# Ground water flow question

1. May 23, 2014

### question dude

Its attached below. I don't understand how you work out the total head. Can someone explain how you do it? I'm really struggling.

I know how to do the elevation, which is just the height above/below the datum level. And I've checked the solutions as well, it seems like you're supposed to work out the total head before the pressure head.

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2. May 23, 2014

### maajdl

Can you explain that to you grand-mother?

3. May 23, 2014

### question dude

'head' is simply stress (or pressure) mulitplied by depth

for total head is the total pressure as it were

4. May 23, 2014

### maajdl

Do you think your grand mother could understand?
Could you explain those things in a tangible way?
For example, by comparing what you measure if free water versus water in a soil?

In addition, I don't think that "pressure x depth" is related to the "head".
As I am from Belgium, I am not used with this terminology.
However, I looked at http://en.wikipedia.org/wiki/Pressure_head and it looks like that "pressure head" is the height of fluid that would produce by gravity the same pressure. In some way, it is the pressure expressed in meters of fluid.

In a "Pressure Casserol", the pressure is unrelated to the depth of water insided the "Pressure Casserol". Yet, it can be expressed in head of fluid, and the numerical value might be meters while the "Pressure Casserol" would only be 20 cm high.

Last edited: May 23, 2014
5. May 23, 2014

### Staff: Mentor

The head is defined as $H=\frac{p}{ρg}+(z-z_0)$, where z-z0 is the distance measured upward from the Ordinance Datum z0. So, at points P and C, the head H is 1 meter (there is no flow resistance between points P and C). At point A, the figure shows that the head is 6 meters above the Ordinance Datum. At point B, because the flow is steady, the head is the average of points A and C, or 3.5 meters. The upward seepage velocity is given by:

$$v=- K\frac{(H_A-H_C)}{(z_A-z_C)}$$

where K is the hydraulic conductivity (10-4 m/s).