Flowing pressure , velocity

The second mechanism can be explained by the wall liquid film flow from one meniscus to another. Thin adsorptive liquid layer exists on the surface of capillary channel. The larger is a curvature of a film, the smaller is a pressure in a liquid under the corresponding part of its film. A curvature is increasing in top s direction. Therefore a pressure drop and flow s velocity are directed to the top. 

Fan Rating. Axial fans have the capabiUty to do work, ie, static pressure capabiUty, based on their diameter, tip speed, number of blades, and width of blades. A typical fan used in the petrochemical industry has four blades, operates neat 61 m/s tip speed, and can operate against 248.8 Pa (1 in. H2O). A typical performance curve is shown in Figure 11 where both total pressure and velocity pressure are shown, but not static pressure. However, total pressure minus velocity pressure equals static pressure. Velocity pressure is the work done just to collect the air in front of the fan inlet and propel it into the fan throat. No useflil work is done but work is expended. This is called a parasitic loss and must be accounted for when determining power requirements. Some manufacturers fan curves only show pressure capabiUty in terms of static pressure vs flow rate, ignoring the velocity pressure requirement. This can lead to grossly underestimating power requirements. 

In contrast, various sensors are expected to respond in a predictable and controlled manner to such diverse parameters as temperature, pressure, velocity or acceleration of an object, intensity or wavelength of light or sound, rate of flow, density, viscosity, elasticity, and, perhaps most problematic, the concentration of any of millions of different chemical species. Furthermore, a sensor that responds selectively to only a single one of these parameters is often the goal, but the first attempt typically produces a device that responds to several of the other parameters as well. Interferences are the bane of sensors, which are often expected to function under, and be immune to, extremely difficult environmental conditions. 

Because of the complexity of designs and performance characteristics, it is difficult to select the optimum atomizer for a given appHcation. The best approach is to consult and work with atomizer manufacturers. Their technical staffs are familiar with diverse appHcations and can provide valuable assistance. However, they will usually require the foUowing information properties of the Hquid to be atomized, eg, density, viscosity, and surface tension operating conditions, such as flow rate, pressure, and temperature range required mean droplet size and size distribution desired spray pattern spray angle requirement ambient environment flow field velocity requirements dimensional restrictions flow rate tolerance material to be used for atomizer constmction cost and safety considerations. 

One-dimensional Flow Many flows of great practical importance, such as those in pipes and channels, are treated as onedimensional flows. There is a single direction called the flow direction velocity components perpendicmar to this direction are either zero or considered unimportant. Variations of quantities such as velocity, pressure, density, and temperature are considered only in the flow direction. The fundamental consei vation equations of fluid mechanics are greatly simphfied for one-dimensional flows. A broader categoiy of one-dimensional flow is one where there is only one nonzero velocity component, which depends on only one coordinate direction, and this coordinate direction may or may not be the same as the flow direction. 

Pressure drop in a venturi scrubber is controlled by throat velocity. While some venturis have fixed throats, marw are designed with variable louvers to change throat dimensions and control performance for changes in gas flow. Pressure-drop equations have been developed by Calvert (R-13, R-14, R-15), Boll [Ind Eng Chem Fundam, 12, 40 (1973)], and Hesketh [J. Air Pollut Control Assoc, 24, 939 (1974)]. Hollands and Goel [Ind Eng Chem Fundam, 14, 16 (1975)] have developed a generalized pressure-drop equation. 

Pressure drop in catalyst beds is governed by the same principles as in any flow system. Consequently, at very low flow, pressure drop is directly proportional to velocity, and at very high flow, to the square of velocity. These conditions correspond to the laminar and turbulent regimes of the flow. 

Figure 7-3 shows the pressure, velocity, and total enthalpy variation for flow through several stages of an axial compressor. As indicated in Figure 7-3,... 

As normally designed, vapor flow through a typical high-lift safety reliefs valve is characterized by limiting sonic velocity and critical flow pressure conditions at the orifice (nozzle throat), and for a given orifice size and gas composition, mass flow is directly proportional to the absolute upstream pressure. 

In the above equation, is the critical velocity (m/s), K is the ratio of specific heats (Cp/C ) at inlet conditions, P is the pressure in the restriction at critical flow conditions (KPa, absolute - Note that this term is known as the critical flow pressure ), and p, is the density of the fluid at the critical flow temperature and pressure (kg/m ). 

If the pressure Pj downstream of the restriction is less than the critical flow pressure, then the maximum obtainable flow which occurs at critical velocity is a function of P, and P but is unaffected by Pj. If Pj is greater than P , however, then the flow is termed "subcritical," and the rate is a function of P, and Pj. There are thus two equations for sizing PR valves in vapor service, depending on whether the flow is critical or subcritical. 

Flow parameter specified is one of mass flow, velocity, or pressure. Usually mass flow or velocity is taken, as these values are known for air supplies. 

