30 - CE/GEOL 485 Principles of Hydrogeology LECTURE 4...

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Unformatted text preview: CE/GEOL 485 Principles of Hydrogeology LECTURE 4 Pressure & Head Lecture Outline • • • • • • Fluid Pressure Pressure, Energy & Head Pressure Head in a Static Saturated System Elevation or Gravitational Head Total or Hydraulic Head Measuring Hydraulic Head Piezometer Manometer Pressure Gauge • Hydraulic (Head) Gradients Pages: 66-69, 113-122 in Fetter Fluid Pressure • In a fluid at rest, pressure is a scalar quantity • This means it is the same in all directions, but can vary from point to point within the fluid • In a fluid at rest, pressure, P, is the force exerted by the fluid per unit area of the fluid P= F A Dimensions = SI Units = Pa = [M] [T 2 ][L] N kg.m kg = = m 2 s2 m 2 s2 m English Units = psi = Ψ = pressure head = height of liquid causing pressure at a point Ψ Liquid Ψ = P/γ P = pressure = [L] We can also express energy as: Energy per unit mass [ML2/T2]/[M] = [L2/T2] Energy per unit weight [ML2/T2]/[ML/T2] = Head, Elevation or Gravitational Head, Zg - in a system at constant pressure, water flows from high elevation to low elevation THEREFORE ELEVATION IS ALSO A MEASURE OF ENERGY & IS REFERRED TO AS GRAVITATIONAL POTENTIAL (OR GRAVITATIONAL HEAD IN LENGTH UNITS) [M] [T 2][L] γ = specific weight of liquid γ = ρ water g Energy per unit volume [ML2/T2]/[L3] = Pressure [M/LT2] lbs in 2 Pressure Head in a Static Saturated System Air Pressure is a Measure of Energy (or Potential) = [M] [T 2][L2] Precipitation Sloping ground surface Subsurface Flow •1 Total or Hydraulic Head (hT or h) What other “forces” can cause flow? - kinetic effects, i.e., momentum of flowing water (as described on p. 114-115 of Fetter) - temperature gradients cause flow because warm water has lower density than colder water - electrical, chemical & osmotic gradients may also induce water movement Measuring Head Piezometer – a tube-like device used to measure hydraulic head, h, at a point in the phreatic zone under field conditions Tube must be: - open to liquid at the measurement point In groundwater systems, “other forces” (including kinetic energy) tend to be small, so we assume flow is controlled only by the pressure & gravitational heads, i.e. h= Ψ+z Open to Atmosphere Standpipe Piezometer • most commonly used type of field piezometer • simple & reliable • can also be used to take water samples & measure aquifer characteristics Casing stick-up Cap Ground Surface Water table Casing (steel, PVC, etc.) must not leak! Average depth ψ of screen h - open to atmosphere at top Annulus, filled with grout to prevent seepage along casing Open end, or “short” screened interval for water intake - sealed along its length z Datum Manometer A tube-like device used to measure hydraulic head, h, at a point in a sample of saturated porous material Laboratory version of a piezometer which can be filled with fluids other than water (e.g., mercury) Mercury Manometer Water Manometer STUDENT PRESENTATION ψ Ψm P1 P2 •2 Gauge Pressure • • • • a gauge measures pressure, P, relative to atmosphere gauge reading is positive if pressure > atmospheric gauge reading is negative if pressure < atmospheric for points at the same elevation, water flows from zones of high gauge pressure to zones of low gauge pressure Example, flow in a water-filled pipe P = 2 Pa Datum P = 10 Pa Pgauge = Ptotal - Patm Which direction is flow? Hydraulic Gradients Pressure Gauge - also used to measure hydraulic head in the laboratory - measures pressure relative to atmosphere (Pg = Ptotal - Patm) - calculate total head using h = Ψ +Z = Pg + Zg γw where γ w = ρwg and Zg = elevation of gauge Flow Water manometer ψ Column of saturated sand Gauge Pg h ZZ Zg Datum - Water always moves from high h to low h - Magnitude of the driving force for flow is the hydraulic gradient, ∆h/∆x or ∆h/∆z - Hydraulic gradient is a vector quantity - Need 2 or more piezometers to measure direction & magnitude of flow TAKE HOME MESSAGE A Practical Definition of Total or Hydraulic Head Q Ψ READING FOR NEXT LECTURE: h Z Elevation Datum Pages: 219-228 in Fetter Total or Hydraulic head = Elevation head + Pressure head Water pressure = air pressure = 0 at the “water table” i,.e., ψ = 0 and h = z = elevation of the water table •3 ...
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This note was uploaded on 11/10/2011 for the course GEOL 455 taught by Professor Perfect during the Fall '11 term at University of Tennessee.

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