HOMEWORK ASSIGNMENT #1

ME 303 FLUID DYNAMICS/ WESTPHAL/ WSU/ FALL 2000

• Follow the Homework Guidelines for preparing your submission. REMEMBER TO PROVIDE THE DISCUSSION UNLESS EXPLICITLY INSTRUCTED TO OMIT IT.
• You are encouraged to work together with other students, but the work you submit cannot be a machine-produced duplication of another student's work - it must be an original, but can represent your version of a collaborative effort.
• Late work not accepted!

The assignment consists of the problems given below.

1. Your instructor weighs 162 lbf and his height is 69 inches. Compute the following quantities BY HAND EXPLICITLY SHOWING UNIT CONVERSIONS (you may certainly check your work using a computer-based unit conversion tool though!). Discussion may be omitted.
   
   • Weight in N.
   • Mass in lbm, slugs, and kg.
   • Height in mm and miles.
   • Volume in cubic ft, cubic m, and gallons, assuming instructor's density is equal to that of 20 deg. C seawater.
   • Average cross-sectional area in sq ft and sq m.
   
   
   
2. USING THE IDEAL GAS LAW (you can check your work using a computer tool or tabulation though!), calculate the density of air at sea level (pressure: 101 kPa absolute) and 10 deg C, as well as at 1500 m elevation (pressure: 84.6 kPa absolute) and 30 deg C. These two conditions represent a cool day at Seattle and a warm day at Denver, respectively. For your discussion: what would be the implication for the difference in travel of a golf ball under these two conditions, assuming fluid drag forces are directly proportional to density when other factors are equal?
   
   
3. An engine crankshaft of 50 mm diameter rotates at 600 rpm when the engine is being started. If one crankshaft main bearing is 30 mm long, its clearance is 0.1 mm, and it is filled with SAE 30 oil at 10 C, what shear stress is developed during starting? What are the torque and power required to overcome the fluid friction for one such bearing? HINT: Assume that the oil velocity varies linearly in the gap. You may omit any discussion for this problem.
   
   
4. Derive equations for the pressure within (a) a water droplet, and (b) a soap bubble. Assume that the soap solution has the same properties as water. Calculate the gage pressure within a 2 mm diameter droplet and a 2 mm diameter bubble. For your discussion, consider how diameter influences droplet and bubble pressures.
   
   
5. Get a transparent drinking straw - smaller diameter, as typical for cocktail straws, are best. Predict the capillary rise height of water in the straw, then put it in a cup of water (add some food coloring to make this observation easier--or, use coffee or tea) and compare the observed rise to your prediction. Now flatten the straw -- you can use a few bent paper clips for this. Re-examine the theoretical analysis and determine whether it indicates that the capillary rise in the flattened straw will be greater or less than the round straw. What do your observations show?
   
   
6. Knowing that the vapor pressure of water at 100 deg C is 101 kPa and decreases linearly with temperature at the rate of 3.1 kPa per deg C (alternatively, you can use a saturated steam table to get more exact temperature-vapor pressure data), create a table or graph showing water boiling point vs. elevation for elevations from sea level to 3,500 m. For your discussion, consider that the proposed application for this chart is to measure the boiling point of a pan of water with a small pocket thermometer as a means to determine elevation while backpacking... will this work? Will pressure variations caused by changing weather (how much does weather influence atmospheric pressure anyway?) influence the readings? NOTE: to work this problem, you'll need to know the atmospheric pressure at various elevations. You may the on-line tool from Ilan Kroo for this purpose. There are also many printed sources for the "US Standard Atmosphere" -- check some of the suggested fluids references.