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FLUID DYNAMICS  | FORMULAS 

(reprinted with Breefcase's permission from works written in reefs.org)

 

 

The flowrate through an overflow driven only by siphon pressure (no motors or pumps) is a function of the cross-sectional area of the tube(s) and the total effective "head" (i.e., how far the outlet is below the intake).

So, the box sizes are of little consequnce, provided the inside box is large enough to feed the outlets freely, and the outside box is large enough so that water doesn't "back up," i.e., cause backpressure that subtracts from your head pressure.

The total square inches of cross-sectional area provided by one 2.75" diameter pipe can be found from multiplying the mathematical constant "pi" (approximated as 3.14) times the radius R in inches, squared, or (A=pi RR):

A = 3.14 X [(2.75/2) x (2.75/2)]
= 3.14 X (1.35 X 1.35)
= 5.94 square inches.

For a 1.25 inch pipe plus two 0.75 inch pipes it is:

4.9 square inches, plus twice 1.76 square inches:
= 4.9 + 3.5
= 8.4 square inches.

So, the three smaller pipes offer quite a bit more cross sectional area than the single larger tube.

Keep in mind that one pipe of cross-sectional area n square inches will flow a bit more freely than two pipes of cross-sectional area n/2 square inches each, due to greater total fluid shear and surface tension on the wall area of the narrower pipes.

(The two narrow pipes have more total inside wetted wall area than the single larger pipe, even though the total cross sectional area is the same.)

The output rate of any size bulkhead is a function of head pressure, so to put an absolute flow rate on a bulkhead size, you must state the head, either as pressure or as "fall distance."

To get rough estimated values of flow through a given siphon for a given head distance, try playing around with this formula, the "Orifice Formuila" for the flow of liquid through an orifice under the influence of gravity:

Q = KA[sqrt(2gH)]

where:

Q = Discharge rate in cubic inches per second
K = Coefficient of Discharge
A = Pipe cross-sectional area in square inches
H = Head, the vertical distance from liquid surface to orifice centerline, or just the height between intake and outlet in inches)
g = constant acceleration due to gravity (384 inches/sec2)
Note: sqrt means "the square root of."

The value of K depends on the shape of the orifice and the Reynolds Number of the fluid -- try a value of about 0.61 for water flowing through a circular orifice.

This formula does not account for any losses inside the pipe due to sheer and wall friction, which may be significant for small diameter pipes bent into a full half-circle.

 

 

Reefscapes.net 2002

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