1. A drip coffee maker has a basket for grounds that is 5" in diameter. When making eight 6oz cups of coffee, ground coffee is added to the basket to a height of 2".
a. If 0.1" of water sits on top of the ground coffee during the entire brew process, what hydraulic pressure is exerted on the coffee grounds by the water?
b. Assume the water flowing through coffee grounds obeys Darcy's law; calculate the resistance of the coffee grounds to water flow.
c. Calculate the rate (ml/min) at which water is permeating through the coffee grounds if all of the water has passed through the grounds in 3½ min.
d. What is the permeability constant for the coffee grounds (cm2)?
2. A certain blood plasma filter has a permeability constant of 1.0 x 10-13 m2. Its area is 1.0 cm2 and its thickness is 1.0 mm. When a net pressure of 10.00 psi is applied across the filter, what is the volume flow rate of blood plasma through the filter? If spherical drops of blood plasma, each of diameter 4.0 mm, come out of the filter, how many drops per second will flow?
3. The blood protein albumin is approximately 66.5 kDa in weight. Assuming that the protein is approximately spherical in shape, what is its diameter?
4. A backpacking water filter that I purchased has a minimum absolute pore size (i.e., a pore diameter) of 2.0 µm.
a. Will this filter trap the hepatitis A virus, which has a total molecular weight (including protein envelope) of about 32,000 kDa? (Calculate the virus diameter assuming it is spherical and using a reasonable estimate of its density.) If it is not trapped, how could you kill the virus in the water when backpacking?
b. Will this filter trap the giardia cyst? If not, how could you kill giardia in the water when backpacking? (Note: you may find it useful to search the internet or reference books for the answers to parts b and c of this problem. Attach reference information for full credit.)
c. Is the E. coli O157:H7 bacterium a "good" bacterium, or a "bad" bacterium? What effects does it have on the body? Will this filter trap the E. coli O157:H7 bacteria? If not, how could you kill these bacteria in the water when backpacking?
5. Using the virus diameter found in Prob. 5a,
a. estimate the total number of hepatitis A viruses that could fit (in one layer) inside the period at the end of this sentence.
[ ans: Approx. 50,000,000. Your answer may vary depending upon your printer & measurement of the period. ]
b. Repeat this estimate for red blood cells. Assume they all lie flat in the plane of the paper.