Problem 1.6 A heat exchanger is being designed as a component of a geothermal power system in which heat is transferred from the geothermal brine to a "clean" fluid in a closed-loop power cycle. The heat exchanger, a shell and tube type, consists of 100 galvanized iron tubes 2cm in diameter and 5 m long, connected in parallel. The temperature of the fluid is 200°C, the density is 860 kg'm', and the viscosity is 1.35×10* Nm'. The total mass-flow rate through the exchanger is 50 kg's. a) Calculate the pumping power required to operate the heat exchanger, neglecting entrance and outlet losses. b) After continued use, 2 mm of scale develops on the inside surfaces of the tubes. This scale has an equivalent roughness of 0.5 mm. Calculate the power required under these conditions.

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.