Streaming velocity calculated

In equation 12, k is the Boltzman constant and m is the atomic mass. The stream velocity is not a constant quantity for any given gas, but varies by less than 5% for Mach numbers in the range 6 - < . For He, v is found to equal 1.78 x lO cm s. Stream velocities calculated from these simple relationships are found experimentally to be accurate to better than 1%. ... 

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... 

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. ... 

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. 

Water flows through a 45° expansion pipe bend at a rate of 200 gpm, exiting into the atmosphere. The inlet to the bend is 2 in. ID, the exit is 3 in. ID, and the loss coefficient for the bend is 0.3 based on the inlet velocity. Calculate the force (magnitude and direction) exerted by the fluid on the bend relative to the direction of the entering stream. 

Table 12.1 Calculated characteristic reaction time tc, residence time tr, and the Mikhelson number Mi for the combustion of the stoichiometric methane-air mixture in a combustor with the open-edge V-gutter flame holder of height H and apex angle 60° at the mean inlet velocity Uin. Also presented is the maximum approach-stream velocity Um- Signs and correspond to stabilized flame and unstable flame, respectively... 

Momentum boundary layer calculations are useful to estimate the skin friction on a number of objects, such as on a ship hull, airplane fuselage and wings, a water surface, and a terrestrial surface. Once we know the boundary layer thickness, occurring where the velocity is 99% of the free-stream velocity, skin friction coefficient and the skin friction drag on the solid surface can be calculated. Estimate the laminar boundary layer thickness of a 1-m-long, thin flat plate moving through a calm atmosphere at 20 m/s. 

Data predictions for droplets moving freely in turbulent gas streams are confounded by the problem of ballistics of droplets. Until the droplet is essentially accelerated or decelerated to the gas stream velocity, Reynolds number, thus Nusselt number, and thus X are changing constantly, and precise calculations require very small steps. The drag coefficient is of considerable importance. El Wakil, Uyehara, and Myers (117) em-... 

In Chapter 2, Eqs (2-9) to (2-11) giving the terminal velocity of particles may be used to calculate the velocities required to move such particles through vertical pipes. The velocities calculated by these formulas are those required to support the particles in a vertical fluid stream. Motion in the direction of the moving stream will be imparted when the velocities exceed the calculated amounts. Little is known with regard to velocities for horizontal transportation of particles. In general, velocities capable of moving particles vertically will be more than sufficient for horizontal transportation. 

The program, as available, will calculate flow over a surface with a varying free-stream velocity and varying surface temperature. These variations are both assumed to be described by a third-order polynomial, i.e., by ... 

Calculate the heat transfer from a 30-cm-square plate over which air flows at 35°C and 14 kPa. The plate temperature is 250°C, and the free-stream velocity is 6 m/s. 

Air at 1 atm and 27°C blows across a 12-mm-diameter sphere at a, free-stream velocity of 4 m/s. A small heater inside the sphere maintains the surface temperature at 77°C. Calculate the heat lost by the sphere. 

Air at 207 kPa and 200°C enters a 2.5-cm-ID tube at 6 m/s. The tube is constructed of copper with a thickness of 0.8 mm and a length of 3 m. Atmospheric air at 1 atm and 20°C flows normal to the outside of the tube with a free-stream velocity of 12 m/s. Calculate the air temperature at exit from the tube. What would be the effect of reducing the hot-air flow in half ... 

Dry air at atmospheric pressure blows over an insulated flat plate covered with a thin wicking material which has been soaked in ethyl alcohol. The temperature of the plate is 25°C. Calculate the temperature of the airstream assuming that the concentration of alcohol is negligible in the free stream. Also calculate the mass-transfer rate of alcohol for a 30-cm-square plate if the free-stream velocity is 7 m/s,... 

In order to calculate the flow we must know something about the distribution of molecular velocities in the gas. Since the gas is not at equilibrium but only in a steady state, we cannot say that we have an equilibrium distribution. However we can make the approximation of assuming that the velocity distribution is flocally Maxwellian, i.e., that the molecules at any given point distant Z from the fixed plate have the normal distribution of velocities with respect to an average which is not zero but is given by the macroscopic stream velocity at that point. Thus at a point Z from the fixed plate the distribution is to be taken as... 

