EML 4304C 1. Why are liquids usually transported in circular pipes?

2.

What is the physical significance of the Reynolds number? How is it defined for (a) flow in a circular pipe of inner diameter D and (b) flow in a rectangular duct of cross section a x b?

3.

Consider a person walking first in air and then in water at the same speed. For which motion will the Reynolds number be higher? Show mathematically.

4. Show that the Reynolds number for flow in a circular pipe of diameter D can be expressed as . Re = & 4m D

5. Which fluid at room temperature requires a larger pump to flow at a specified velocity in a given pipe: water or engine oil? Why?

6. What is the generally accepted value of the Reynolds number above which the flow in smooth pipes is turbulent?

7. Consider the flow of air and water in pipes of the same diameter, at the same temperature, and at the same mean velocity. Which flow is more likely to be turbulent? Why?

8. What is the hydraulic diameter? How is it defined? What is it equal to for a circular pipe of diameter D?

9. How is the hydrodynamic entry length defined for flow in a pipe? Is the entry length longer in laminar or turbulent flow?

10. Consider laminar flow in a circular pipe. Will the wall shear stress w be higher near the inlet of the pipe or near the exit? Why? What would your response be if the flow were turbulent?

11. How does surface roughness affect the pressure drop in a pipe if the flow is turbulent? What would your response be if the flow were laminar?

12. Derive the equation for the velocity profile in the annulus shown in the figure below. The steady flow is fully developed and v = w = 0.

Hint: Use the x-momentum equationdp d du + r dx r dr dr

0=