My son is doing science project regarding action and reaction of the boat propelled by a water jet through a straw connected to a water tank on the boat. Got surprisingly unexpected results.

There are 2-sets of experiments depending on the water amount of the water released. Both started with full-tank water.

1st set is half release(from top to mid-level of tank) and 2nd set is full release of water of water from the tank.

The average velocity of the boat is greater in the case of half water release. Why? I could not give him why.

Thanks.

Off the top of my head. Perform a momentum balance on the boat. As the water level drops, so does the relative thrust due to 'potential head' getting lower, but, at the same time, the momentum of the boat also reduces - & I guess the thrust per momentum loss reduces as the level drops. It must be balanced by friction on boat sides.

There will no doubt be a break-even point. The first case should be better, with performance dropping until it hits the breakeven point.

So, back to your Newton's Second Law you go...

diaw...

This is a guess. When you start with a full tank, the boat is heavier and probably experiences more drag since the boat is immersed to larger amount in the water. When you start with half tank, drag might be less and hence you see larger velocity.

I see that you are measuring average speed. Does the boat travel the same distance in each case? If the boat travels farther when emptying the whole water tank, then it is reasonable to assume that the boat gradually loses its speed as the pressure is reduced by the emptying of its water tank. If you average the speed over the distance traveled, then it might seem as if it travels "slower" overall. Is this what happened?

Well, for both cases, starting water levels are from the top. Only end level of water is different, one case to the moddle, and the other case to thr bottom. So, they experience the same drag at least until the water level reaches the middle level of the tank.

-Kevin

Of course, the case of releasing full water traveled longer distance compared to the half-water release case.

As you said, "If you average the speed over the distance traveled, then it might seem as if it travels "slower" overall" can explain what happened. But still not sure.

-Kevin R.

I also think that's what it is. The momentum that the boat gets from the water jet depends on the velocity of the jet, which depends on the pressure in the tank. As the water level drops in the tank, so does the pressure. Jet and boat will be faster in the first half of the experiment, and should slow down significantly towards the end. There are some other effects countering this, and it really depends on your boat, but maybe the influence of pressure is dominant, here. Anyway, the average velocity is certainly larger if only considering the fast period.

I suggest one relatively easy way to verify this: Starting with a full tank, measure distance and time the boat travels >after< the tank is half empty, i.e. measure only the second half of the experiment. You should see that this will give you a relatively small velocity (even smaller than the overall velocity). The overall average velocity (completely emptying the tank) should be somewhere between the average velocity of the first part (which is large), and the average velocity of the second part (which is small).

Could it be that : Due to viscous force, a box filled of water will travel a shorter distance than the same box filled with a solid of same mass. Of course, both box have the same initial conditions...