Up = Eve + (Pe - V elte where the subscripts (e) refer to exit quantities, and the subscript (a) refers to ambient quanth ties V = product stream velocity, p - static pressure, A = area, m= rate of mass flow g = gravitational acceleration (Ref 1). Typical values of ISp for ordinary systemsis 200-270 lb-sec/lb and 270-400 lb-sec/lb for high-energy systems (Ref 2). Theoretical calculations of lSp (based on thermodynamics thermochemistry) are in good agreement with experimental measurements (Ref 3)... 

In the molecular dynamics calculations the trajectories of methane molecules in the pore are followed using the equation of motion with appropriate temperature control. A diffuse reflection condition is applied at the pore wall. For the EMD simulations a collective transport coefficient obtained from autocorrelation of the fluctuating axial streaming velocity via a Green-Kubo relation [S]... 

We notice from Eq. (1) that the wall shear stress x is constant within the laminar boundary layer, and for this case is 0.25 dyne/ cm. As far as calculation of the wall shear stress for a known stream velocity is concerned, we point out that the use of Fanning s factor alone suffices to determine its value, and we do not need all the formulas stated above. 

Figure 7. The theoiy of rolling developed for turbulent flow conditions can used to calculate (at 300 bars) the radius of the smallest particle that can be moved as a function of the stream velocity for 325 K solid line) and 375 K dashed line). Notice the sensitivity to temperature. Velocities of 100 cm/s to 200 cm/s are needed to move particles with a radius of about a tenth of a micron.

The most immediate way of calculating viscosities and studying flow properties by molecular dynamics is to simulate a shear flow. This can be done by applying the SLLOD equations of motion [8]. In angular space they are the same as the ordinary equilibrium Euler equations. In linear space one adds the streaming velocity to the thermal motion,... 

When wood particles are introduced in the CFB, they stay in the bottom part of the bed, considered as the dense bed, until their terminal velocity becomes small enough to carry them up the riser with the gas stream. The transport of large particles in the riser occurs not only due to the drag force of the gas but also due to the impact of the fine sand particles on the large wood particles. Geldart et al. [II] demonstrated that particles are elutriated when the gas velocity in the riser is larger than the terminal velocity calculated with an elTective gas density. This effective density can be calculated as ... 

Larger structures have lower calculated deposition velocities as a result of their larger Reynolds numbers. This effect will be partially countered by higher free-stream velocities for taller structures. Blunt objects will tend to have lower average deposition as a result of their zones of separated flow. This may not pertain to local hot spots, however. 

This important result is known as Faxen s law.22 According to this law, if we specify the undisturbed velocity u°°(x), then the force on a sphere can be calculated directly from the formula (8-220), without any need to actually solve the flow problem corresponding to the free-stream velocity u°°(x). 

An example of how the model works is shown in Figure 252, in which a typical commercial activation is represented. 273 kg of Cr/silica was charged to an activator. The catalyst was heated to 800 °C at the standard linear ramp rate of 1.4 °C min 1 and an air velocity of 6.4 cm s Then the temperature was held at 800 °C for 12 h. To obtain a predicted conversion, the activation profile (temperature vs. time) was first plotted (Figure 252) and the concentration of water vapor in the gas stream was calculated from the temperatures shown in the plot and a library of laboratory TGA curves that indicate how much water is evolved at each temperature and heat-up rate. The conversion of the chromium to Cr(VI) was calculated at each temperature from the calculated concentration of water vapor by use of the stability curves shown in Figure 251. The Cr(VI) content was found to be high when the temperature reached 500 °C, but it dropped quickly as the temperature was raised, reaching only 0.37% Cr(VI) at 800 °C (Figure 252). 

This expected linearity is usually experimentally confirmed. A theoretical prediction of the size of the linear rate constant in Eq. (6) for a given temperature and composition of medium and material is possible, when thermodynamic data are available to calculate the reaction, and boundary parameters such as the geometry of the sample, viscosity, stream velocity, Schmidt and Reynold s numbers are known or can be estimated [16]. 

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