Cylindrical pipes

Fig. 2. Friction factors for cylindrical pipe where line A represents drawn tubing line B, commercial steel C, galvanised iron and lines D, E, and F,...

This method [54] is for applications involving air or steam in cylindrical piping under conditions of (a) turbu-... 

FIGURE 31.4 Velocity distribution in the electroosmotic solution flow in a cylindrical pipe (pore). 

Perhaps the most simple flow problem is that of laminar flow along z through a cylindrical pipe of radius r0. For this so-called Poiseuille flow, the axial velocity vz depends on the radial coordinate r as vz (r) — Vmax [l (ro) ] which is a parabolic distribution with the maximum flow velocity in the center of the pipe and zero velocities at the wall. The distribution function of velocities is obtained from equating f P(r)dr = f P(vz)dvz and the result is that P(vz) is a constant between... 

Stainless steel coil and sheet stock is unloaded and stored outdoors under protective cover. As it is needed, the coil stock is moved indoors by a forklift to one of six automatic tube mills where the sides of unrolled metal strips are curled up to form a continuous, cylindrical pipe. The seam of the resulting pipe is fused in an electric in-line welding operation. An abrasive saw is used to cut the continuously formed pipe to specified lengths sections of poorly welded pipe are cut away. 

Consider a section of uniform cylindrical pipe of length L and radius R, inclined upward at an angle 0 to the horizontal, as shown in Fig. 6-2. The steady-state energy balance (or Bernoulli equation) applied to an incompressible fluid flowing in a uniform pipe can be written... 

For several years M. Delmotte et al. have designed a microwave reactor for high pressure chemistry [63]. The microwave applicator and reactor are identical in order to accommodate the mechanical constraints induced by high pressure within liquids. This is the main interest of this device. The metallic cylindrical pipe is simultaneously a waveguide and the reactor. The device is described by Fig. 1.15. 

An incompressible fluid flows upwards in steady state in a cylindrical pipe at an angle 8 with the horizontal. Assume that the head loss due to friction is negligible. 

APf/L for a liquid in steady state turbulent flow in a rough cylindrical pipe in terms of the liquid density p, the mean velocity u, the inside pipe diameter d, and the roughness e. (b) Use this to calculate AP//L for... 

A liquid flows in a steady state in a cylindrical pipe of inside diameter d, = 0.05 m at a flow rate Q = 2 x 10 3 m3/s. Calculate the head loss and the pressure drop for a sudden expansion to a pipe of inside diameter 0.1 m, if the liquid density p — 1000 kg/m3. 

Plot laminar and turbulent velocity profiles for steady state flow in a cylindrical pipe for a maximum velocity gm = 5 m/s using the radial positions 2r d - 0, 0.2, 0.4, 0.6 and 0.8. 

Example 2.2. Fluid is flowing through a constant-diameter cylindrical pipe sketched in Fig. 2.2. The flow is turbulent and therefore we can assume plug-flow conditions, i.e., each slice of liquid flows down the pipe as a unit. There are no radial gradients in velocity or any other properties. However, axial gradients can exist. 

Example 2.11. As an example of a force balance for a microscopic system, let us look at the classic problem of the laminar flow of an incompressible, newtonian liquid in a cylindrical pipe. By newtonian we mean that its shear force (resistance that adjacent layers of fluid exhibit to flowing past each other) is proportional to the shear rate or the velocity gradient. 

Figure 6 Heat transfer through a cylindrical pipe wall...

Hagen-Poiseuille equation — predicts the laminar flow of an incompressible and uniform viscous liquid (Newtonian fluid) through a cylindrical pipe of constant cross-section. The rate of movement of a liquid volume V, during a time t, may be predicted using ... 

In the extrusion die, the flow is driven simply by the pressure drop, as shown in Figure 13.23 and Figure 13.24. This type of flow can be analyzed relatively easUy, even for complicated rheological behavior. We will look at two geometries in detail flow between two flat plates and flow in the annular space between two cylinders. Both these geometries are used commonly to make floor tiles, cylindrical pipe pieces, and by cutting in half, semicylindrical roof tiles. 

Eggels, J. G. M., Direct and large eddy simulation of turbulent flow in a cylindrical pipe geometry, Ph.D. Thesis, Delft University (1994). 

The flow rate of a process stream may be expressed as a mass flow rate (mass/time) or as a volumetric flow rate (volume/time). Suppose a fluid (gas or liquid) flows in the cylindrical pipe shown below, where the shaded area represents a section perpendicular to the direction... 

A long cylindrical pipe (or spherical shell) with specified inner and outer surface temperatures 7", and Tz. 

Adding insulation to a cylindrical pipe or a spherical shell, however, is a different matter. The additional insulation increases the conduction re.sistance of... 

Consider a cylindrical pipe of outer radius r whose outer surface temperature T( is maintained constant (Fig. 3-30). The pipe is now insulated with a material whose thermal conductivity is k and outer radius is 12. Heat is lost from the pipe to the sunouuding medium at temperature T , with a convection heat transfer coefficient h. The rate of heat transfer from the insulated pipe to the surrounding air can be expressed as (Fig. 3-31)... 

An insulated cylindrical pipe exposed to convection from the outer surface and the thermal resistance network associated with it. 

In addition to the CSTR and batch reactors, another type of reactor commonly used in industry is the tubular reactor. It consists of a cylindrical pipe and is normally operated at steady state, as is the CSTR. For the purposes of the material presented here, we consider systems in which the flow is highly turbulent and the flow field may be modeled by that of plug flow. That is, there is no radial variation in concentration and the reactor is referred to as a plug-flow reactor (PFR). (The laminar flow reactor is discussed in Chapter 13.)... 

Let us consider now the deformation and stresses of a cylindrical pipe under two different boundary conditions (Fig. 16.2). In both eases the length of the pipe is considered constant according to the requirements for a plane strain problem. The external and internal radii are R2 and R, respectively. If the applied forces and the displacements are also uniform, the deformation is purely radial, and in cylindrical coordinates = u r). According to the Navier equations, rot u = 0. Hence, Vdiv u = 0, which implies... 

Figure 16.2. Cylindrical pipe with internal and external radii R] and i 2-...

With these premises, analytical solutions have been presented for the dense phase (M25, M29). The solutions show essential features of Taylor dispersion with chemical reaction, similar to the case treated by Cleland and Wilhelm and others (C8, S2, W15) for cylindrical-pipe flow (see M29). Here, the axial dispersion coefficient of gas affecting the steady reaction diminishes as the rate of chemical reaction increases, compared with the dispersion coefficient affecting axial mixing without accompanying chemical reaction. These solutions are general, but inconvenient for computation. Several simplifications have been discussed one simplification potentially applicable to the usual fluid-bed operations is to adopt the restriction ... 

Cylindrical pipe with dish end and bottom orifice... 

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