Hydraulic slope

Consider a liquid flowing in an open channel of uniform cross section under the influence of gravity. The liquid has a free surface subjected only to atmospheric pressure. If the flow is steady, the depth of the liquid is uniform and the hydraulic slope of the free liquid surface is parallel to the slope of the channel bed. Consider a length AL in Figure 2.6 in which the... 

An important factor of the surface s role in the water balance is infiltration of precipitation into the soil both during rainfall and in run-off. The rate of water take-up by soil wSH is described by the formula wsll = ksl, where ks is the coefficient of filtration, and l is the hydraulic slope. Let us denote the volume mass of the soil as k, which, on average, varies from 1.4g/cm3 to 1.5g/cm3, then for ks it is convenient to use the Azizov formula ks = 256.32k-7 28-1.27k1 14 (cm/da). The parameter / can be calculated using formula l = (z0 + zj + z2)/z0, where z0 is the depth of the column that leaches out, zx is the capillary pressure, and z2 is the height of the... 

By hydraulic slope is meant the value of S, which is given by... 

It was found that the pressure gradient and flow friction in micro-channels were higher than that predicted by the conventional laminar flow theory. In a low Re range, the measured pressure gradient increased linearly with Re. For Re > 500, the slope of the /(c-Re relationship increases with Re. The ratio C was about 1.3 for micro-channels of hydraulic diameter 51.3-64.9pm and 1.15-1.18 for microchannels of hydraulic diameter 114.5-168.9pm. It was also found that the ratio of C depends on the Reynolds number. 

It is assumed that the moisture content of the soil has been determined to be approximately 50% under worst-case conditions. Using this information and the results from vendor tests, it has been determined that a minimum dose of one part solidification reagent to two parts soil is required for the migration control of lead. Testing has shown that the optimum solidification reagent mixture would comprise ca. 50% fly ash and ca. 50% kiln dust. Thus, ca. 7000 t (6364 T) each of fly ash and cement kiln dust would be required. The reagents would be added in situ with a backhoe. As one area of the soil is fixed, the equipment could be moved onto the fixed soil to blend the next section. It may be anticipated that the soil volume would expand by ca. 20% as a result of the fixation process. This additional volume would be used to achieve the required slope for the cap. An RCRA soil/clay cap placed over the solidified material is necessary to prevent infiltration and additional hydraulic stress on the fixed soil. It is estimated that the fixation would reduce lead migration by 40% and that the fixed soil may pass the U.S. EPA levels for lead. 

Saturated hydraulic conductivity >1CL 1 2 3 4 5 cm/s Bottom slope >2% (after settlement/subsidence)... 

Hydraulic fracturing fluids are solutions of high-molecular-weight polymers whose rheological behavior is non-Newtonian. To describe the flow behavior of these fluids, it is customary to characterize the fluid by the Power Law parameters of Consistency Index (K) and Behavior Index (n). These parameters are obtained experimentally by subjecting the fluid to a series of different shear rates (y) and measuring the resultant shear stresses (t). The slope and Intercept of a log shear rate vs log shear stress plot yield the Behavior Index (n) and Consistency Index (Kv), respectively. Consistency Indices are corrected for the coaxial cylinder viscometers by ... 

When designing sewer networks, particularly gravity sewers, reaeration is the major process that should be focused on to reduce sulfide formation and the formation of organic odorous substances (cf. Section 4.4). A number of hydraulic and systems characteristics can be managed to increase the reaeration rate and avoid or reduce sulfide-related problems. The hydraulic mean depth, the hydraulic radius, the wastewater flow velocity and the slope of the sewer pipe are, in this respect, important factors that are dealt with in Section 4.4. It should be stressed that it is not necessarily the objective to avoid sulfide formation (in the sewer biofilm), but the sulfide that occurs in the bulk water phase should be at a low concentration level. Therefore, the DO concentration in the bulk water phase should not be lower than about 0.2-0.5 g02 m-3, sufficiently high to oxidize sulfide before a considerable amount is emitted to the sewer atmosphere. 

R = hydraulic radius, i.e., the cross-sectional area of the water volume divided by the wetted perimeter (m) s = pipe slope (m m-1)... 

