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Re: [PSUBS-MAILIST] formula for leak volume?
Alec, the basic (i.e. not calculus) formula is:
Q = K * A* sqrt(2*g*h)
where
Q = flow rate (m^3 / s)
K = discharge coefficient
A = area of orifice (m^2)
g = gravitational constant (m / s^2)
h = head above orifice (m)
Now, the K value above is where this becomes a difficult problem, as it
is dependent on the size and shape of the orifice, length ratio to
diameter, constricting or opening transition, surface roughness,
pressure differential, and whether the orifice boundaries are static or
moving with respect to one another. Determining the correct K value
requires an involved fluid mechanics analysis, and for your example in
which you have an annular orifice of extremely narrow aperture,
turbulent fluid flow, moving boundaries which may have non-constant
relative velocity, varying pressure differential across the orifice (due
to both vehicle movement in the water column, and increasing pressure
inside the hull as it takes on water), it is of questionable value to
calculate it that accurately.
Approximating your problem as the simplest case, where you have a single
perfectly round hole, through a thin frictionless wall, into a fluid on
the other side of negligible density, completely incompressible fluid,
zero pressure gradient across the inlet area (i.e. orifice parallel to
sea surface), constant differential pressure across the orifice, etc.,
you have:
A = pi * (0.0127254^2 - 0.0127^2) = 2.028856746E-6 m^2
h = P / rho * g = 3447378.645 / 1000 * 9.80665 = 351.5347897 m
Q = (1) * 2.0288566746E-6 * sqrt(2 * 9.80665 * 351.5347897) =
1.68465455E-4 m^3/s = 0.168 liters / second
This is about 10 liters / minute, coming in at a velocity of about 82
meters per second (V = sqrt (2*g*h)). (186 miles per hour - a good
reason to have some sort of separation between your operator and likely
through-hull failure points).
So, you only have about 10 liters per minute to deal with at the bottom
depth, provided your tolerance is as tight as you propose, which I would
guess is unlikely (0.001" gap on a prop shaft?). Recalculate for a more
realistic installation tolerance, and then make sure that your bilge
pumping arrangements can handle enough flood water to permit you to
initiate an ascent and reach the surface without accumulating enough
water to either prevent surfacing because you're too heavy, or to
disable critical system components. Once surfaced, as long as the
pumping arrangement is able to remove more water than comes in at
whatever depth the partially flooded hull exposes the breach to, you
will eventually pump it all out.
-Sean
Smyth, Alec wrote
I'm trying to calculate something but haven't found the right formula.
Let's say the seal on my 1" prop shaft disintegrates. Just inboard of
the seal, the shaft goes through an opening that is 1.002". This
opening is not of any significant length The ambient pressure is 500
psi. How many gallons or liters per minute would come in?
I'd really appreciate any pointers!
thanks,
Alec
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