Question

The best football club in the world (Juventus F. C.) have hired you to develop a turf heat exchanger system for their practice ground in Vinovo (outside Turin, Italy). The premise of this new turf is that you can control the surface properties (firm or soft) by controlling its temperature and will enable their team to practice in the most diverse conditions. You design a heat exchanger system that uses coolant pipes below the turf, through which you will circulate a temperature regulated heat exchanger fluid to control the turf temperature conditions. The pipes are run across the width of the pitch below the turf (?50 m long) and have an inner flow diameter of 1 cm, and the heat exchanger fluid has the following properties: ? = 1000 kg/m3 , µ = 2 × 10-2 Pa·s. If the maximum expected volumetric flowrate through one pipe is calculated to be 3600 L/hour, estimate the pressure drop required to meet that volumetric flowrate requirement by the following method:

(a) Sketch the diagram of the problem and specify your coordinate system.

(b) State your assumptions for fluid flow.

(c) Starting with the appropriate governing equations in the differential form, simplify them based on your assumptions.

(d) From the simplified governing equations, first derive an expression for the velocity distribution in the pipe and then derive an expression for the volumetric flowrate.

(e) Using the given volumetric flowrate and your derived expression, calculate the pressure drop for the coolant flow through the pipe.

Answer 1