Finding the velocity of water flowing through a gravel filled pipe

Question

I have a scenario where I have water flowing through a gravel filled pipe, and I need to find the velocity. The pipe is gravity fed (no pumps). My approach is to find the seepage velocity ($V_s$) which is the Velocity divided by the porosity. My understanding is that the seepage velocity is defined as the apparent velocity through the bulk of the porous medium. So that is what I need to find.

I found the velocity using the Darcy Weisbach equation and porosity of gravel from online research, however I am getting a very high value for the seepage velocity (about 56 m/s) even when using the highest porosity value.

Another method that was suggested to me would be to use $Q = KIA$ where $k$ = hydraulic conductivity of gravel, $I$ = hydraulic gradient and $A$ = cross sectional area. However, this condition is only for laminar flow conditions (very slow velocities - such as groundwater under an aquifer. So I don't think I can use this equation. This method gives me a very low velocity which also seems incorrect.

Both methods seem to give me odd values so could anyone assist me with this problem?

user15789 · Answer

Theoretically, assuming your pipe is completely full of gravel and fluid this http://www.deq.idaho.gov/media/60177882/rpa-lesson-plan-1.pdf should provide the material you need. If it is not completely full of fluid, and is a sewer/channel with gravel in it, use the manning’s equation.

Below are some answers a professional may give depending on the application:

Calibrate – You seem to know the answer you want, reverse engineer to find the friction co-efficient of the material you are using.
For drainage – Replace, augment or clean the pipe;
For filtering – Can’t change filter material, gravel is about as course as it gets, increase pipe diameter or apply an increased pressure – either through a pump, static head, or increased slope.

Practically, depending on your situation, do one of the following:

Seek professional advice; the implications of your answer can have real world consequences such as flooding either upstream or downstream.  Such risk requires monetary reward, if only to pay insurance. A “perfect” (always correct) engineer still faces a high risk of their design being incorrectly applied, and to prove you’re correct in a court is expensive. 
If you are a professional either tell the client you are not qualified, or seek the advice of a principal engineer in your company.

Finding the velocity of water flowing through a gravel filled pipe

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