For short, the answer lies in a concept widely used in pipe engineering: hydraulic load or just load. Unfortunately, this concept is not well understood.
The hydraulic load can be understood as the amount of energy available to drive a fluid through a pipe or conduit. And if you compare the load at two different points along a pipe you could easily check for the direction in which the fluid travels.
The hydraulic load can be, mathematically, written as:
$H_L=\dfrac{p}{\gamma}+z$ Eq. (01)
where:
$H_L$ stands for the hydraulic pressure at a given point along th pipe,
$p$ for pressure at that point along the pipe,
$\gamma$ for specific weight of the fluid,
$z$ vertical height of that point along the pipe.
As you may have already noticed: the hydraulic load only makes sense when talking about a given location along a certain pipe.
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| Fig. 01 Flow direction cases according to the hydraulic load $H_L$ at two different locations. |
In case 1 in Fig. 01 the flow travels upward and the only way of making sure this is so is by checking that $H_{L1}$ is greater than $H_{L2}$. Otherwise, the fluid will travel backwards.
This concept is a mechanical balance coming from the Bernoulli equation. However, estimations on how greater $H_{L1}$ is with respect to $H_{L2}$ depends on some pipe features and equipments taken into account in the general energy balance equation.
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