Flow through curved pipes

If a pipe is not straight, the velocity distribution over the section is altered and the direction of flow of the fluid is continuously changing. The frictional losses are therefore somewhat greater than for a straight pipe of the same length. If the radius of the pipe divided by the radius of the bend is less than about 0.002, the effects of the curvature are negligible, however. 

White found that stable streamline flow persists at higher values of the Reynolds number in coiled pipes. Thus, for example, when the ratio of the diameter of the pipe to the diameter of the coil is 1 to 15, the transition occurs at a Reynolds number of about 8000. 

Friction losses occurring as a result of a sudden enlargement or contraction in the cross-section of the pipe, and the resistance of various standard pipe fittings, are now considered. 

Substituting from the relation mjAi = U2A2 into equation 3.76  

The loss can be substantially reduced if a tapering enlarging section is used. For a circular pipe, the optimum angle of taper is about 7° and for a rectangular duct it is about 11°. 

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Curved Pipes and Coils For flow through curved pipe or coil, a secondary circiilation perpendicular to the main flow called the Dean effect occurs. This circulation increases the friction relative to straight pipe flow and stabilizes laminar flow, delaying the transition Reynolds number to about... 

White, C.M., "Streamline Flow through Curved Pipes", Proc. Royal Soc., A 123, 645 (1929)... 

Curved Pipes and Coils For flow through curved pipe or coil, a... 

In 1963, Barua assumed that the flow through curved pipe consisted of an inviscid core plus a thin boundary layer, the flow in the core lay in planes parallel to the plane of symmetry he used Pohlhausen momentum integral method to solve the... 

White, C. M., Streamline Flow through Curved Pipes, Proc. Roy. Soc. (London), A123, 645-663 (1929). 

Plot the system-friction curve. Without static head, the system friction curve passes through the origin (0,0) (Fig. 6.22), because when no head is developed by the pump, flow through the piping is zero. For most piping systems, the friction-head loss varies as the square of the liquid flow rate in... 

In the long term, filters and strainers become clogged this is their purpose. Minerals and scale start forming on the internal pipe walls and this reduces the interior diameters on the pipe. A 4 inch pipe will eventually become a 3.5 inch pipe. This moves the pump on its curve beeause as the pipe diameter reduces, the velocity must increase to maintain flow through a smaller orifice. The Hf and Hv increase by the square of the velocity increase. 

The pump suction pressure is constant at 10 psig. The design flow rate is 500 gpm. At this flow rate the pressure drop over the flow orifice is 2 psi, through the piping is 30 psi, over three heat exchangers is 32 psi, and over the furnace is 60 psi. Assume a flat pump curve and a specific gravity of 1. 

Figure 7.4 Representations of hydrodynamic flow, showing (a) laminar flow through a smooth pipe and (b) turbulent flow, e.g. as caused by an obstruction to movement in the pipe. The length of each arrow represents the velocity of the increment of solution. Notice in (a) how the flow front is curved (known as Poiseuille flow ), and in (b) how a solution can have both laminar and turbulent portions, with the greater pressure of solution flow adjacent to the obstruction.

A 12-m length of pipe is packed with 1 m of 2-mm material, 9 m of 1-cm material, and 2 m of 4-mm material. Estimate the variance in the output C curve for a pulse input into this packed bed if the fluid takes 2 min to flow through the bed. Assume a constant bed voidage and a constant intensity of dispersion given by IMudp = 2. 

When a dilute gas-solid suspension flow passes through a curved pipe, the particle velocity is lowered by the wall friction, the effects of gravitation, and collision with the wall. The analysis of flows in pipe bends may be represented by three typical arrangements of bends ... 

Pump Characteristic and System Head. The pump characteristic curve needs to be matched with the head loss through a piping system, which is known as the system head. The system head increases approximately in proportion to the square of the flow rate (Ap cc z/2). An example of a system head calculation is given in Section 3.10. 

Table 1 lists the characteristics of the measured RTD for five different conditions. The first one is shown in Figure 2. The evolution of this curve can be explained by equation (1), although the peaks are not ideal Dirac pulses, because the flow inside the reactor (i.e. the reactor tube (c) and the recirculation pipe (d) in Figure 1) is not of the ideal plug flow type. Therefore, the tracer pulse broadens and eventually spreads throughout the reactor. Nevertheless, the distance between two peaks is a reasonably accurate estimate of the circulation time r/(R+1) in the reactor, and from this the flow through the reactor can be calculated. The recycle ratio R is calculated from the mean residence time r and the circulation time r/(R+l). 

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