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The duct enlarges until it takes on a square cross-section with sides of 15 inches. Considering that the air can be regarded as an incompressible fluid V₂ is 0.94 ft/sec.
By the equation of continuity
(Rate of volumetric flow rate is constant)
A₁v₁ = A₂v₂
(6×6)×5.9(inch²ft/sec) = (15×15)×v₂
V₂ = 5.9(36/225) ft/sec
V₂ = 0.944 ft/sec
In fluid dynamics, or more broadly in continuum mechanics, an incompressible fluid (also known as an isochoric flow) is a flow in which the material density within a fluid parcel—an infinitesimal volume that moves with the flow velocity—remains constant. The idea that the flow velocity has zero divergences is comparable to the idea that incompressibility exists (see the derivation below, which illustrates why these conditions are equivalent).
The fact that fluid flows incompressibly does not mean that it cannot be compressed. In the derivation that follows, it is demonstrated that even compressible fluids can be roughly described as incompressible flow under the appropriate circumstances. If a fluid parcel flows with the flow velocity, it is said to have incompressible flow, meaning the density stays constant.
Learn more about incompressible fluid here:
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