Pressure in seepage

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1. Apr 23, 2017

fonseh

1. The problem statement, all variables and given/known data
Can anyone explain why the pore pressure at C is given by( H1 + z + (h/ H2)(z) ) (y_w) ?

2. Relevant equations

3. The attempt at a solution
Shouldnt it be ( H1 + z + ) (y_w) only ?

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2. Apr 23, 2017

Staff: Mentor

The quantity $(H+z)\gamma_w$ is the hydrostatic contribution to the pore pressure at C. The additional contribution of seepage flow to the pore pressure at C is $\frac{k}{\mu}vz$, where z is the pore flow distance between C and A, k is the permeability, $\mu$ is the water viscosity, and v is the seepage velocity. For point B, the contribution of seepage flow to the pore pressure at B is $\frac{k}{\mu}vH_2=h\gamma_w$, where $H_2$ is the pore flow distance between B and A and h is the additional head above the water table as a result of seepage flow. So, from the relationship at B, we have:
$$\frac{k}{\mu}v=\frac{h}{H_2}\gamma_w$$Therefore, substituting this into the additional contribution of seepage flow to the pore pressure at C, we obtain $\frac{h}{H_2}z\gamma_w$. Therefore, the total pore pressure at C is $$(H+z)\gamma_w+\frac{h}{H_2}z\gamma_w=\left(H+z+\frac{h}{H_2}z\right)\gamma_w$$

3. Apr 24, 2017

fonseh

I have another example here . In this case , it's downwards seepage ... Why for this case , the Pressure at B is (H1 + z -iz )yw ??? Shouldn't the pressure increases with the depth ?

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4. Apr 24, 2017

Staff: Mentor

The hydrostatic portion of the pressure variation does increase with depth. But, if the viscous seepage flow is downward, its contribution to the pressure variation must involve a pressure gradient component that can drive the fluid downward.

5. Apr 24, 2017

fonseh

so , do you mean as the water flow from top to the bottom , so the water is saying to be flow from higher pressure to low pressure ? So , in the case of downwards seepage , the pressure at A > C >B ?

6. Apr 24, 2017

Staff: Mentor

Only the viscous seepage portion of the pressure variation, which superimposes linearly upon the hydrostatic portion of the pressure variation, to give the overall total pressure variation.

7. Apr 24, 2017

fonseh

So , the pressure due to seepage variation is A > C >B ??

8. Apr 25, 2017

Staff: Mentor

Yes, if the flow is downward.

9. Apr 29, 2017

fonseh

Can you explain what causes The additional contribution of seepage flow to the pore pressure at C is $\frac{k}{\mu}vz$ ?? Is there any name for the term ?

10. Apr 30, 2017

Staff: Mentor

The differential equation for the variation of pressure in a porous medium (in the vertical direction) is $$\frac{dp}{dz}+\gamma=-\frac{k}{\mu}v$$ where, in this equation, z is the elevation and v is the superficial upward seepage velocity. This is Darcy's Law.