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bilge pump as propulsion
Shaun
snip If i understand what you're saying here, it sounds prettymuch counterintuitive. I may be mis-using some of the terms? let me give an example just to be sure that i understand what you're saying here, and bear in mind that of course the numbers im going to use are entirely made up in my head, so they'd be wrong.... It seems counterintuitive if you're thinking in terms of the discharge stream "pushing against the water". lets say that you have two identical boats with the same pump on each one, running at whatever flow you like, say 5,000GPH. Boat A has a huge outlet... say 5 inches in diameter. for arguements sake, because i dont know how to calculate the speed of the water for that given outlet, lets say the speed of the water coming out the back is slow. i dont know how slow, but lets say it comes out at 3 knots. Now boat B has the same pump, but the outlet is so small, that even though its using the same pump, the water is coming out at a speed of 20 knots. what you're saying is that both boats because they have the same amount of energy put into them, and the same total force.... they'd go the same speed? Yes, that is the case. It's no different than if you used your hands, and applied the same force to boat A, using only one finger, as you apply to boat B, using the whole palm of your hand. It would "seem" that you're pushing much harder with the finger than you have to with the hand, but you're really not. With the finger, you have to apply a much greater force *per unit of area* than with your palm (which has a much larger surface area). For example, if you apply 10 lbf/sq.in. to one square inch on Boat A, and 1 lbf/sq.in. to 10 square inches on Boat B, the total force applied to both is the same, and the resulting acceleration would be the same (assuming the same time interval of force application). is there no relationship between the speed the water comes out and the speed of the boat ie. it seems pretty obvious boat A could never go faster than 3 knots, It may seem obvious, but that is incorrect. The discharge water is being *accelerated* to 3 knots faster than the intake water. So there is a constant force being applied that is totally independent of boat speed. If there were no friction (and bow waves, etc.) the boat would continue to accelerate indefinitely (well...see below). This is for an axial system, where water comes in the bow, leaves the stern, the only practical way to do it. As I said earlier, if your intake isn't pointed forward, then you have Bernoulli effects, and you have pump cavitation problems that reduce the flowrate. In the axial configuration, the boat speed increases system efficiency by pressurizing the suction line and overcoming the intake line pressure drop. At some speed, you'll reach a point where the pump cannot maintain an acceleration of 3 knots (outlet vs inlet), and your thrust will drop from that point on. snip F = m x a Where F = Force m = mass (proportional to the volumetric flow rate) a = acceleration (proportional to the velocity of the water leaving the pump versus velocity entering the pump) ok, wait i should have read this first and thought about it more.... so there is a direct relationship between water velocity and boat speed, if you can maintain the same volume of water flowing.... right? Exactly. It takes more pressure (force per unit area) to get that higher velocity, so you have to do more work on the system (by the pump). That additional 'work' is then available in the form of thrust. so the sweet spot would be just before the pump starts to be slowed by the backpressure? Just before the discharge *volume* (mass flow techically) decreases. Keep in mind that shrinking the nozzle is not "free", since that creates higher pressure requirements, and thus higher load on the pump (i.e. more amp draw). now this may be pure conjecture on all our behalfs, but assuming you could get double the pressure (which you probably cant) at the same flow rate by having pumps in series as opposed to parallel, and for the same current draw, which boat do you think would go faster, the boat with double the flow and half the speed, or the boat with double the speed and half the flow? the total numbers add up the same right, but wouldnt the boat with higher speed water jet go faster? Nope, 'cause it's the accelerated mass of water that supplies the thrust, not the discharge water 'pushing against' anything. Does the boat you push with your finger (above) go faster than the one you push with your palm because your fingertip is applying so much more pressure (over a small area) than your palm is? No, if the total force applied is the same. It doesn't matter whether it's great force on a small area (fingertip, small water stream) or a lesser force over a greater area (palm, large water stream) if the total force is the same, the thrust is the same. Keith Hughes |
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