Laminar flow in a triangular duct (Figure 3B.2)² one type of compact heat exchanger is shown in Figure 3B.2 (a). In order to analyze the performance of such an apparatus, it is necessary to understand the flow in a duct whose cross section is an equilateral triangle. This is done most easily by installing a coordinate system as shown in Fig. 3B.2 (b). 

(a) Verify that the velocity distribution for the laminar flow of a Newtonian fluid in a duct of this type is given by Fig. 3B.2. (a) Compact heat-exchanger element, showing channels of a triangular cross section; (b) coordinate system for an equilateral-triangular duct

(b) From Eq. 3B.2-1 find the average velocity, maximum velocity, and mass flow rate. 

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(Po - PL) v, = (y – H)(3x² – y) 4µLH (a) У y = H y = -V3x `y = v3 x (b)