An incompressible fluid flows steadily through a pipe that has a change in diameter. the fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. what is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

5.10 m/s

Explanation:

The volumetric flow rate for an incompressible fluid through a pipe is constant, so we can write:

(1)

where

is the cross-sectional area of the first part of the pipe

is the cross-sectional area of the second part of the pipe

is the speed of the fluid in the first part of the pipe

is the speed of the fluid in the second part of the pipe

Here we have:

is the radius in the first part of the pipe, so the area is

is the radius in the first part of the pipe, so the area is

Using eq.(1), we find the fluid speed at the second location:

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