The volume flow ($J_V$) can be calculated from the hydraulic conductance ($G_h$) and the pressure difference ($\Delta p$) using the following equation:

$ J_V = G_h \Delta p $

Furthermore, using the relationship for the hydraulic resistance ($R_h$):

$ R_h = \displaystyle\frac{1}{ G_h }$

results in:

$ \Delta p = R_h J_V $

(ID 3179)

Since the hydraulic resistance ($R_h$) is equal to the hydraulic conductance ($G_h$) as per the following equation:

$ R_h = \displaystyle\frac{1}{ G_h }$

and since the hydraulic conductance ($G_h$) is expressed in terms of the viscosity ($\eta$), the tube radius ($R$), and the tube length ($\Delta L$) as follows:

$ G_h =\displaystyle\frac{ \pi R ^4}{8 \eta | \Delta L | }$

we can conclude that:

$ R_h =\displaystyle\frac{8 \eta | \Delta L | }{ \pi R ^4}$

(ID 3629)

In the case where there is no hystrostatic pressure, Bernoulli's law for the density ($\rho$), the pressure in column 1 ($p_1$), the pressure in column 2 ($p_2$), the mean Speed of Fluid in Point 1 ($v_1$) and the mean Speed of Fluid in Point 2 ($v_2$)

$\displaystyle\frac{1}{2} \rho v_1 ^2 + p_1 =\displaystyle\frac{1}{2} \rho v_2 ^2 + p_2 $

can be rewritten with the variación de la Presión ($\Delta p$)

$ dp = p - p_0 $

and keeping in mind that

$v_2^2 - v_1^2 = \displaystyle\frac{1}{2}(v_2-v_1)(v_1+v_2)$

with

$ \bar{v} = \displaystyle\frac{ v_1 + v_2 }{2}$

and

$ \Delta v = v_2 - v_1 $

you have to

$ \Delta p = - \rho \bar{v} \Delta v $

(ID 4835)