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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 ?Chestermiller said: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 $$(H+z)\gamma_w+\frac{h}{H_2}z\gamma_w=\left(H+z+\frac{h}{H_2}z\right)\gamma_w$$
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 ?Chestermiller said: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.
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.fonseh said: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 ?
So , the pressure due to seepage variation is A > C >B ??Chestermiller said: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.
Yes, if the flow is downward.fonseh said:So , the pressure due to seepage variation is A > C >B ??
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 ?Chestermiller said: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 $$(H+z)\gamma_w+\frac{h}{H_2}z\gamma_w=\left(H+z+\frac{h}{H_2}z\right)\gamma_w$$
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.fonseh said: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 ?
The equation for pressure in seepage is (H1 + z + (h/H2)(z))(y_w), where H1 and H2 are the heights of the upper and lower boundaries of the seepage zone, z is the depth below the water table, and y_w is the unit weight of water.
H1 and H2 represent the heights of the upper and lower boundaries of the seepage zone, z represents the depth below the water table, and y_w represents the unit weight of water.
The pressure in seepage is directly proportional to the height of the seepage zone. As the height increases, the pressure also increases.
The pressure in seepage is directly proportional to the depth below the water table. As the depth increases, the pressure also increases.
The unit weight of water is a constant in the equation and represents the weight of a unit volume of water. It is necessary in the calculation of pressure in seepage as it accounts for the influence of water in the seepage zone on the overall pressure.