Prandtl tube

Pitot-static traverse The set positions of a Prandtl tube m a duct run required to provide a statistically valid set of readings, A series of measurements of the torn 1 and static pressure taken across an area of a duct to determine the air veloc-it> at that point. The sampling distance should be at least 7.5 times the diameter of the duct away from any disturbances of air flow. 

Pitot-static tube A measuring device consisting of two concentric tubes used to measure the total and static pressures in a duct run, known as a Prandtl tube. 

The burning rate (kg fuel/h) is not constant over the combustion cycle. However, since a fan is used for the air supply to the boiler the actual flue gas flow does not vary too much with time. Based on calculations from the total fuel consunqition and oxygen content in the flue gas and on measurements using a Prandtl-tube in the chimney, the average flue gas flow was estimated to be 100 m /h. 

Nowadays, non-invasive tomographic methods, such as NMR spectroscopy, are used to reveal hydrodynamics [19] and temperature profiles [20] in CEC capillaries. The EOF in CEC is in the microliter or nanoliter per second range and can be measured by weighing the mass of eluent transferred, by determining the zeta potential or the current under different EOF conditions and evaluating the residence time of neutral markers (e.g. alcohols). Otherwise, miniaturized flow sensors comprising Prandtl tubes, piezoelectric elements, etc., can be used (21). 

Circular Tubes Numerous relationships have been proposed for predicting turbulent flow in tubes. For high-Prandtl-number fluids, relationships derived from the equations of motion and energy through the momentum-heat-transfer analogy are more complicated and no more accurate than many of the empirical relationships that have been developed. 

V. Tubes, turbulent, smooth tubes, constant surface concentration, Prandtl analogy... 

A = Surface area ft based on tube ID C = Gas specific heat. Btu/lb°F d = Tube inner diameter, in. k = Gas thermal conductivity, Btu/ft-h°F L = Tube length, ft N = Total number of tubes in boiler Pr = Gas Prandtl number Q = Duty of the boiler. Btu/h... 

J4 = Colburn factor given by equation proposed by Pierce length of tube, m = Prandtl number Reynolds number = velocity, m/sec p = dynamic viscosity, sPa (pascal-sec) p = density, kg/m b = evaluate at bulk temperature w = evaluate at wall temperature kg = kilogram... 

Figure 10-67A has been initially represented by McAdams from several investigators. This figure represents the mean coefficient for the entire vertical tube for two values of the Prandtl number, Pq, which = cp/k. 

Figure 10-67B. Correlation of McAdams representing the condensing film coefficient on the outside of vertical tubes, integrated for the entire tube length. This represents the streamline transition and turbulent flow conditions for Prandtl numbers 1 and 5. Do not extrapolate Prandtl numbers, Pr beyond 5. (Used by permission Engineering Data Book II 1984, Wolverine Tube, Inc.)...

Derive the Taylor-Prandtl modification of the Reynolds Analogy between momentum and heat transfer. In a shell and tube condenser, water flows through the tubes which are 10m long and 40 mm diameter. The... 

Thus at small Pol the growth rate of the oscillations is negative and the capillary flow is stable. The absolute value of sharply increases with a decrease of the capillary tube diameter. It also depends on the thermal diffusivity of the liquid and the vapor, as well as on the value of the Prandtl number. 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

Deissler, R. G., 1955, Analysis of Turbulent Heat Transfer, Mass Transfer, and Friction in Smooth Tubes at High Prandtl and Schmidt Numbers, NACA Rep. 1210, Lewis Res. Ctr., Cleveland, OH. (5)... 

Equation (6-37) represents the friction factor for Newtonian fluids in smooth tubes quite well over a range of Reynolds numbers from about 5000 to 105. The Prandtl mixing length theory and the von Karman and Blasius equations are referred to as semiempirical models. That is, even though these models result from a process of logical reasoning, the results cannot be deduced solely from first principles, because they require the introduction of certain parameters that can be evaluated only experimentally. 

