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Rules for drawing flow nets, equipotential lines parallel constant head boundaries. flow lines parallel no flow boundaries, streamlines are perpendicular to equipotential lines. equipotential lines are perpendicular to no flow boundaries. the aspect ratio of the shapes formed by intersecting stream. and equipotential lines must be constant, e g if squares are formed the flow net must be squares. throughout, areas near boundaries are exceptions, Each flow tube will represent the same discharage Q KiA. Procrastination is common It is best to dive in and begin drawing Just. keep an eraser handy and do not hesitate to revise. Draw a very simple flow net, equipotential lines parallel constant head boundaries.

flow lines parallel no flow boundaries, streamlines are perpendicular to equipotential lines. equipotential lines are perpendicular to no flow boundaries. Interescting equipotential and flow lines form squares. Here is a simple net with, 4 stream lines, 3 flow tubes nf. 6 equipotential lines, 5 head drops nd, Rate of flow through 1 square q A K i A aA. headloss in A is H1 H 2 H H is total head loss, aA w 1 KHw. l nd so for a unit width q A l n, since A is square w l qA.

Total Q per unit width nf, Q q A n f KH Consider an. nd application, A sand filter has its base at 0 meters and is 10 meters high It is the same from top to. bottom A plan view to scale diagram of it is shown below There is an impermeable. pillar in the center of the filter Reservoirs on the left and right are separated from the. sand by a screen that only crosses a portion of the reservoir wall The head in the inlet. reservoir on the left is 20 m and the outlet reservoir on the right is 12m Properties of. the sand are K 1x10 3 m s S 1x10 3 SY 0 2 Draw and label a flow net Calculate the. discharge through the system using units of meters and seconds What is the head at. the location of the at the top of the tank What is the pressure at that location. equipotential lines parallel constant head boundaries. flow lines parallel no flow boundaries, streamlines are perpendicular to equipotential lines. equipotential lines are perpendicular to no flow boundaries. form squares by intersecting stream and equipotential lines. Try this before next class, K 0 53m day, Draw the flow net. Calculate Q, What is the maximum gradient, What are the head and pressure at the.

We can use the flow net to identify areas where critical gradients may. occur and determine the magnitude of the gradient at those locations. equipotential lines parallel constant head boundaries. flow lines parallel no flow boundaries, streamlines are perpendicular to equipotential lines. equipotential lines are perpendicular to no flow boundaries. form squares by intersecting stream and equipotential lines. Stress caused in soil by flow j i w, If flow is upward stress is resisted by weight of soil. If j exceeds submerged weight of soil soil will be uplifted. For uplift to occur j submerged soil t w, where t unit saturated weight of soil. w unit weight of water, then for uplift to occur, the critical gradient for uplift then is. icritical t w, What is the critical gradient for a soil with 30 porosity and a particle.

density of 2 65 g cc 165 lb ft3, t 0 7 165 lb ft3 0 3 62 4 lb ft3 134 lb ft3. We can use the flow net to identify areas where critical gradients may. occur and determine, 134magnitude of the, lb ft3 62 4 gradient. lb ft at those locations, 62 4 lb ft3, What is the flux under the sheet pile wall if K 2ft day. Will piping occur, Q q A n f KH, A PLAN VIEW FLOW NET BY CONTOURING USING FIELD HEADS AND. DRAWING FLOW LINES PERPENDICULAR can t assume constant K or b. assuming no inflow from above or below we can evaluate relative T. Q AAV1 ABV2 B 96, AAKA ABKB A 94, AAKA AB KB K A ABlA.

lA lB KB AAlB 100, Irregularities in Natural flow nets. A wb b aquifer thickness varying K, varying flow thickness. K A w Bb B l A recharge discharge, vertical components of flow. K B w Ab A l B, wBlA 125 200 25000 Nature s flow nets provide. K A b A w B l A TA w l 33 100 3300 clues to, geohydrologic conditions.

B B w l A BT T 8 times T, A the higher, transmissivity. shape indicates, in this diagram, higher T ata Ashorter. or B wider shape low T, ANISOTROPY How do anisotropic materials influence. Conductivity Ellipsoid Kz, In the case where, Flow lines will not meet equipotential Kz is smaller. lines right angles stretch z, but they will if we transform the domain.

into an equivalent isotropic section, draw the flow net and transform it back x x z. For the material above we would either or shrink, expand z dimensions or compress x. dimensions x Kz, To do this we establish revised x z z. coordinates, Most noticeable is the lack of orthogonality when the net is. transformed back, Size of the transformed region depends on whether you.

choose to shrink or expand but the geometry is the same. To calculate Q or V work with the transformed sections. But use transformed K, If the pond elevation is 8m ground surface is 6m the. drain is at 2m with 1m diameter so bottom is at 1 5m. and top is at 2 5m bedrock is at 0m Kx is 16m day, and Kz 1m day what is the flow at the drain. Transform the flow field for this system and draw a. surface x x z, bedrock x z z, If you want to know flow direction at a specific point. within an anisotropic medium undertake the following. construction on an equipotential line, 1 Draw an INVERSE K ellipse for semi axes ft. 2 Draw the direction of the hydraulic gradient through the. center of the ellipse and note where it intercepts the ellipse. 3 Draw the tangent to the ellipse at this point, 4 Flow direction is perpendicular to this line.

try it above for K x 16ft day and K z 4ft day, Toth developed a classic application of the Steady State flow. equations for a Vertical 2D section from a stream to a divide. His solutions describe flow nets both are methods for. solving the flow equations, he solved the Laplace Equation. boundaries, left 0 z 0 right h s z 0, lower x 0 0, upper water table h x z o z o cx z o tan x. Toth s result, h x z z o a, cos 2m 1 cosh 2m 1, 2m 1 2 cosh 2m 1 z o. Toth s result for system of differing depth, Discharge Zone Recharge Zone.

with depth, with depth, Regional Flow Classic Papers by Freeze and Witherspoon. homogeneous isoptropic with and without hummocks, Hierarchy of flow systems Dominance controlled by. Local Basin Depth, Intermediate Slope of water table. Regional Frequency of Hummocks, Size of Hummocks, Regional Flow Classic Papers by Freeze and Witherspoon. Layered systems High K at depth, Regional Flow Classic Papers by Freeze and Witherspoon.

Layered systems Low K at depth, Regional Flow Classic Papers by Freeze and Witherspoon. Layered systems High K at depth and hummocks, Regional Flow Classic Papers by Freeze and Witherspoon. Partial layers and lenses, Regional Flow Classic Papers by Freeze and Witherspoon. Layered systems sloping stratigraphy, Regional Flow Classic Papers by Freeze and Witherspoon. Anisotropic systems, transformed, head in shallow, intermediate.

Explore the Flow Net Software at, http www mines edu epoeter GW 11FlowNets topodrive. A PLAN VIEW FLOW NET BY CONTOURING USING FIELD HEADS AND DRAWING FLOW LINES PERPENDICULAR can t assume constant K or b A longer narrower shape indicates higher T a shorter wider shape low T Irregularities in Natural flow nets varying K varying flow thickness recharge discharge vertical components of flow Nature s flow nets provide clues to