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 .
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,
Treat the manometer as two static column problems.
Substitute the difference of pressure into the result from part 1 to get