2. Suppose that an incompressible fluid passes through a pipe that changes in cross-sectional area from 0.25 m2 to 0.125 m2. How will this affect the fluid velocity? (10 points)

Answers

Answer 1

Answer:

The fluid velocity will increase as it passes through the pipe with the decreasing cross-sectional area.

Explanation:

According to the principle of continuity in fluid dynamics, the product of the fluid's cross-sectional area and its velocity remains constant as it flows through a pipe, assuming the fluid is incompressible and there are no sources or sinks of fluid along the pipe.

In this scenario, as the cross-sectional area of the pipe decreases from 0.25 m² to 0.125 m², the fluid velocity will increase. This is because the product of the area and velocity must remain constant, and since the area decreases, the velocity must increase to compensate and maintain the constant product.

Mathematically, we can express this relationship as:

A₁V₁ = A₂V₂

Where A₁ and A₂ are the initial and final cross-sectional areas of the pipe, and V₁ and V₂ are the initial and final velocities of the fluid.

Since A₂ (0.125 m²) is smaller than A₁ (0.25 m²), V₂ must be larger than V₁ to satisfy the equation. Therefore, the fluid velocity will increase as it passes through the pipe with the decreasing cross-sectional area.

Hope this helps!

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