, and the interface should be perpendicular to the boundary.
The tension in the fluid in pure shear (gradient) for no stretching along the fluid flow lines, described by the second of equations. It shows that the shear stress is proportional to viscosity and the value of the shift.
If the liquid in a cylindrical vessel, which has a viscosity (x is rotated about a vertical axis with a tangential velocity v, equal to k / r, then this motion is irrotational, as it has the potential q> = k lg g, and the momentum of the cylindrical shell of a given mass and radius r is independent of torque shear stresses between the cylindrical volume of the liquid and the wall of the vessel does not depend on r, since it is proportional ts2pg-r (dvfdr),
The same distribution of velocities is set around a solid rotating cylinder placed in a large jar. Velocity of the fluid between two solid cylinder of radius r, and r2, rotating with angular velocities fii and Q2, obtained by adding the velocity of irrotational motion and rotation of a rigid body, which do not occur in the fluid shear stress.
Therefore, the flow in a plane parallel to the wall, irrotational. It is the same in all planes parallel to the wall, but the speed and the width of the gap varies. Since the potential flow is unique for the given boundary conditions, the two-dimensional irrotational flow around obstacles can be played in the gap between the parallel plates, placing them between the corresponding obstruction. Such a device is called a Hele-Shaw cell. Visualization of the streamlines in it is achieved by having tinted liquid.
The same principle is at the basis of the law of the Kings for the flow through a porous medium:
v = - O grad p.
This law is valid in three dimensions. It is assumed that the indicated flow must obey Darcy's law, as it is directed against the pressure gradient is proportional to the ratio of porosity and slow enough to justify the neglect of the forces of inertia. |