A bigger splash

The crawling baby is now undertaking a series of physics experiments. His favourite is the investigation of vibrational modes on biscuit tins and their coupling to longitudinal waves in the atmosphere. But he’s also repeating Galileo’s (supposed) famous experiment in studying the free-fall acceleration of various objects. In this case the elevated position  is not the Leaning Tower of Pisa, but the spare bed, and the objects take the form of anything he can lay his hands on, including himself. But the one I’ll comment on today concerns energy transfer from rapidly moving objects to fluid. 

His method takes the form of sitting in the bath and whacking the surface in such a manner as to create the largest splash of water. What he needs to work out is the relationship between the area of the object hitting the water (his hand), the speed at which he strikes the surface, and the height to which the splash goes.

Fluid dynamics is governed by a collection of dimensionless numbers that relate various quantities. The most commonly used is probably the Reynolds number, which is the ratio of the intertial force to the viscous force on an object. A high Reynolds number shows that intertial effects are prevelant; a low Reynolds number shows that viscous effects dominate.  In baby’s case, he probably needs to look at the Froude number. This tells us that gravitational-velocity effects depend on the dimensionless term v/sqrt(gL), where v is the velocity of an object, g the acceleration due to gravity (9.8 m/s2) and L is a characteristic length. The pattern of flow obtained, for example the height h of the splash in terms of the length scale L,  is likely to be a function of the Froude number. So, if we want the height of the splash, we can say that h/L = f(v/sqrt(gL)) which tells us h  = L f( v /sqrt(gL) ) where f is some function to be determined. We’d expect it to be an increasing function – if we increase v we’d expect  h to increase – and if we did the experiment on the moon where g was lower we’d expect h to increase too. 

A series of experiments should tell us whether such a relationship indeed holds for whacking the surface of the water with a hand of length L, at a speed v, and the form of the function f. We shall collect the data over the next couple of weeks and hope to have a paper  published soon. 

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