Displacement of water for a boat and raft

[donquixote17]

If you have a perfectly flat, rectangular raft and a perfectly flat, rectangular boat, which will displace more water? Or will the water displacement be the same.

I remember that the water displacement is dependent on the shape of the floating object and the weight, but I can't remember exactly how to calculate the water displaced.

This is for a cardboard boat design in a pretty shallow creek, so vertical displacement is the most important factor. Thanks!

 

[DaveC426913]

First thing we need to understand is the functional difference is between a raft and a boat in your world.

I am going to guess that the functional difference between the two is that a boat is a hollow rectangle, whereas a raft is a solid rectangle. Would this be correct?

 

[russ_watters]

...assuming that's the case and assuming the mass is the same, displacement, as Archimedes figured out, is equal to the weight of the boat/raft, so...

 

[DaveC426913]

... assuming the mass is the same...

That was going to be my next question. The OP has not provided enough detail and I wasn't prepared to take it for granted (If you assume the mass is the same then there is no functional difference at all between a raft and a boat). I figured I'd tease it out of him while he worked it through.

 

[PJC01]

I can provide some insight into the water displacement for a boat and a raft. The amount of water displaced by an object is determined by its volume, which is directly related to its shape and weight. In general, a boat will displace more water than a raft due to its larger volume and weight. However, if the boat and raft have the same weight and are both perfectly flat and rectangular, they will displace the same amount of water.

In this scenario, the vertical displacement of the object is the most important factor. This is because the depth of the water is directly affected by the weight of the object pushing down on it. So, if the boat and raft have the same weight, they will both push down on the water with the same force and displace the same amount of water vertically.

However, it is important to note that the shape of the object can also impact the stability and buoyancy in the water. A boat with a more streamlined shape may be able to displace the same amount of water as a raft while also being more stable and less likely to capsize.

In terms of calculating the water displaced, you can use the formula for volume (V = l x w x h) to determine the amount of water displaced by a rectangular object. The length (l) and width (w) would be the dimensions of the object, and the height (h) would be the depth of the water displaced.

I hope this helps in your cardboard boat design for the shallow creek. Remember to consider both the vertical displacement and the stability of the object when designing for optimal performance.