Question

1) Consider a soap bubble with radius, r. The pressure inside the bubble must be greater than the pressure outside of the bubble. The surface tension of the bubble, y, supports the difference in pressure, delta p. Using dimensional analysis, formulate an expression for the pressure difference.

2) In 1945 the first atomic bomb was tested in New Mexico. The destructive power (Energy) of the bomb was kept classified however, following the release of *time* stamped pictures showing the bomb's explosion *radius* a British physicist, G. I. Taylor, was able to estimate the power released by the explosion. Identify the missing parameter and use dimensional analysis to formulate an expression for the Energy.

Answer 1

1) Let us consider,

this means that the pressure difference is some function of radius r and surface tension y.

We assume,

C is a constant constant and hence dimensionless. We need to determine alpha and beta

Using dimension,

Hence, we have

Comparing LHS and RHS we have

Hence, we have

Our expression hence becomes,

2) The missing parameter here is the density of air

We assume,

i.e., the energy is a function of some power of radius, density and time

Let,

C is a constant and hence dimensionless.

using dimension,

Putting the values,

Comparing LHS and RHS,

Hence, solving,

Putting the values,