A soap bubble, blown by a mechanical pump at the mouth of a tube...

$\dfrac{dV}{dt} = k$

$⇒ V = kt$

$⇒ \dfrac{4}{3}\pi{r}^{3} = kt$

$⇒ r = {\left(\dfrac{3k}{4\pi}\right)}^{\dfrac{1}{3}}{t}^{\dfrac{1}{3}}$

$P - {P}_{0} = \dfrac{4T}{r}$

$⇒ P - {P}_{0} = 4T . \left(\dfrac{3k}{4\pi}\right)\dfrac{1}{3} . \dfrac{1}{t\dfrac{1}{3}}$$⇒ P = 4T . \left(\dfrac{3k}{4\pi}\right)\dfrac{1}{3} . \dfrac{1}{t\dfrac{1}{3}} + {P}_{0}$