Hydraulic length

The constant K, which maintains the equaUty, has been termed the hydraulic conductivity, permeabiUty, or simply conductivity. The permeabiUty is generally accepted to be a constant for a saturated soil, except for very small gradients (2—4). Here represents the hydraulic head at location whereas A/is the hydraulic length between points 1 and 2. is an area perpendicular to the discharge vector. In differential form... 

In sodium, corrosion rates have been shown to decrease as soon as heat input ceases to cause a temperature rise [7]. This phenomenon is known as the downstream effect and is applicable only in reference to isothermal zones. This effect is related to the hydraulic length-to-diameter ratio in the isothermal zone, and can be expressed c s UD, where L is the linear distance from the end of the temperature rise zone and D is the hydraulic diameter, defined as... 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

Hydraulic Gradient Hydraulic gradient, the head of hquid necessary to overcome the frictional resistance to hquid (froth) passage across the plate, is impoiTant for plate stabihty inasmuch as it is the only liquid head that varies across the length of passage. If the gradient is excessive, the upstream portion of the plate may be rendered inoperative because of increased resistance to gas flow caused by increased liqmd head (Fig. 14-34). In general the empirical criterion for stable operation is /j > 2.5/j/,g. 

Figure 11 shows a t pical liquid collector plate for a column that uses one side downcomer to withdraw the liquid. The maximum diameter for such a design is about 12 ft, which is limited by the hydraulic gradient necessary for such a liquid flow-path length, For larger diameter columns, two opposite side downcomers or a center downcomer normally is used unless the total amount of liquid collected is relatively small. 

Individual fins may be preformed and inserted over the tube, after which the mechanical bond may be obtained by either shrink fitting the fins onto the tube or by expanding the tube radially outward to make pressure contact with the fin material. The means to expand the tube may be hydraulic by pressurizing the tube beyond its yield point or it may be of a mechanical nature, in which an oversized ball or rod is pushed through the length of the tube, forcing the tube material outward against the fin. 

Darcy s law is considered valid for creeping flow where the Reynolds number is less than one. The Reynolds number in open conduit flow is the ratio of inertial to viscous forces and is defined in terms of a characteristic length perpendicular to flow for the system. Using four times the hydraulic radius to replace the length perpendicular to flow and conecting the velocity with porosity yields a Reynolds number in the form ... 

When dealing with water treatment applications you carmot avoid pipe flow calculations. We have a pipeline in which the throughput capacity of 500 Liter/sec. The flow is split into two pipelines and the inside diamter of the pipe is 350 mm. The length of the pipeline is 55 m. The entry loss is 0.70 and the exit loss is 1.00. There are two 45° bends and two 90° bends in the lines, (a) Determine the flow per pipe (b) determine the line velocity (c) determine the resulting hydraulic loss in meters. 

The characteristic length L denotes the pipe diameter or the hydraulic diameter djjyj = 4A/F A is the cross-sectional area and P is the wet periphery). If the cross-section is not circular, or in the case of a plane, the length is measured in the flow direction. 

This section provides a general overview of the properties of lake systems and presents tlie basic tools needed for modeling of lake water quality. The priiiciptil physical features of a lake are length, depth (i.e., water level), area (both of the water surface and of tire drainage area), and volume. The relationship betw een the flow of a lake or reserv oir and the volume is also an important characteristic. The ratio of the volume to the (volumetric) flow represents tlie hydraulic retention time (i.e., the time it would take to empty out the lake or reservoir if all inputs of water to the lake ceased). This retention time is given by the ratio of the water body volume and tire volumetric flow rate. 

For the narrow shapes with width small relative to length, the hydraulic radius is approximately [3] ... 

For other length-to-diameter ratio, refer to Ref. [27]. For cross sections other than circular or square, use the hydraulic diameter ... 

---