Problem

Venturimeter.gif

Consider an ideal fluid of density flowing through a horizontal pipe of variable cross-sectional area. The fluid at the portion of the pipe with cross-sectional area is moving at and has a measured pressure of . The fluid at the portion of the pipe with cross-sectional area is moving at and has a measured pressure of .

Part 1: Determine in terms of and .

Part 2: Two different fluids of density (fluid in the horizontal pipe) and (fluid in the u-shaped manometer), where . The height difference of the fluid in the manometer is . It helps to let . Determine in terms of and .

Solution

Part 1

There are two important equations for this problem:

1) The continuity equation
2) Bernoulli’s equation

From the first equation we find

.

Since there is no change in the altitude of the pipe; hence,

.

Isolate for

.

Part 2

Treat the manometer as two static column problems.

Substitute the difference of pressure into the result from part 1 to get

.
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