Thus the velocity differences velocity gradient are the main measure of regional contraction, and has become the most important employment of colour tissue Doppler, in the method of strain rate imaging.
22.
A difficulty arises in that the laser sheets should be maintained close enough together so as to approximate a two-dimensional plane, yet offset enough that meaningful velocity gradients can be found in the z-direction.
23.
By tradition it has become traditional to use the Velocity gradient, but in integrating strain rate it is converted to Lagrangian strain by the formula "'? L = e ? E-1 " '.
24.
Where \ tau = shear stress; \ tau _ y = yield stress; H = Magnetic field intensity \ eta = Newtonian viscosity; \ frac { dv } { dz } is the velocity gradient in the z-direction.
25.
In 1843 he published the correct derivation of the Navier Stokes equations for a viscous flow and was the first to " properly identify the coefficient of viscosity and its role as a multiplying factor for the velocity gradients in the flow ".
26.
The boundary conditions to obtain the solution for the two differential equations presented above are that the velocity gradient is zero in the tube center, no slip occurs at the tube wall and the velocity and the shear stress are continuous at the interface between the two zones.
27.
In ultrasound it is usually measured from the velocity gradient "'SR = ( v 2-v 1 ) L "'where v 2 and v 1 are the myocardial velocities at two different points, and L is the instantaneous distance between them.
28.
A mean-flow velocity gradient ( shear flow ) creates an additional, additive contribution to the inertial subrange pressure spectrum which varies as " k " " 11 / 3; but the " k " " 7 / 3 behavior is dominant at higher wavenumbers.
29.
The Newton's constitutive law, for any general geometry ( including the flat plate above mentioned ), states that shear tensor ( a second-order tensor ) is proportional to the flow velocity gradient ( the velocity is a vector, so its gradient is a second-order tensor ):
30.
For fluids that are sufficiently dense to be a continuum, do not contain ionized species, and have flow velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier Stokes equations which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on flow velocity gradients and pressure.
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