510 - 6 - 



In a recent paper G. I. Taylor and Oavies t have shown that a smaU Bubble rising steaOlly 

 through water tends to assume the shape o' the cap of a sphere with a turbulent wake in Its rear, and 

 with a drag co-ef'icient of between 0.5 and 1.2. Using, thus, a drag co-efficient of i the energy 

 loss By turbulence of the i-oz. explosion bubble has been calculated up to the first minimum. The 

 observed value of the velocity Is given in Figure 5, arfi the maximum horizontal radius of -the bubble 

 in Table 2 below. It is found that 62% of the energy loss occurs in the last J millisecond before 

 the minimum, 86* of the loss occurring in the last millisecond. The total loss, however, only, 

 amounts to about 500 calories, i.e. to about 3. 71 of the total bubble energy. since the velocity 

 enters as the cube in this calculation, if the actual bubble velocity were double the assumed figure 

 for the last half or one millisecond the energy loss would be about 25% of the total bubble energy, 

 It is also possible that the drag co-efficient of the bubble is somewhat higher than unity, perhaps 

 owing to the needle-lil<e projections from its surface. 



(c) ve locity-Time Curve . Momentum Considerations:- An attempt has been made to estimate 

 the velocity of the bubble from the displacement-time curve. Figure 3. As was remarked above, this 

 velocity data is only very approximate. The estineted value has been plotted in Figure 5, together 

 with the theoretical curve. 



The failure of the bubble to reach anything like the theoretical maximum velocity is very 

 probably due to turbulence, but also ia part to the change of shape of the bubble. in Table 2 are 

 tabulated f^^r a few times the observed values of the velocity u, the mean radius a, and the maximum 

 horizontal radius a cf the actual bubble. The vertical momentum factor 2m - \]s? has been tabulated 

 in columns 5 and 6 calculated in two ways. In the fifth column the effective volume of water rraving 

 with the bubble is assumed tc be half that 'actual ly displaced by the bubble; in the sixth column the 

 volLTie of water moving is assumed to be half that displaced by a sphere of radius equal to the greatest 

 horizontal radius a cf the bubble. 



It will be seen that in the first case the calculated momentum of the water decreases rapidly 

 as the minimum is approached, whereas in the second method of calculation (i,e. assuming the volyme of 

 water moving is half that displaced by a sphere of radius equal to the greatest horizontal radius of 

 the bubble) the momentum appears to remain more nearly constant, as in fact it should. 



Vertical Velocity and Momentum Data. 



w 



4 The Rate of Rise of Large Volumes of Gas in water. G. I. Taylor and B. M. Davics. 



