Problem 65
The Reynolds number for condensate flow is defined as $\operatorname{Re}=4 \dot{m} / p \mu_{l}\(, where \)p$ is the wetted perimeter. Obtain simplified relations for the Reynolds number by expressing \(p\) and \(\dot{m}\) by their equivalence for the following geometries: \((a)\) a vertical plate of height \(L\) and width \(w,(b)\) a tilted plate of height \(L\) and width \(w\) inclined at an angle \(u\) from the vertical, (c) a vertical cylinder of length \(L\) and diameter \(D,(d)\) a horizontal cylinder of length \(L\) and diameter \(D\), and (e) a sphere of diameter \(D\).
Problem 67
A vertical 0.5- \(\mathrm{m} \times 0.5-\mathrm{m}\) square plate is used in a process to condense saturated water vapor. If the desired rate of condensation is \(0.016 \mathrm{~kg} / \mathrm{s}\), determine the necessary surface temperature of the plate at atmospheric pressure. For this problem, as a first approximation, assume a film temperature of \(90^{\circ} \mathrm{C}\) for the evaluation of the liquid properties and a surface temperature of $80^{\circ} \mathrm{C}$ for the evaluation of modified latent heat of vaporization. Are these good assumptions?
Problem 69
Saturated steam at 1 atm condenses on a \(2-\mathrm{m}\)-high and 10 -m-wide vertical plate that is maintained at \(90^{\circ} \mathrm{C}\) by circulating cooling water through the other side. Determine (a) the rate of heat transfer by condensation to the plate, and (b) the rate at which the condensate drips off the plate at the bottom. Assume wavy-laminar flow. Is this a good assumption?
Problem 72
Saturated steam at \(100^{\circ} \mathrm{C}\) condenses on a $2-\mathrm{m} \times 2-\mathrm{m}\( plate that is tilted \)30^{\circ}$ from the vertical. The plate is maintained at \(80^{\circ} \mathrm{C}\) by cooling it from the other side. Determine (a) the average heat transfer coefficient over the entire plate and (b) the rate at which the condensate drips off the plate at the bottom. Assume wavy-laminar flow. Is this a good assumption?
Problem 74
Saturated steam at \(30^{\circ} \mathrm{C}\) condenses on the outside of a 4 -cm-outer-diameter, 2-m-long vertical tube. The temperature of the tube is maintained at \(20^{\circ} \mathrm{C}\) by the cooling water. Determine \((a)\) the rate of heat transfer from the steam to the cooling water, \((b)\) the rate of condensation of steam, and (c) the approximate thickness of the liquid film at the bottom of the tube. Assume wavy-laminar flow and that the tube diameter is large relative to the thickness of the liquid film at the bottom of the tube. Are these good assumptions?
Problem 75
Saturated water vapor at atmospheric pressure condenses on the outer surface of a \(0.1-\mathrm{m}\)-diameter vertical pipe. The pipe is \(1 \mathrm{~m}\) long and has a uniform surface temperature of \(80^{\circ} \mathrm{C}\). Determine the rate of condensation and the heat transfer rate by condensation. Discuss whether the pipe can be treated as a vertical plate. Assume wavy-laminar flow and that the tube diameter is large relative to the thickness of the liquid film at the bottom of the tube. Are these good assumptions?
Problem 76
Saturated steam at \(55^{\circ} \mathrm{C}\) is to be condensed at a rate of $10 \mathrm{~kg} / \mathrm{h}$ on the outside of a 3 -cm-outer-diameter vertical tube whose surface is maintained at \(45^{\circ} \mathrm{C}\) by the cooling water. Determine the required tube length. Assume wavy-laminar flow and that the tube diameter is large relative to the thickness of the liquid film at the bottom of the tube. Are these good assumptions?
Problem 81
Saturated refrigerant-134a vapor undergoes conASTM A268 TP443 stainless steel tube at \(133 \mathrm{kPa}\). The tube is \(50 \mathrm{~cm}\) long and has a diameter of \(15 \mathrm{~mm}\). According to the ASME Code for Process Piping, the minimum temperature suitable for ASTM A268 TP443 stainless steel tube is \(-30^{\circ} \mathrm{C}\) (ASME B31.3-2014, Table A-1M). Determine whether the condensation of refrigerant- \(134 \mathrm{a}\) on the tube surface at a rate of \(3 \mathrm{~g} / \mathrm{s}\) would cool the surface below the minimum suitable temperature set by the ASME Code for Process Piping.
Problem 85
The condenser of a steam power plant operates at a pressure of $4.25 \mathrm{kPa}$. The condenser consists of 144 horizontal tubes arranged in a \(12 \times 12\) square array. The tubes are \(8 \mathrm{~m}\) long and have an outer diameter of \(3 \mathrm{~cm}\). If the tube surfaces are at $20^{\circ} \mathrm{C}\(, determine \)(a)$ the rate of heat transfer from the steam to the cooling water and (b) the rate of condensation of steam in the condenser. Answers: (a) \(5060 \mathrm{~kW}\), (b) \(2.06 \mathrm{~kg} / \mathrm{s}\)
Problem 90
Four long ASTM A437 B4B stainless steel bolts are used to hold two separated plates together. The bolts are cylindrical, and each has a diameter of \(13 \mathrm{~mm}\). Between the two plates, the horizontal bolts are exposed to saturated propane vapor. The length of each bolt between the plates is \(15 \mathrm{~cm}\). The bolts are arranged in a vertical tier, and condensation of saturated propane occurs on the bolts at 344 \(\mathrm{kPa}\). The minimum temperature suitable for ASTM A437 B4B stainless steel bolts is \(-30^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-2M). Determine the highest rate of condensation that can occur on the bolts, without cooling the bolts below the minimum suitable temperature set by the ASME Code for Process Piping.
