Condensation rates can be restricted by the speed of sound of the vapor phase. Hence, condensation can approach a sonic limit. Consider an \(S=2 \mathrm{~mm}\) wide, \(L=200 \mathrm{~mm}\) long vertical slot in a solid metal block. The slot is long into the page, so the fluid flow is two-dimensional. Saturated water vapor at atmospheric pressure condenses on the two large vertical surfaces of the slot, which are maintained at \(T_{s}=40^{\circ} \mathrm{C}\). As condensation proceeds, liquid water leaves the slot through the bottom opening and is replenished by saturated water vapor flowing upward through the same opening. Estimate the Mach number of the water vapor flowing upward through the slot opening. At what slot width does the Mach number of the water vapor reach unity?

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L x S T Condensate at low velocity Water vapor at high velocity