Figure 25.3 The hydraulic gradient, defined as the slope of the (unconfined) groundwater table, Swl = A/i /Ax, is a measure for the horizontal pressure gradient that drives the flow through a porous medium from high to low pressure.

The continuous-flow nonsteady state measurements can be made after the reactor has reached steady state, which usually takes at least 3 to 5 times the hydraulic retention time under constant conditions. Then an appropriate amount of the compound to be oxidized (e. g. Na2S03) is injected into the reactor. An immediate decrease in the liquid ozone concentration to c, 0 mg L-1 indicates that the concentration is correct. Enough sulfite has to be added to keep cL = 0 for at least one minute so that it is uniformly dispersed throughout the whole reactor. Thus a bit more than one mole of sodium sulfite per mole ozone dissolved is necessary. The subsequent increase in cL is recorded by a computer or a strip chart. The data are evaluated according to equation 3-24, the slope from the linear regression is - (2/,/Vj + KLa(03)). 

The stability of flow in open channels has been investigated theoretically from a more macroscopic or hydraulic point of view by several workers (Cl7, D9, DIO, Dll, 14, J4, K16, V2). Most of these stability criteria are expressed in the form of a numerical value for the critical Froude number. Unfortunately, most of these treatments refer to flow in channels of very small slope, and, under these circumstances, surface instability usually commences in the turbulent regime. Hence, the results, which are based mainly on the Ch<5zy or Manning coefficient for turbulent flow, are not directly applicable in the case of thin film flow on steep surfaces, where the instability of laminar flow is usually in question. The values of the critical Froude numbers vary from 0.58 to 2.2, depending on the resistance coefficient used. Dressier and Pohle (Dll) have used a general resistance coefficient, and Benjamin (B5) showed that the results of such analyses are not basically incompatible with those of the more exact investigations based on the differential rather than the integral ( hydraulic ) equations of motion. The hydraulic treatment of the stability of laminar flow by Ishihara et al. (12) has been mentioned already. 

In addition to the theories reviewed above, there are many treatments in the literature which deal with the hydraulics of wavy flow in open channels. Most of these refer to very small channel slopes (less than 5°) and relatively large water depths. Under these conditions, surface tension plays a relatively minor part and is customarily neglected, so that only gravity waves are considered. For thin film flows, however, capillary forces play an important part (K7, H2). In addition, most of these treatments consider a turbulent main flow, while in thin films the wavy flow is often... 

The zero-point analysis characterizes the rotor hydraulics in two ways. First, the zero-point value gives the liquid flow rate over the more-dense-phase weir just as the liquid in the separating zone rises to the edge of the less-dense-phase weir. Second, the slope of the curve above the zero point measures the liquid rise over the more-dense-phase weir relative to the liquid rise over the less-dense-phase weir. Thus, if all rotors in a set have about the same zero point and the same slope above the zero point, then they can all be expected to operate about the same in two-phase flow. 

The hydraulic radius is the cross-sectional area divided by the wetted perimeter, where the wetted perimeter does not include the free surface. Letting S = sin 0 = channel slope (elevation loss per unit length of channel, 0 = angle between channel and horizontal), Eq. (6-53) reduces to... 

In a closed pipe conveying fluid under pressure, there is no relation between the slope of the pipe and the slope of the hydraulic gradient. In uniform flow in an open channel, the water surface must be parallel to the bed of the stream, and consequently S is then also the slope of the bed, S0 thus we arrive at the important relation, for uniform flow only, that... 

It has already been pointed out that the cross section most commonly encountered in open-channel hydraulics is not rectangular but trapezoidal. As repeated trial-and-error solutions of Eq. (10.119) become very tedious, practicing hydraulic engineers avail themselves of numerous tables and curves which have been prepared for finding the critical depth in trapezoidal channels of any bottom width and side slopes. 

In the case of pressure conduits, we have dealt with uniform and nonuniform flow without drawing much distinction between them. This can be done because in a closed pipe the area of the water section, and hence the mean velocity, is fixed at every point. But in an open channel these conditions are not fixed, and the stream adjusts itself to the size of cross section that the slope of the hydraulic gradient requires. 

S = overall energy gradient slope from point 1 to point 2 Sw = hydraulic gradient slope from point 1 to point 2 V = velocity of fluid flow downslope... 

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