Must.... resist.... the... pull..... Must... resist...
Arrrgh!!! I can't stand it!!!! I'm taking the bait!!!
Imagine a tin can with water inside. Now poke holes in the side of the can at three different heights. The exit velocity will be a function of the pressure. The pressure is a function of the head. (Not that head! Sheesh!) By "head" I mean the distance below the surface of the water.
Since my intent was to use effective orifice size as a evaluation tool and guide I made some assumptions and kept those constant throughout my recovery process.
I used standard hydraulic equations assuming water and nominal pressures at sea level. For low values of Reynolds number, Re, flow is laminar. For high values of Re, flow is turbulent. (Unfortunately I cannot paste equations here but I do supply a link, below, for interested parties.)
From Bernoulli’s equation, the total energy loss is the energy converted to heat by friction of particles against the wall and each other.
Assuming, away from the orifice, that v1 = v2 and A1 = A2, the flow becomes a product of the area and speed. We know the speed from the distance measurement.
Flow Rate Q is a function of the area times the square root of the pressure drop and ξ where ξ is a dimensionless loss coefficient, representing the energy loss associated with the pressure drop. For hydraulic systems, this equation is normally written using the standard orifice flow equation.
Inspection of the equation indicates that the flow rate varies proportionally with area if the Δp is held constant, and that the flow rate varies with the square root of Δp if the flow area is held constant.
Notational charts of the flow behavior are located
here I assumed the natural pressure at the beginning of urination is the same as the pressure pushing against my formerly leaking sphincter. Using that pressure and the leak rate determined by meticulously weighing pads on my Mettler balance and correcting for evaporation (studied in another post) I could determine a representative orifice size for my leaky sphincter.
At 16 months I had a cystoscopy and learned that a portion of my bladder sphincter was removed resulting in a length of only 10mm instead of the nominal 18- 20 mm.
At that point I could have gone back and recalculated all the dimensions I had obtained for the previous 16 months to correct them for pipe flow of a known length instead of simple orifice flow but
that would have been ridiculous waste of time.
At that point I had my AdVance Sling installed and had moved on to fixing ED.
Whew! I feel much better.
Jeff Notitio ergo sum. (I take data therefore I am.)