It seems to me that any losses due to water movement in the bottle are going to come from shear resulting from the flow. So, there'll be some kinetic energy lost as heat due to liquid movement. It's not going to be very large IMO and it'll be rather difficult to estimate. Flows in an agitated bottle are going to be highly turbulent and entirely dependent on liquid properties, bottle size, shape and surface, bottle orientation and location on the bike, and exact motion of the bike. When your cadence changes, the frequency of the motion will change. When power or your position or the gradient, or wind changes, the amplitude and orientation of motion will change. As the volume of water in the bottle changes, everything changes. Far too many variables and any solution would be based on a myriad of questionable assumptions, making it worthless. The problem is an absurd one for which to attempt to produce a figure by calculation.
Now, if you put in a baffle, you can reduce the range of motion of the fluid. But how will that reduce energy loss?
In order for a baffle to prevent motion it must produce resistance. You can change the size, location and orientation of flows within the body of liquid, but you can't eliminate liquid movement. The same volume of liquid will remain in motion. What makes you think the baffle will reduce the losses due to that movement?
It's not a very intuitive problem! It's not immediately obvious whether a baffle will increase or reduce energy loss, but I'm pretty sure it'll increase it: see below.
You've described your proposal as a "wave breaker". Waves move potential and kinetic energy about incredibly effectively. To "break" the wave you would be introducing turbulence to mix the flow and damp the wave. Therefore wouldn't the breaker actually be the means of converting the energy from a useful form into heat more effectively than a simple bottle would ever achieve? And that's the opposite of what you want.
If it helps, consider a fluid trainer. The resistance is not created by moving a wave around. It is created by generating turbulence, i.e. lots of fluid shear in the resistance unit, and this creates heat which is dissipated into the ambient air through the body of the resistance unit. A bottle with baffles would do essentially the same thing by creating small scale turbulence that effectively converts kinetic energy to heat. I believe it would make things considerably WORSE not better than a standard bottle.
As others have pointed out, the comparisons made in some posts to rocket and motor vehicle fuel tank baffles are missing the point. Those are used to control the liquid to allow reliable access and to maintain control and stability. It's not about efficiency.
Now, if you put in a baffle, you can reduce the range of motion of the fluid. But how will that reduce energy loss?
In order for a baffle to prevent motion it must produce resistance. You can change the size, location and orientation of flows within the body of liquid, but you can't eliminate liquid movement. The same volume of liquid will remain in motion. What makes you think the baffle will reduce the losses due to that movement?
It's not a very intuitive problem! It's not immediately obvious whether a baffle will increase or reduce energy loss, but I'm pretty sure it'll increase it: see below.
You've described your proposal as a "wave breaker". Waves move potential and kinetic energy about incredibly effectively. To "break" the wave you would be introducing turbulence to mix the flow and damp the wave. Therefore wouldn't the breaker actually be the means of converting the energy from a useful form into heat more effectively than a simple bottle would ever achieve? And that's the opposite of what you want.
If it helps, consider a fluid trainer. The resistance is not created by moving a wave around. It is created by generating turbulence, i.e. lots of fluid shear in the resistance unit, and this creates heat which is dissipated into the ambient air through the body of the resistance unit. A bottle with baffles would do essentially the same thing by creating small scale turbulence that effectively converts kinetic energy to heat. I believe it would make things considerably WORSE not better than a standard bottle.
As others have pointed out, the comparisons made in some posts to rocket and motor vehicle fuel tank baffles are missing the point. Those are used to control the liquid to allow reliable access and to maintain control and stability. It's not about efficiency.