Streaming velocities

Application. Merriman ( The Method of Least Squares Applied to a Hydraulic Problem, y, Franklin Inst., 23.3-241, October 1877) reported on a study of stream velocity as a function of relative depth of the stream. 

Values of and m for various configurations are hsted in Table 5-5. The characteristic length is used in both the Nusselt and the Reynolds numbers, and the properties are evaluated at the film temperature = (tio + G)/2. The velocity in the Reynolds number is the undisturbed free-stream velocity. 

Modify the cross-sectional design (Fig. 6-35) the slot is thus farther away from the influence of feed-stream velocity. 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Flat Plate, Zero Angle of Ineidenee For flow over a wide, thin flat plate at zero angle of incidence with a uniform free-stream velocity, as shown in Fig. 6-47, the eritieal Reynolds number at which the boundaiy layer becomes turbulent is normally taken to be... 

D = diameter of cylinder or effective width of objecl V = free-stream velocity p = fluid density [L = fluid viscosity... 

The ionic mobility is the average velocity imparted to the species under the action of a unit force (per mole), i is the stream velocity, cm/s. In the present case, the electrical force is given by the product of the electric field V in V/cm and the charge per mole, where S" is the Faraday constant in C/g equivalent and Z is the valence of the ith species. Multiplication of this force by the mobihty and the concentration C [(g mol)/cm ] yields the contribution of migration to the flux of the ith species. 

The reaction turbine, shown schematically in Figure 2-2, is generally more efficient. In its primary (stationary) nozzles only half the pressure energy of the gas stream is converted to velocity. The rotor with a blade speed matching the full-jetted stream velocity receives this jetted gas stream. In the rotor blades the other half of the pressure energy is used to jet the gas backward out of the rotor and, hence, to exhaust. Because half the pressure drop is taken across the rotor, a seat must be created around the periphery of the rotor to contain this pressure. Also, the pressure difference across the rotor acts on the full rotor area and creates a large thrust load on the shaft. 

Finer particles ( < 3 pm), termed respirable particles, pass beyond the ex-trathoracic airways and enter the tracheobronchial tree. Impaction plays a significant role near the tracheal jet, but sedimentation predominates as the effects of rapid conduit expansion dampen in the distal trachea and beyond. Sedimentation occurs when gravitational forces exerted on a particle equal drag forces, i.e., when particle velocity falls to u . As mean inspiratory air-stream velocity gradually declines along the tracheobronchial tree, particle momentum diminishes and 0.5-3 pm MMAD particles settle out of the airflow and onto mucosal surfaces. 

It is seen that it is important to be able to determine the velocity profile so that the flowrate can be calculated, and this is done in Chapter 3. For streamline flow in a pipe the mean velocity is 0.5 times the maximum stream velocity which occurs at the axis. For turbulent flow, the profile is flatter and the ratio of the mean velocity to the maximum... 

A boundary layer close to the surface in which the velocity increases from zero at the surface itself to a near constant stream velocity at its outer boundary. 

A region outside the boundary layer in which the velocity gradient in a direction perpendicular to the surface is negligibly small and in which the velocity is everywhere equal to the stream velocity. 

The thickness of the boundary layer may be arbitrarily defined as the distance from the surface at which the velocity reaches some proportion (such as 0.9, 0.99, 0.999) of the undisturbed stream velocity. Alternatively, it may be possible to approximate to the velocity profile by means of an equation which is then used to give the distance from the surface at which the velocity gradient is zero and the velocity is equal to the stream velocity. Difficulties arise in comparing the thicknesses obtained using these various definitions, because velocity is changing so slowly with distance that a small difference in the criterion used for the selection of velocity will account for a very large difference in the corresponding thickness of the boundary layer. 

It is convenient first to consider the flow over a thin plate inserted parallel to the flow of a fluid with a constant stream velocity us. It will be assumed that the plate is sufficiently wide for conditions to be constant across any finite width w of the plate which is being considered. Furthermore, the extent of the fluid in a direction perpendicular to the surface is considered as sufficiently large for the velocity of the fluid remote from the surface to be unaffected and to remain constant at the stream velocity m.,. Whilst part of the fluid flows on one side of the flat plate and part on the other, the flow on only one side is considered. 

That the stream velocity does not change in the direction of flow. On this basis, from Bernoulli s theorem, the pressure then does not change (that is, dP/dx — 0). In practice, 3P/ dx may be positive or negative. If positive, a greater retardation of the fluid will result, and the boundary layer will thicken more rapidly. If dP/ dx is negative, the converse will be true. 

At the distant edge of the boundary layer it is assumed that the velocity just equals the main stream velocity and that there is no discontinuity in the velocity profile. 

This relation for the thickness of the boundary layer has been obtained on the assumption that the velocity profile can be described by a polynomial of the form of equation 11.10 and that the main stream velocity is reached at a distance 8 from the surface, whereas, in fact, the stream velocity is approached asymptotically. Although equation 11.11 gives the velocity ux accurately as a function of v, it does not provide a means of calculating accurately the distance from the surface at which ux has a particular value when ux is near us, because 3ux/dy is then small. The thickness of the boundary layer as calculated is therefore a function of the particular approximate relation which is taken to represent the velocity profile. This difficulty cat be overcome by introducing a new concept, the displacement thickness 8. ... 

If the velocity profile is the same for all stream velocities, the shear stress must be defined by specifying the velocity ux at any distance y from the surface. The boundary layer thickness, determined by the velocity profile, is then no longer an independent variable so that the index of < in equation 11.25 must be zero or ... 

The procedure here is similar to that adopted previously. A heat balance, as opposed to a momentum balance, is taken over an element which extends beyond the limits of both the velocity and thermal boundary layers. In this way, any fluid entering or leaving the element through the face distant from the surface is at the stream velocity u and stream temperature 0S. A heat balance is made therefore on the element shown in Figure 11.10 in which the length l is greater than the velocity boundary layer thickness S and the thermal boundary layer thickness t. 

If equation 12.29 is applied to the outer edge of the boundary layer when y = S (boundary layer thickness) and ux = us (the stream velocity), then ... 

The quantity a, which is the ratio of the velocity at the edge of the laminar sub-layer to the stream velocity, was evaluated in Chapter 11 in terms of the Reynolds number for flow over the surface. For flow over a plane surface, from Chapter 11 ... 

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Besides pure chemical corrosion, solid products of corrosion in the system will give rise to erosive corrosion, in which the particles moving with the fluid will impact onto the surfaces and can remove protective surface layers. Such corrosion effects are most pronounced in regions of high fluid-stream velocity. 

If the vapor stream velocity exceeds this value, vapor cannot easily get away and thus a partial vapor blanketing (film boiling) may occur. This result is used to predict the maximum heat flux by relating the heat flux to the vapor velocity (see Sec. 2.4.4). 

It will be noted that asp2 is greater than pu v2 must be less than v and W2 (known as the streaming velocity) is positive, meaning that the explosion products travel in the same direction as the detonation wave. This positive streaming velocity is a characteristic and identifying property of a detonation wave. 

Compound Density Energy Streaming velocity Velocity of detonation (m s ) ... 

Explosive Density (g ml 1) Detonation velocity (ms 1) Streaming velocity (ms1) Detonation pressure (10 Pa)... 

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