Oxygen is supplied to an astronaut through an umbilical hose that is $7 \mathrm{~m}$ long. The pressure in the oxygen tank is $200 \mathrm{kPa}$ at a temperature of $10^{\circ} \mathrm{C}$, and the pressure in the space suit is $20 \mathrm{kPa}$. If the umbilical hose has an equivalent roughness of $0.01 \mathrm{~mm}$, what should the hose diameter be to supply oxygen at a rate of $0.05 \mathrm{~kg} / \mathrm{s}$ ? If the suit springs a leak and the pressure drops to zero, at what rate will the oxygen escape?