A. Do people who fire guns straight up into the air run the risk of hurting somebody?
B. Rowing shells used in college competitions are designed to minimize drag due to wave-making. They suffer primarily from boundary-layer drag. Furthermore, rowing shells of different sizes are isometric: their hull width is a constant fraction of their hull length. How does the maximum speed of a rowing shell scale with its length?
C. Shabu-shabu, which translates as "swish swish", is a method of Japanese cooking in which thin pieces of meat are moved through near-but-not boiling water. How does the heat flux into the meat vary with the speed at which the meat is moved?
D. Sterl's problem on automatic plant watering system (for homework or lecture/notes): A circular pipe of radius r and open at the bottom is tilted at an angle of 45 degrees to the vertical. Water is supplied at the top to replace what gravity pushes out the bottom. (a) What is maximum pipe radius r_max for which the flow will be laminar, not turbulent? (b) To keep the pipe supplied with water, the top end is stuck into a hole in the bottom of a standard coffee mug. Suppose the pipe has radius r_max and is 5 cm long. (i) There is a depth z_* of water in the mug below which the rate of outflow from the pipe does not depend on the depth in the mug, and above which the rate begins to increase significantly. Estimate z_*. (ii) How long would it take the pipe to empty the mug from the depth z_*? What changes would you make to turn this into a device to water your houseplants while away on vacation?
E. Towing icebergs: What size iceberg (assume it is a cube) would supply the needs of 20 million people for one year? How fast could we afford to tow it? Would melting in transit be a serious problem? At fixed speed, is it cheaper to tow one large iceberg or many smaller ones? To be economically feasible, the cost must be competitive with the current price of 15 cents per 100 gallons.
F. Estimate the mileage rating of your car from first principles.
G. Heat loss by sweating: A champion cyclist pedals at 50 km/hr over a level course for 0.5 hr. How much water does he/she lose through sweating?
H. Mars has an atmospheric pressure of 5e-3 Earth atmospheres, and a radius of 0.5 Earth radii. (a) Equipped with an oxygen mask, could an Earthling bird fly on Mars? (b) Could it land? (c) Could a mouse on Mars (also equipped with an oxygen mask) hear a falcon coming towards it in a free-fall dive?
I. Evaporating puddles (a) Estimate the evaporation time per centimeter depth of water maintained at 15 C in vacuum. At 15 C, the equilibrium vapor pressure is 13 mm of Hg. (b) Estimate the evaporation time per centimeter depth as a function of wind speed for water maintained at 15 C in air. Consider a puddle of 50 cm diameter. (c) Compare (a) and (b) to your experience with the disappearance of puddles in cloudy weather following a rain storm.
J. In a vertical climb, the F15 fighter plane can rise from sea level to 30 km altitude in 3 minutes. Its take-off weight (including fuel) is 18 tons. Its twin engines produce a combined 22.6 tons of thrust. (a) Estimate the mass of fuel used in the climb to 30 km. (b) Estimate the area of the F15's air intakes.
K. Estimate the plasma kinetic temperature at the base of the Space Shuttle at the time of re-entry.
L. Micrometeoroids are extraterrestrial particles 2-50 microns in size that rain continuously down to the Earth's surface. How do they survive entry into the atmosphere without burning up?
M. Estimate the radii of parachutes.
N. Brownian motion: A sphere is embedded within a gas at temperature T. The sphere random walks as it is bombarded by gas molecules. Estimate the rms displacement of the sphere after time t.
O. The solid core of a planet is found spinning faster than the surrounding liquid mantle. The liquid mantle has dynamic viscosity mu. Estimate the timescale for the core to de-spin relative to the mantle.
P. Estimate the wind speed of the tornado that swept up Dorothy's body.
Q. Compare the amount of fuel expended in automobiles to the amount of fuel expended in airplanes, globally.
R. Naked bodies: Estimate the net rate in watts at which your naked body loses or gains energy under the following conditions. (a) The sun is not shining, the air is still and its temperature is 20 C. (b) You are sunbathing beneath the noonday sun and the air temperature is 20 C. (c) The wind is blowing at 10 m/s, the sun is not shining, and the air temperature is 20 C. S. Estimate the sizes of lava tubes. T. Launching rockets: Does atmospheric drag represent a significant sink of energy when trying to launch a Saturn V rocket?