Depth averaged velocity

Given the material parameters 6 and and the elevation of the basal topography, b, above the curved reference surface, equations (1)- (3) allow h, u and v to be computed as functions of space and time once appropriate initial and boundary conditions are prescribed, where h is the avalanche depth, and (u, v) are the depth-averaged velocity profiles parallel to the flow path. 

Figure 3.38 Depth-averaged velocity distribution (signs) measured by Nuding in flume experiment No 11004, [470] there is a local minimum near the interface between vegetated (left) and free streams.

In vegetated area, the shear velocity to govern sediment transport is evaluated by using equation 6 from the obtained depth-averaged velocity in horizontal 2D flow analysis, and it is applied to evaluate bed load transport rate, entrainment flux of suspended sediment and so on. 

The measured data and the results of 2D depth averaged model longitudinal changes of depth and depth-averaged velocity are compared in figure 6. The calculation was conducted... 

Figure 6. Comparison between measured and calculated results of depth and depth-averaged velocity.

The modification of the resistance law by introducing the bed roughness boundary layer brings less changes in flow calculation represented by depth and depth-averaged velocity but significant correction of shear velocity and subsequently sediment transport. The proposed modification will affect other aspects in fluvial processes, which will be clarified successively. 

Lateral mixing of momentum and lateral distribution of depth-averaged velocity The governing equations of flow in depth-averaged 2D scheme are written as follows ... 

Figure 1. Lateral distribution of depth-averaged velocity (A) Sensitivity due to or value (B) Comparison with flume experiment (Tsujimoto 1996).

In real glaciers, variations in thickness, width, and other factors produce many deviations from this simple flow pattern. But these are important ideas to keep in mind. Extending and compressing flow also enable a glacier to flow past large bumps in its bed. A quantitative derivation of flow lines would provide a time scale for an ice core. This cannot be based solely on mass conservation as were the previous arguments, which dealt only with depth-averaged velocities. Stresses and deformation rates have to be calculated. 

Bearing in mind the conditions of the problem, we can assume that pressure drop per unit length is determined by viscosity, average velocity, as well as the depth and width of the micro-channel ... 

Here, c, the effective particle Knudsen number, is the ratio of the relaxation time f 1 for Brownian motion of the particle to the time needed for the fictitious particle to traverse the distance Rs with its average velocity, 6 is the dimensionless surface temperature, and is the dimensionless depth of the potential well. 

A rapid-mix tank, 2 m in diameter is tilled to a depth of 2 m with water and alum introduced continuously in the influent. The turbine is running at 3.24 hp and the average velocity gradient in the tank is 950 s. At what temperature is the alum being mixed with water Determine the influent rate of flow to the mixer corresponding to an effective mixing. 

N-m/s and the downstream depth of the jump is 0.94 m. The rate of inflow into the jump is 0.048 mVs. The upstream depth of the jump is 5 cm and the temperature of mixing is 25°C. What is the channel width At a motor efficiency of 90% and a brake efficiency of 75%, the power input into a mixer was found to be 16,459 N-m/s. The average velocity gradient in the mixer tank is 1500s and the temperature of mixing is 25°C. Find the volume of the mixer. 

A river of 2-m depth moving at an average velocity of 0.2 m/sec receives particles of 200-/r,m diameter from a storm drain emptying at the river surface. Assume that the particles are of mineral origin with a density of approximately 2.6 g/cm3 and that the kinematic viscosity of water is 1.3 X 10-2 cm2/sec (at 10°C). What is the minimum distance the particles will travel before settling to the river bottom ... 

A river has a cross section that is approximately a rectangle 10 ft deep and 50 ft wide. The average velocity is Ift/s. How many gallons per minute pass a given point What is the average velocity (assuming steady flow) at a point downstream, where the channel shape has changed to 7 ft in depth and 150 ft in width ... 

Field current patterns imposed on the model were approximated from data collected by Southern California Edison (17), owners of the station. For purposes of the demonstration simulation, a changing sequence of currents was selected to represent the history of local transport over a half tidal cycle of 6 hr. It consisted of a 0.3 knot current down-coast (south) for the first hour while copper discharge was occurring, a null period of zero current velocity for 2 hr, and a 3-hr period of 0.3 knot current upcoast. Current vectors were directed parallel to the coastline and were considered to represent average velocities through the full depth of the water column. Dispersion characteristics of the nearshore waters were represented by values of = 3 m sec and Ey = 2 m sec in the mixing zone, and were increased to 4 m sec and 3 m sec for all other elements (16). They were maintained steadily at these values throughout the 6-hr period simulated. 

Where tt(d) is the travel time to depth d and V = V/d), V/dJ is the timed average velocity to a depth of d. Even though this method is simple, it is found to imder estimate the values, since in... 

Note h is water depth, B is flume width, Q is discharge, Vis average velocity of section, is Reynolds number (=4hVlv), v is kinematic viscosity, is Froude number ( VI ghY ), is the duration (s) in rising period of unsteady flow, index b and p is base flow and peak flow, P is unsteadiness parameter (Ma 2012) proposed by the author, and the expression is as follows ... 

All the tests were conducted in under-critical flow conditions (Fr <1). 3 water depths were tested. For each water-depth condition, several flow discharges or cross-sectional averaged flow velocities were obtained through adjusting the power of the driving water pumps. Flow velocity was measured by the propeller velocimeter. For each test, the water pumps kept at a constant power value so that the flow can be considered steady. Several stem densities of vegetation were used for each flow depth and velocity condition. 

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