Hydraulic head and Darcy's Law Flashcards
What is hydraulic head in relation to piezometers?
Height of water in a piezometer above an arbitrary line beneath the surface (datum)
What does the principle of minimum total potential energy state?
That an object will go to a position where’s it’s total potential energy reduces
What is elevation head?
It’s a form of potential energy related to gravity, the potential energy is higher between two objects with the same mass if one of the objects has a larger distance from the ground
What is pressure head?
Is a form of potential energy, is the amount of pressure exerted on the piezometer and is measured as the height of the water column starting from the bottom of the piezometer.
What is total hydraulic head a sum of?
The elevation and pressure heads
What is hydraulic gradient? Give the formula?
The difference in hydraulic head between two points divided by the distance between two points,
formula i = (H2-H1)/(X2-X1)
What is hydraulic gradient, i, always negative?
Because point 1 is always the point water is flowing from (higher hydraulic head)
Does having a difference in hydraulic head guarantee that water will flow?
No! The porosity and permeability of the material the water is flowing through matters
What was Darcy’s experiment to predict flow?
He filled a small pipe with sand and hooked up a hose to one end to let water flow through, he put two piezometers in the sand tube and calculate their hydraulic heads and the overall gradient, then he measured the the water flow (discharge)
What did Darcy find out through his experiment?
That a larger hydraulic gradient resulted in more discharge, that a larger tube area resulted in more discharge, that the material in the tube effected the discharge, and that the temperature of the water effected the viscosity so cold more viscous water flowed slowly.
What equation did Darcy come up with to measure discharge Q? Explain all variables
Q= -k i A
-k= the hydraulic conductivity, is the type of material plus the properties of the water flowing through it (permeability and viscosity)
i= the hydraulic gradient
A= The cross sectional area of the tube
How does hydraulic conductivity allow us to measure permeability of a material?
k (intrinsic permeability) = K (u (Dynamic viscosity)/p(water density)*g(gravitational acceleration)
What is specific discharge?
It’s the discharge over the cross sectional area of the tube, eqn= q= Q/A
Why is specific discharge not the same as velocity?
Because the cross sectional area we are dividing by includes all the space that the water is not even moving through, to find the actual velocity need to divide discharge by the area that is participating in the movement of water
What’s the equation of effective velocity?
It’s ve= Q/ A X ne
or ve= q/ne
