Problem 110
The mass diffusivity of ethanol $\left(\rho=789 \mathrm{~kg} / \mathrm{m}^{3}\right.\( and \)M=46 \mathrm{~kg} / \mathrm{kmol}$ ) through air was determined in a Stefan tube. The tube has a uniform cross-sectional area of \(0.8 \mathrm{~cm}^{2}\). Initially, the ethanol surface was $10 \mathrm{~cm}$ from the top of the tube; after 10 hours elapsed, the ethanol surface was \(25 \mathrm{~cm}\) from the top of the tube, which corresponds to \(0.0445 \mathrm{~cm}^{3}\) of ethanol being evaporated. The ethanol vapor pressure is \(0.0684 \mathrm{~atm}\), and the concentration of ethanol is zero at the top of the tube. If the entire process was operated at $24^{\circ} \mathrm{C}$ and 1 atm, determine the mass diffusivity of ethanol in air.
Problem 111
Methanol \(\left(\rho=791 \mathrm{~kg} / \mathrm{m}^{3}\right.\) and $\left.M=32 \mathrm{~kg} / \mathrm{kmol}\right)$ undergoes evaporation in a vertical tube with a uniform cross-sectional area of \(0.8 \mathrm{~cm}^{2}\). At the top of the tube, the methanol concentration is zero, and its surface is $30 \mathrm{~cm}$ from the top of the tube (Fig. P14-111). The methanol vapor pressure is \(17 \mathrm{kPa}\), with a mass diffusivity of $D_{A B}=0.162 \mathrm{~cm}^{2} / \mathrm{s}$ in air. The evaporation process is operated at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). (a) Determine the evaporation rate of the methanol in \(\mathrm{kg} / \mathrm{h}\) and (b) plot the mole fraction of methanol vapor as a function of the tube height, from the methanol surface \((x=0)\) to the top of the tube \((x=L)\).
Problem 112
A tank with a 2-cm-thick shell contains hydrogen gas at the atmospheric conditions of \(25^{\circ} \mathrm{C}\) and \(90 \mathrm{kPa}\). The charging valve of the tank has an internal diameter of \(3 \mathrm{~cm}\) and extends $8 \mathrm{~cm}$ above the tank. If the lid of the tank is left open so that hydrogen and air can undergo equimolar counterdiffusion through the 10 -cm- long passageway, determine the mass flow rate of hydrogen lost to the atmosphere through the valve at the initial stages of the process. Answer: \(4.20 \times 10^{-8} \mathrm{~kg} / \mathrm{s}\)
Problem 116
The pressure in a pipeline that transports helium gas at a rate of $7 \mathrm{lbm} / \mathrm{s}\( is maintained at \)14.5$ psia by venting helium to the atmosphere through a \(0.4\)-in-internal-diameter tube that extends $30 \mathrm{ft}$ into the air. Assuming both the helium and the atmospheric air to be at \(80^{\circ} \mathrm{F}\), determine \((a)\) the mass flow rate of helium lost to the atmosphere through the tube, (b) the mass flow rate of air that infiltrates into the pipeline, and (c) the flow velocity at the bottom of the tube where it is attached to the pipeline that will be measured by an anemometer in steady operation.
Problem 119
What is the physical significance of the Schmidt number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Schmidt number of 1 indicate?
Problem 120
What is the physical significance of the Lewis number? How is it defined? What does a Lewis number of 1 indicate?
Problem 121
Under what conditions will the normalized velocity, thermal, and concentration boundary layers coincide during flow over a flat plate?
Problem 122
Heat convection is expressed by Newton's law of cooling as $\dot{Q}=h A_{s}\left(T_{s}-T_{\infty}\right)$. Express mass convection in an analogous manner on a mass basis, and identify all the quantities in the expression and state their units.
Problem 123
What is the physical significance of the Sherwood number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Sherwood number of 1 indicate for a plane fluid layer?
Problem 124
In natural convection mass transfer, the Grashof number is evaluated using density difference instead of temperature difference. Can the Grashof number evaluated this way be used in heat transfer calculations also?
