|MadSci Network: Physics|
ok, I have a minor point of possible confusion over what you mean by "at rest in a flowing stream." So depending upon what you mean by the statement, there are two different answers. Pick the one that applies. ************ CASE A) you mean that it's at rest relative to the ground so that water must flow around the stick. Then ... You're correct that the water resistance is the same for the stick being "pulled" and the stick held fixed to the ground. However, the force holding the stick fixed to the ground is also the same force as that exerted by the person pulling the stick through the water. In each case there must be exactly the same amount of force applied to the stick to counteract the water resistance. In one case it's a force being applied by whatever is pulling and in the other it's a force applied by the ground (or whatever the stick is stuck to). Now, in actual streams and flowing water things will be a little different. For slow, smooth flowing water and low speed sticks things will be nearly equivalent. But for fast (turbulent water) and a fast moving stick the two examples will begin to differ. In turbulent conditions, there will be eddy currents already present in the water. For more information, you can investigate turbulent and "laminar" flows. Or, said in different words, at low velocity the water doesn't care if it has to go around a fixed stick in the stream or if it's being pushed out of the way by a moving stick. ************ CASE B) you mean that it's at rest relative to the flowing stream, ie relative to the moving water. So the stick is moving continuously with the water. Then ... Actually, your intuition is correct that something isn't right. They are not the same! The resistance of the stick floating in the stream (with the water) is going to be close to zero (assuming the stick is moving at the same rate as the water). If it is moving at the same speed as the average velocity of the fluid, then there will be no net force exerted on the stick to cause it to move at a different rate than the stream of fluid(let's ignore buoyancy for the moment as well as ebbs and flows of the stream). In this case the stick does not need to displace any water. (Ideally) the water in front of the stick will always remain in front and the water behind it will always remain behind. In practice, this isn't actually the case as the stick will move at a slower rate than the stream and streams do not flow smoothly. A stick being pulled through water at a constant rate has two opposite forces being exerted on it. First it has the force of whomever is pulling it through the water. Secondly it has the resistance force of the water opposing it. When the two forces are equal, then it will be moving at a constant rate. However, in the case the stick has to displace the water in its path. This displacement causes the resistance. Think of it this way : Contrast the difference between swimming forwards in a pool and just floating along in a stream.
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