Parameters specified are mass flow or velocity. Usually at one outlet, pressure equal to a constant is specified in incompressible flow. If several outlets are present, this pressure boundary condition can only be applied to one outlet, as there are some (unknown) pressure differences between the different outlets. The flow conditions in the rooms are better represented by taking the outlet mass flows when they are known. 

The first term on the right-hand side of Eq. (14.113) comes from the inertial forces. Because of the pressure drop the density of gas decreases in the di rection of the flow and therefore, on the basis of mass balance of gas flow, the velocity v increases along the flow. If the pipe is isolated, then the flow can be treated as adiabatic, which on the basis of energy balance implies that along the flow we have... 

Pressure, velocity The kinetic pressure exerted in the direction of flow that is necessary to cause a fluid at rest to flow at a given velocity. 

Future operation pressures Sizing of lines must consider operating pressures expected as the reser oir depletes. Diameter requirement calculations should be made using both initial and future conditions to determine the governing case. Often in gas and two-phase lines the greatest flow velocity occurs late in life when flowing pressures are low even though flow rates may be lower than initial conditions. 

Pj = shell-side pressure drop, psi friction factor, fP/ in. cross-flow mass velocity, lb/ (ft ) (hr) shell I.D., ft = number of baffles... 

For the computation of compressible flow, the pressure-velocity coupling schemes previously described can be extended to pressure-velocity-density coupling schemes. Again, a solution of the linearized, compressible momentum equation obtained with the pressure and density values taken from a previous solver iteration in general does not satisfy the mass balance equation. In order to balance the mass fluxes into each volume element, a pressure, density and velocity correction on top of the old values is computed. Typically, the detailed algorithms for performing this task rely on the same approximations such as the SIMPLE or SIMPLEC schemes outlined in the previous paragraph. 

From Table 3 it can be seen that by optimizing the configuration of pipeline, it is possible to reduce pressure loss, air flow, transport velocity, and hence, pipe/bend wear. Depending on hardware requirements and reliability, which would to some extent govern the maximum operating pressure of the system (e g., say, 400 or 500 kPag), Pipeline Nos. 5 or 6 could be selected for this long-distance application. However, if diverter valves are required at the end of the pipeline, it may be more convenient to select Pipeline No 5 (i.e., D1 = 154 mm instead of 203 mm). 

In turbulent flow, properties such as the pressure and velocity fluctuate rapidly at each location, as do the temperature and solute concentration in flows with heat and mass transfer. By tracking patches of dye distributed across the diameter of the tube, it is possible to demonstrate that the liquid s velocity (the time-averaged value in the case of turbulent flow) varies across the diameter of the tube. In both laminar and turbulent flow the velocity is zero at the wall and has a maximum value at the centre-line. For laminar flow the velocity profile is a parabola but for turbulent flow the profile is much flatter over most of the diameter. 

For potential flow, ie incompressible, irrotational flow, the velocity field can be found by solving Laplace s equation for the velocity potential then differentiating the potential to find the velocity components. Use of Bernoulli s equation then allows the pressure distribution to be determined. It should be noted that the no-slip boundary condition cannot be imposed for potential flow. 

The process parameters influencing droplet sizes may include liquid pressure, flow rate, velocity ratio of air to liquid (mass flow rate ratio of air to liquid), and atomizer geometry and configuration. It has been clearly established that increasing the velocity ratio of air to liquid is the most important practical method of improving atomization)211] In industrial applications, however, the use of mass flow rate ratio of air to liquid has been preferred. As indicated by Chigier)2111 it is difficult to accept that vast quantities of air, that do not come into any direct contact with the liquid surface, have any influence on atomization although mass flow rates of fluids include the effects of velocities. 

The next more complicated treatment of liquid water is to have a way in which to model also its transport without going to a two-phase model. The models of this sort assume that the liquid water exists as droplets that are carried along in the gas stream. - - Thus, while evaporation and condensation occur, a separate liquid phase does not have to be modeled. Instead, the liquid is assumed to be a component of the gas, and usually one that has a negligible effect on the gas-phase flow and velocity. There is a change in the gas-phase volume fraction due to the water, however. This type of model allows for the existence and location of liquid water to be noted, and to a limited extent the change in the water pressure or concentration. 

Shock Relationships and Formulas, which include Changes During Steady Reversible Compressible Flow (61-4) Pressure-Velocity Relationship (65-6) Irreversibility and Degradation (66-8) Derivation of Formulas (68-70) Pressure Efficiency Factor and Recovery Factor (70-2) and Oblique Shocks in Air (72). Shock Wave Interaction, which includes Strong Shock Waves (81) Superposition of Plane Shock Waves (81-2) ... 

Taylor (Ref 23) stated that ignition of TNT chge at some point inside the expl, results in a very rapid drop in pressure velocity behind the deton front. A fixed proportion of the whole vol of burnt gas is at rest and the radial rat e of change of the variables velocity, pressure density become finite at the deton front. The fact that the velocity drops to ze ro at some point between the deton surface the center shows that a spherical deton wave can maintain itself in the case of TNT. It is not known whether this is true in all cases Lutzky (Ref 86) determined the "Flow ... 

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