Unit 32: Continuity & Bernoulli's Equation
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q32.1) Water flows through the pipe shown below.
a) Find the flow rate through the pipe.
b) Find the flow speed at the wider end of the pipe.
**Q32.2) An incompressible fluid flows through the pipe shown below. The pipe splits into 3 identical branches, each half the cross-sectional area of the original pipe. Find the flow speed in each of the branches.
**Q32.4) Water flows through the horizontal pipe shown below. Find the water pressure at the wider end. You may treat water as an ideal fluid.
**Q32.3) Consider the pipe shown below with three sections of varying width. If an ideal fluid were to flow through this pipe, which of the following would be true?
A) Section A would have the highest pressure.
B) Section B would have the highest pressure.
C) Section C would have the highest pressure.
D) All three sections would have the same pressure.
**Q32.5) Water flows through the pipe shown below. Find the pressure difference P₂ - P₁. You may treat water as an ideal fluid.
***Q32.6) Air flows through a tapering pipe as shown below. The narrow end of the pipe has half the radius of the wide end, and a mercury-filled manometer connects the two ends. Find the flow speeds v₁ and v₂.