Radial velocity calculations

The point sink can approximate airflow near a hood with round or square/rectangular shape. The point sink will draw air equally from all directions (Fig. 7.83). The radial velocity (mys) at a distance r (m) from the sink can be calculated as a volume rate of exhaust airflow q (mVs) divided by the surface area of an imaginary sphere of radius r ... 

In order to calculate 0> it is necessary to evaluate ur and u, for the region outside the central core. The radial velocity ur is found to be approximately constant at a given radius and to be given by the volumetric rate of flow of gas divided by the cylindrical area for flow at the radius r. Thus, if G is the mass rate of flow of gas through the separator and p is its density, the linear velocity in a radial direction at a distance r from the centre is given by ... 

Carlos and Latif both fluidised glass particles in dimethyl phthalate. Data on the movement of the tracer particle, in the form of spatial co-ordinates as a function of time, were used as direct input to a computer programmed to calculate vertical, radial, tangential and radial velocities of the particle as a function of location. When plotted as a histogram, the total velocity distribution was found to be of the same form as that predicted by the kinetic theory for the molecules in a gas. A typical result is shown in Figure 6.11(41 Effective diffusion or mixing coefficients for the particles were then calculated from the product of the mean velocity and mean free path of the particles, using the simple kinetic theory. 

With Eq. (6.4), the radial distance of the position where the maximum radial velocity of gas flow appears, rmax, can be calculated to be 1.974 times the diameter of the accelerating tube, R.dC. Assume the particles are carried out of the impingement zone at r = 1.974R.dC with an initial radial velocity of zero. From the force balance, the movement equations of sphere particles after leaving the impingement zone can be obtained as... 

Work on the fluid mechanics of radial flow reactors can be traced back to the calculations of radial velocity profiles by Soviet investigators (1,2). This analysis was later repeated by... 

The velocities of liquid water and gas are calculated from Darcy s law, and the radial velocities are expressed as ... 

Radial velocity U can be derived from the assumption of ideal fractiod of the bed can be calculated below ... 

In the case of radial velocity (b), the magnitude of the required additional force can be calculated from the rate at which energy must be added to (or removed from) the parcel. (Recall that energy per time is power.) A fixed observer can see that the velocity of the parcel, and hence its kinetic energy, must increase as it moves radially outward and its tangential velocity increases. 

This equation assumes that the liquid velocity can instantaneously adjust to the balance drag against centrifugal force. This assumption has been shown to be a reasonable one. Burns et al. and Eq. (2) can be used as the starting point for film thickness modeling. The fully synchronized flow model can be used to provide reasonable estimates for a wide range of measures that characterize the flow over the spinning disk. The first of these is the radial velocity of the film at radius r that can be calculated from... 

Solve for the flow of a Newtonian fluid in a pipe, following the example. Plot the shear rate as a function of radial position. Calculate the average velocity. Plot the shear stress as a function of radial position. 

Solve the flow of a non-Newtonian fluid in a pipe, following the example, for pressure drops of 10, 10, 10, and 10 Pa. The parameters are tjq = 0.492 Pa s, A = 0.1 and n = 0.8. Plot the shear rate as a function of radial position. Calculate the average velocity. Plot the shear stress as a function of radial position. How do these curves change as the pressure drop is increased ... 

Co(ti/2 = 18 hr) are produced in explosive, incomplete Si burning as well as in normal freezeout of nuclear statistical equilibrium, in the inner ejecta of core collapse supernovae. However, no evidence of the 5.9 keV line emission from Mn could be found in 400 ks of Chandra ACIS data and the upper limit to the mean flux was < 3 x 10-7 cm-2s-1. Rauscher et al. [148] calculated the ejected mass of A = 55 radioactive nuclei to be 7.7 x 10 4 M for 20M models of which most was 55 Co. If only about half this mass of55Fe were ejected, the reduced flux would be consistent with the observed upper limit. On the other hand, even if the total mass inside were as much as 1 x 10-3 M , but the 55 Fe abundance was zero outside the radial velocity shells at 1500 kms-1, the line flux would be still consistent with data, as at late times the emerging flux depends sensitively on the presence of 55Fe in the outer zones. 

Collision efficiency was calculated by the method proposed for the first time by Dukhin Derjaguin (1958). To calculate the integral in Eq. (10.25) it is necessary to know the distribution of the radial velocity of particles whose centre are located at a distance equal to their radius from the bubble surface. The latter is presented as superposition of the rate of particle sedimentation on a bubble surface and radial components of liquid velocity calculated for the position of particle centres. Such an approximation is possibly true for moderate Reynolds numbers until the boundary hydrodynamic layer arises. At a particle size commensurable with the hydrodynamic layer thickness, the differential of the radial liquid velocity at a distance equal to the particle diameter is a double liquid velocity which corresponds to the position of the particle centre. Such a situation radically differs from the situation at Reynolds numbers of the order of unity and less when the velocity in the hydrodynamic field of a bubble varies at a distance of the order ab ap. At a distance of the order of the particle diameter it varies by less than about 10%. Just for such conditions the identification of particle velocity and liquid local velocity was proposed and seems to be sufficiently exact. In situations of commensurability of the size of particle and hydrodynamic boundary layer thickness at strongly retarded surface such identification leads to an error and nothing is known about its magnitude. 

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