Head Loss Computation - Perf Pipe and Stone Bed

[geocivil]

Stuck I am. Any thoughts on the following?

Runoff enters a flat grated inlet, flows through a solid 12" HDPE Pipe into a manhole then into a 60 foot long perforated pipe equipped with 5/16-inch diameter holes 8 per ring and spaced every two inches along the 45-foot length. From the perforation water flows into a gravel/stone bed which is 8 feet longer than the pipe and 50-foot wide. The stone outlets runoff through a 12-inch Perf HDPE of same configuration but 4-feet lower in elevation than the first perf pipe and daylights in a box equipped with an orifice plate and weir.

Routing calculations show no flow over the weir during the 100-year storm event. The outlet structure orifice is 6-inches and free flow is available downstream.

How does one compute headloss through the perforated pipe knowing that both pipes are flowing full during the 100-year storm event. Note the stone bed extends above the pipe by 6-inches and routed water level is theoretically 1-inch above the overt upper pipe.

Head loss at inlet grate
Head loss at perforations
Head loss due to friction of sloped pipe laid on 1% slope
Head loss due to flow through perforated pipe laid level
Head loss through stone (assuming void space of 40%)

Any thoughts on computing an overall head loss for the system?

 

[gbam]

Ok,
I'll take a stab. First make sure that the volume of the pipes & Catch basin does not exceed the R/O Volume. If it does then no need to continue because the entire 100-year event is stored inside the system.

Grate loss will only occur if the system is surcharged creating a hgl greater in elevation than the grate. Then I would apply a coefficient of 0.5-1.0 depending on the grate configuration.

Headloss through stone can be acheived using groundwater flow properties, Darcy's Law, I think (its been a while for ground water).

Headloss at perfs, I am not sure but one could apply a conservative inlet and outlet loss, K=0.5 inlet & K=1.0 outlet. Resulting in a combined coeff of 1.5. hl=Kv2/2g.

Pipe loss is straight foward. hf=sfxL, sf=(Q/K)^2, K=conveyance from Mannings (1.486/n A R^(2/3)).

I am not sure I would try to increment the flow out of the perf pipe. Just compute the stand hydraulic grade based on your tailwater condition.

Sounds like an interesting situation. I hope I helped a little!

 

[bltseattle]

I'll take a stab too.

You describe what sounds like a stone detention reservoir. These systems typically use large open graded stone aggregate with typical porosities in the 30-40% range. You could do a quick check with Darcy's law but the hydraulic conductivity on open graded stone is usually very high (can be 100s of feet per day), and it would be fairly safe to assume that the stone reservoir will act as a level pool controlled by the downstream orifice/weir flow control structure.

If the stone is open-graded, the head loss through the system is more likely to be head created by the orifices in the upper perf pipe. The equation for each orifice is
Q = C * A * (2 * g * H)^1/2
where C is the discharge coefficient for the orifice (typ. .59 to .62), A is the orifice open area (effective, taking into account a clogging factor) in sf, H is the change in hydraulic head ("delta H") across the orifice in ft, and Q is in cfs.

So one can estimate the number of effective orifices and use the above equation to develop a rating curve of delta-H vs Q for the inlet perf pipe manifold.

Note again that the H is really "delta H", so if the water level is over the upper pipe as a result of the weir/orifice downstream, then you need to add the "delta H" to that water level to find out what the water level/HGL is upstream of the perf pipe.

Then use the computed water level/HGL at the perf pipe as the downstream water level and apply typical pipe friction equations as noted by gban from the reservoir inlet back to the inlet grate.