Unit 33: Viscosity & Poiseuille’s Law
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.
*Q33.1) Water undergoes viscous flow through a horizontal capillary of radius 1mm. What flow rate would result from a pressure gradient of 10 Pa/m across the length of the capillary?
***Q33.4) Consider two capillaries through which water flows. Both capillaries have the same length and are subjected to the same pressure difference, but one capillary has four-times the radius of the other. If it takes 2 minutes for a certain volume of water to flow through the larger capillary, how long would it take the same volume of water to flow through the smaller capillary?
**Q33.2) Plaque can build up on the inside of arteries causing a narrowing of the arterial passage as shown below. Consider a portion of an artery with sufficient plaque to reduce the cross-sectional area of the artery to 30% of the healthy region’s. Find the ratio of the blood pressure gradient at the narrow region to that of the wide region.
**Q33.3) Water undergoes viscous flow through two horizontal capillaries attached to a tank of water at different depths as shown below. Both capillaries have the same length, but the upper capillary has three times the radius of the lower one. Calculate the ratio of the flow rate through the upper capillary to that through the lower one.