Homework assignments in *.pdf format

  1. Assignment due Friday, 28 February 2003

    1. List as many factors as you can think of, that limit the maximum stepping frequency in walking.

    2. An ultra-marathon involves a run of 100 Km. A time of 6 hours, 40 minutes is world-class for this race. Estimate the chemical energy burned and the water evaporated by an 80 Kg runner during such a race. A typical fruit juice provides about 680 Kcal (mostly sugar) per liter. Assuming the runner wishes neither to lose weight nor to urinate, but to eliminate all water by evaporation, how much juice does he need to drink during the race, and should the juice be diluted with water or concentrated, and by how much?

    3. The following table exhibits the Reynolds numbers and stopping distances for various living organisms in H2O. That is, it will list them when you fill in the columns marked “R” and “Stopping distance”.

      Reynolds numbers for various organisms in H2O
      Animal Speed (cm/sec) Size (cm) R Stopping distance
      Porpoise 1340 200                                            
      Barracuda 670 100                                            
      Human 170 150                                            
      Bacterium 0.003 0.0001                                            

    4. Suppose you have a network of smaller and smaller pipes that branch and re-branch, as shown below.
      1. Under what condition (on the areas of the pipes before and after the junction) will the flow velocity of an incompressible fluid be the same after a junction as before? (Consider separately the cases of pulsatile and steady flow.)

      2. Suppose the impedance of the n'th pipe (and all its subsequent branches) is Zn. If a pipe branches into a constant number, K, of identical smaller pipes at a junction, and if the individual impedances of those pipes (and all their subsequent branches) are Zn+1, and if the impedance of a pipe of length Ln and radius rn is zn = gLn/rn2, express Zn in terms of zn and Zn+1. (Hint: pretend these are series and parallel resistances in an electrical circuit.)

    5. In Q 4b above, I gave a formula for the flow impedance of a pipe: zn = gLn/rn2
      1. Does this formula apply to steady or to pulsatile flow?
      2. Express g in terms of geometric constants, viscosity, etc.

    6. Please supply three possible term-paper topics. (Nag, nag ;-)


    Solutions to HW#3


  2. AssignmentDue 21 March 2003 (in *.pdf format)      Solutions to HW#4


  3. AssignmentDue 11 April 2003 (in *.pdf format)      Solutions to HW#5


  4. AssignmentDue 25 April 2003 (in *.pdf format)     Solutions to HW#6