**Problem**

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

- .