[u.sub.s](r) is steady parabolic velocity
of blood flow, which is relation to the corresponding Poiseuille flow velocity in steady blood flow; [u.sub.[phi]](r, t) represents the oscillatory velocity of blood flow in the rigid blood vessel; [u.sub.ave] is the average velocity of blood flow; [mu] is dynamic viscosity of blood; [eta] = [r.sub.0]/[square root of [mu]/[[rho].sub.b][[omega].sub.p]] is the Womersley number; fac characterizes the relative intensity of the pulsatile flow; [[omega].sub.p] is the angular frequency of heartbeat; [f.sub.p] = [[omega].sub.p]/2[pi] denotes the heartbeat frequency varied from 1 to 3Hz ; and [J.sub.0] is zero-order Bessel function of the first kind.
Though discussions in the above paragraph refer to entry length and entry conditions at the pipe entry, the discussions in Massey (1984) are associated with the formation and development of boundary layers up to a point where a uniform parabolic velocity
profile has been reached.
It is clear that the parabolic velocity
profile was developed in the pressure-driven flow.
In practice, the taper angle is higher at the top surface of the work piece where the jet has a parabolic velocity
The ratio [L.sub.e]/D [1.75/2.2] = 0.8 shows that a parabolic velocity
profile is fully developed about one-third of a diameter's length from the inhalant opening; hence entrance effects may be ignored.
In general, field-flow fractionation is employing a laminar flow of a carrier liquid between two walls, which are placed at a short distance from each other and creates a parabolic velocity
profile with zero carrier velocity at the walls and the maximum velocity along the centre axis of the so formed open channel.
The velocity field through the pipe is obtained and inlet length section [z.sub.L] is calculated after which a parabolic velocity
showed that the simplifying assumptions of parabolic velocity
profile, constant physical properties and isothermal operation conditions were sufficient to describe reasonably well the experimental dynamic behavior of a tubular reactor carrying out the solution polymerization of styrene, in spite of the significant flow distortions expected at the analyzed operation conditions, as computed with the help of a very detailed reactor model.
As the flow rate is constant in a cross-section of the channel, the parabolic velocity
profile is not influenced by the wall roughness.