Flow coefficient calculation

Figure 17.8 Flow coefficients calculated at different aspect ratios for various shapes using the same equation...

The basic form of the equation is normally modified so that the differential is expressed in pressure units and the flow coefficient is divided into the product of an experimentally deterrnined discharge coefficient, iC, and a series of calculated coefficients. In this form, for concentric restrictions ... 

To reflect this type of reasoning, a KBS captures quaHtative relationships between variables. By contrast, a conventional program that implements the flow equation calculates the value of the flow rate for numerical values of the input variables, ie, orifice diameter, orifice coefficient, and Hquid height. 

Flow coefficients and pressure coefficients can be used to determine various off-design characteristics. Reynolds number affects the flow calculations for skin friction and velocity distribution. 

L sc the inlet and the last stage volume for the uncooled section and use the following equation to calculate the inlet flow coefficient 8. 

To obtain an efficiency for the geometry selected, the value of the flow coefficient must be calculated using Equation 5.19 for the first inlet and the last stage flow. 

Using the flow coefficients just calculated and Figure 5-26, the corresponding efficiencies may be looked up ... 

Willi the volumes just calculated, calculate the inlet flow coefficient fm each of the two stages using Equation 5.19. 

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. 

Figure 3.42 Evolution of a pulse at the entrance of a micro channel for different diffusion coefficients. Calculated concentration profile (left) and cumulative residence time distribution curve (channel 300 pm x 300 pm x 20 mm flow velocity 1 m s f = 10 s) [27],...

Batalla et al. [11] assessed the changes produced by reservoirs on monthly flows by means of a correlation coefficient calculated for each flow series (<2>pre post> where... 

Drag coefficient Q/l. .Re) is the drag coefficient calculated using the correlation for subsonic flow with Ma=l. f V/1.75, Re ) is the drag coefficient calculated using the correlation for supersonic flow with Ma00=1.75 Mach number based on relative velocity between gas and sphere ... 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

Calculate for both flow regimes I and II (Illustrative Example 24.1) the initial maximum atrazine concentration and its reduction at x = 10 km due to dispersion. Use the dispersion coefficients calculated in Illustrative Example 24.4. Remember that 200 kg of atrazine enters the river within 30 minutes. 

Fig. 7. kf versus linear flow rate calculated for BSA adsorption to fluidized controlled pore glass after Rowe (A, Eq. 19, Ref. 74) and after Fan et al. ( , Eq. 20, Ref. 75). Physical data of adsorbent average particle diameter 200 pm, average particle density 1240 kg/m3, BSA diffusion coefficient in solution 7.3-10 11 m2/s, bed expansion calculated according to Richardson and Zaki, U, and n estimated according to Eqs. (3-5)... 

The flow coefficient is constant for the system based mainly on the construction characteristics of the pipe and type of fluid flowing through the pipe. The flow coefficient in each equation contains the appropriate units to balance the equation and provide the proper units for the resulting mass flow rate. The area of the pipe and differential pressure are used to calculate volumetric flow rate. As stated above, this volumetric flow rate is converted to mass flow rate by compensating for system temperature or pressure. 

Van Zyl et al. reported on the diffusion of ipratropium through porcine bronchial epithelium tissue [74], In principle, ipratropium is administered via the respiratory tract by inhalation to treat pulmonary diseases associated with bronchoconstriction. Therefore, pulmonary absorption by bronchial tissue determines its local efficacy and was thus investigated in a diffusion cell in vitro. Bronchial epithelium was equilibrated in PBS and discs of 4 mm2 were mounted on that diffusion cell separating the donor and receiver compartment. The donor compartment contained the drug dissolved in PBS (1 mg/ml) and the receiving chamber was permanently flushed with a low flow (1.5 ml/h) of PBS thus allowing time-resolved fractionation for subsequent direct analysis by LC-ESI MS/MS in MRM mode. Transition to the product ion at m z 124 was monitored for quantification (Table 9). The transfer of ipratropium was characterized by the flux (about 220 ng/cm2/min) and the permeability coefficient calculated to be 1.6 x 10-8 cm/s. 

If the vapor to be condensed is superheated, the preceding equations may be used to calculate the heat-transfer coefficient, provided the heat flow is calculated on the basis of the temperature difference between the surface and the saturation temperature corresponding to the system pressure. When a noncondensable gas is present along with the vapor, there may be an impediment of the heat transfer since the vapor must diffuse through the gas before it can condense on the surface. The reader should consult Refs. 3 and 4 for more information on this subject. 

For shells with triple or double segmental baffles, the heat-transfer coefficient calculated for turbulent flow (DG/fi greater than 8000) should be multiplied by a value of 1.3. 

Related Calculations. The flow coefficient C of the usual 1-in-diameter (2.5-cm) double-seated control valve is 10. For any other size valve, the approximate C valve can be found from the product 10 x d2, where d is nominal body diameter of the control valve, in inches. Thus, for a 2-in-diameter... 

Already in a relatively early study, Evans [121] had concerned himself with the theoretical treatment of the diffusion process, according to which an injected dye is uniformly mixed in a turbulent pipe flow. He calculated the courses of the standardized concentration c/cg (cg is the average concentration after molecular mixing) over the standardized radius r/R for a uniform and for a parabolic distribution of diffusion coefficients and compared them with the measured concentration profiles at various distances along the mixing length... 

At the start of the calculations the liquid flow rates in the column, Q and E in Equation 12.45, may be assumed equal to the inlet feed and solvent rates. The initial values for the activity coefficients may also be based on the inlet compositions and thermal conditions of the streams. The temperature and pressure variations in the extractor column are usually small, but the compositions will vary, and this may require recalculating the activity coefficients. The column calculations may be repeated with updated values of Q and E, taken as respective averages of each phase inlet and outlet stream flow rates calculated in the first trial. The activity coefficients can also be refined by recalculating them at the column top and bottom compositions for each phase. Averages of the top and bottom coefficients for each phase can be used in Equation 12.47 to calculate the new E-values. The extraction factors are then recalculated with the new values of Q, L, and E by Equation 12.45. The product component flow rates E v and Q i are Anally calculated by Equations 12.43 and 12.44. If large variations appear between the first and second trials, more trials may be considered. 

IS A one-shell pass and multiple-of-two-tube-passes heat exchanger will be designed. Water flows at the rate of 360,000 kg/hr (Vc = 3 m/s) in the tubes (2 cm ID, 2.5 cm OD, k = 20 W/m-K). The inlet and outlet temperature of the water are Ta- = 10 "C and Tc0 = 65 °C, respectively. Ethylene glycol flows (Vs = 1.5 m/s) through the shell at the rate of 720,000 kg/hr [cp = 2 kJ/kg-K), and its temperature decreases from Tki = 180 C Evaluate the shell-side heat transfer coefficient on the basis of cross flow, (a) Calculate the heat transfer area, (b) Recalculate the exit temperatures after reducing the water flow rate to 240,000 kg/hr. 

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