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Chapter 4: Problem 19

Air flows steadily through a circular, constant-diameter duct. The air is perfectly inviscid, so the velocity profile is flat across cach flow area. However, the air density decreases as the air flows down the duct. Is this a one-, two-, or three-dimensional flow?

Short Answer

Expert verified
The flow of air in this duct is one-dimensional.

Step by step solution

01

Identify Characteristics

Identify the characteristics of the given problem - the air is flowing at a steady rate, the velocity profile is the same across the duct, but the density of the air decreases down the duct. This means that while there are no changes horizontally or vertically inside the duct, there are changes longitudinally in density.
02

Determine Dimension of Flow

Compare identified characteristics to the definitions of types of flow. One dimensional flow: Changes are happening only in the direction of the flow.Two-dimensional flow: Changes are happening in two directions, not necessarily parallel to the flow.Three-dimensional flow: Changes are happening in all directions, in the plane of the flow and the direction of the flow.In this case, the variation in air density happens only in one direction along the streamline (length of the duct), while the velocity profile stays the same across the area of the duct, which means changes are only happening in one direction - the direction of the flow. This shows that it's a one-dimensional flow.

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