1. To maintain the flow of a fluid at a steady rate, one must continually apply a force to the fluid (i.e. a pressure gradient) to overcome the frictional resistance to flow that is represented by the viscosity. The greater the viscous forces in the fluid, the greater the magnitude of pressure gradient that must be applied.
Consider the flow of water through a pipe of diameter 5 cm that is made of commercial steel. Let us say that we have a section of the pipe that is 10 m long and that the pressure at the end of the pipe is 1 atm.
(a) Plot (in atm) the pressure drop across the section of pipe vs. Reynolds' number for values of Re from 0.1 to 2100 and from 4000 to 106. Use a log-log plot for clarity. What is the range of velocities that these Reynolds' numbers represent?
Hint: You can specify the Reynolds' number, and then from the velocity calculate the pressure drop. Or, you can specify the pressure drop and then calculate the corresponding velocity. Examine both options and chose the easiest approach.
(b) On the same plot, for Reynolds' numbers above 4000 plot the pressure drop that you would expect if laminar flow were observed rather than turbulent flow.
Explain in physical terms why this laminar pressure drop is greater or less than the pressure drop observed in real-life because of the presence of turbulence.
(c) If you had flow at a Reynolds' number of 100,000, what length of pipe would be required for the pressure drop to be 10% of the absolute pressure at the exit (atmospheric pressure)?
(d) If you keep the velocity of the fluid at the same value, but now increase the diameter of the pipe to a value of 1 m, what is the length of pipe that would be required for the pressure drop to be 10% of the magnitude of atmospheric pressure?
2. Solve problem 3.14, p. 146 of Munson
3. Solve problem 3.26, p. 147 of Munson
4. Solve problem 3.34, p. 149 of Munson
5. Solve problem 3.61, p. 152 of Munson