Question #162649

Air flows through a heating duct with a square cross-section with 9-inch sides at a speed of 5.7 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 13 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid.


1
Expert's answer
2021-02-10T15:20:34-0500

By the equation of continuity

(Rate of volumetric flow rate is constant)

A1V1=A2V2(9×9)×5.7=(13×13)×V2461.7=169×V2V2=461.7169=2.73  ft/sA_1V_1 = A_2V_2 \\ (9 \times 9) \times 5.7 = (13 \times 13) \times V_2 \\ 461.7 = 169 \times V_2 \\ V_2 = \frac{461.7}{169} = 2.73 \;ft/s

Answer: 2.73 ft/s


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