Therefore his equation assumes the following:. The equation above describes the simplest form of fluid flow encountered in porous medium. Although this is not what actually occurs in real life, it is a building block that helps describe more complicated fluid flow systems. Just remember that. This is analogous to flow through a pipe for you mechanical and chemical engineers out there. I will show you why:.
By inspection we know that the equation needs a negative sign. Because the expression ends up giving us a negative flow rate which does not make sense because we know that fluid flow goes from high pressure to low pressure. Therefore, a negative sign is included in the Darcy equation to ensure that the flow rate is positive, i. In the sketch below the aquifer height follows the topography on the hill adjacent to the valley with the stream.
Water flows from high pressure head height toward valley and leaves the aquifer at the stream. We can use Darcy's Law to estimate the rate of water flow form the aquifer. One of the implicit assumptions in Darcy's law is that the flow is laminar. Laminar flow is characterized as consisting of thin layers or laminae of fluid all moving parallel to one another.
In contrast turbulent flow is characterized by swirls, vortices and eddies, in which adjacent layers of fluid diverge and take different paths down stream. One way that we can quantify whether a fluid is laminar or turbulent is by calculating the Reynold's number for the flow, defined as. The Reynold's number is found by considering the two terms in the momentum balance for the flow.
These two terms must balance, so we can set them equal,. Next, we rewrite the terms, in a simplified way to capture only the relevant dimensions of the variables. To do, we go through what is called a dimensional analysis, in which we replace each variable, with a reference values, times a non-dimensional form of the variable. Substituting these into the equation, we get. By going through this analysis, we find that any flow that is characterized by the balance of these two terms can by compared by simply knowing the value of the Reynolds' number.
For example, if one flow has a viscosity that is 10 times the viscosity in another flow, the two flows will behave the same is the density or velocity or length is also increased by a factor of 10 for the higher viscosity case; that is, the Reynolds number for the two flows is the same. To have Darcy flow, the Reynold's number must be less than about laminar.
To have turbulent flow, the Reynold's number must be greater than about Understanding that the constants in the numerator and denominator affect the characteristics of the flow in the opposite way, also help to think about how different fluids will behave under similar external conditions.
For example, a denser fluid that also has a fast velocity will have a higher Re and exhibit turbulent behavior. In contrast, a fluid such as ice that has a high viscosity and moves very slowly will have a low Re and will likely have laminar flow.
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