Question

Air flows through a heating duct with a square cross-section with 6-inch sides at a speed of 4.5 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 15 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.

Answer 1

For incompressible fluid we can write continuity equation:

$$A_1 v_1 = A_2 v_2 (1)$$

where A₁=d² , A₂=D²

Using (1) we got:

$$v_2=\frac {A_1v_1}{ A_2} (2)$$

We got:

v₂=0.72 ft/s

Answer:

0.72 ft/s