For turbulent flow in smooth tubes, the semiempirical Prandtl-von Karman/Nikuradse or Blasius models represent the friction factor quite well. Whether a tube is hydraulically smooth or rough depends upon... 

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

Mathematical formulation of Prandtl-Meyer flow is given in Ref 66, p.p 162—64, equations 5.3 1 to 5.3.25 inclusive. In Fig 34 is shown the Prandtl-Meyer flow within a steady- deton zone characteristics are solid lines and stream lines are dashed line AB is the shock front, r = ratio of radius of axial stream tube to its initial radius and c = sound speed... 

In order to obtain the coefficient and the two exponents —0.7), Rohsenow used experimental data for five systems water boiling on a 0.024-in.-diam. platinum wire (Al), water on a 1.5-in.-diam. horizontal tube (C6), and benzene, ethyl alcohol, and n-pentane on a chromium-plated horizontal surface (C2). The exponents for the Reynolds and Prandtl numbers were constant at % and —0.7 as shown. Unfortunately the coefficient varied from 0.006 to 0.015 from system to system. 

Deissler (D3) recently extended the analysis of thermal and material transfer associated with turbulent flow in tubes to include the behavior of fluids with high molecular Prandtl and Schmidt numbers. If the variation in molecular properties of the fluid with position are neglected, the following expression for the temperature distribution was suggested (D3) ... 

Water is flowing through a 150 mm diameter pipe and its flowrate is measured by means of a 50 mm diameter orifice, across which the pressure differential is 2.27 x 104 N/m2. The coefficient of discharge of the orifice meter is independently checked by means of a pitot tube which, when situated at the axis of the pipe, gave a reading of 100 mm on a mercury-under-water manometer. On the assumption that the flow in the pipe is turbulent and that the velocity distribution over the cross-section is given by the Prandtl one-seventh power law, calculate the coefficient of discharge of the orifice meter. 

Dipprey, D.F. and Sabersky, R.H., Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers , Int. /. Heat Mass Transfer, Vol. 5, pp. 329-353, 1963. 

Equation (5-114) is called the Reynolds analogy for tube flow. It relates the heat-transfer rate to the frictional loss in tube flow and is in fair agreement with experiments when used with gases whose Prandtl numbers are close to unity. (Recall that Pr = 1 was one of the assumptions in the analysis.)... 

In heat-exchanger applications, it is frequently important to match heat-transfer requirements with pressure-drop limitations. Assuming a fixed total heat-transfer requirement and a fixed temperature difference between wall and bulk conditions as well as a fixed pressure drop through the tube, derive expressions for the length and diameter of the tube, assuming turbulent flow of a gas with the Prandtl number near unity. 

Equation (6-4) is valid for fully developed turbulent flow in smooth tubes for fluids with Prandtl numbers ranging from about 0.6 to 100 and with moderate temperature differences between wall and fluid conditions. 

Suppose a number of experiments are conducted with measurements taken of heat-transfer rates of various fluids in turbulent flow inside smooth tubes under different temperature conditions. Different-diameter tubes may be used to vary the range of the Reynolds number in addition to variations in the mass-flow rate. We wish to generalize the results of these experiments by arriving at one empirical equation which represents all the data. As described above, we may anticipate that the heat-transfer data will be dependent, on the Reynolds and Prandtl numbers. An exponential function for each of these parameters is perhaps the simplest type of relation to use, so we assume... 

Note that the relation in Eq. (6-12) is the same as Eq. (5-114), except that the Stanton number has been multiplied by Pr2/3 to take into account the variation of the thermal properties of different fluids. This correction follows the recommendation of Colburn [15], and is based on the reasoning that fluid friction and heat transfer in tube flow are related to the Prandtl number in the same way as they are related in flat-plate flow [Eq. (5-56)]. In Eq. (6-12) the Stanton... 

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