Water at 120F flows in an iron pipe 10 ft long, whose

Chapter , Problem 7.50

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Water at \(120^{\circ} \mathrm{F}\) flows in an iron pipe 10 ft long, whose inner and outer radii are 1/2 in. and 3/4 in. The temperature of the surrounding air is \(70^{\circ} \mathrm{F}\).

(a) Assuming that the water temperature remains constant along the length of the pipe, compute the heat loss rate from the water to the air in the radial direction, using the following values. For iron, \(k=10.1 \ \mathrm{lb} / \mathrm{sec}-{ }^{\circ} \mathrm{F}\). The convection coefficient at the inner surface between the water and the iron is \(h_{i}=16 \ \mathrm{lb} / \mathrm{sec}-\mathrm{ft}-{ }^{\circ} \mathrm{F}\). The convection coefficient at the outer surface between the air and the iron is \(h_{o}=1.1 \ \mathrm{lb} / \mathrm{sec}-\mathrm{ft}-{ }^{\circ} \mathrm{F}\).

(b) Suppose the water is flowing at 0.5 ft/sec. Check the validity of the constant-temperature assumption. For water, \(\rho=1.94 \ \mathrm{slug} / \mathrm{ft}^{3}\) and \(c_{p}=25,000 \ \mathrm{ft}-\mathrm{lb} / \text { slug- }{ }^{\circ} \mathrm{F}\).