Question

Calculate the Reynolds number, Re = (2rρv)/ η , for the following situations and decide whether the flow of fluid around them is laminar or turbulent. Then calculate the frag force using the appropriate formula.

For the radius, use r = 2(Area/perimeter) which, for a circle, gives the radius. Densities and viscosities are in the table on page 2. Also, to keep things uniform, we will use the boundaries for laminar and turbulent flow from Engineer's Toolbox, also on pg. 2

[1] A car with 1.5 m² square cross-sectional area moving at 2 m/s through the air at 20°C.

[2] Same car at 27 m/s (just over 60 mph)

[3] The fastest human swimmers can travel at 2.3 m/s. Use this speed for a swimmer underwater (an overestimate) and use a radius of 0.7 meters.

[4] For a blue whale, a fast speed is 13.9 m/s and the radius for their cross-section is 1.9 meters. Calculate the Reynolds number.

[5] Many microscopic organisms and small multi-cell creatures who live (and move) in water move by using flagella or shorter cilia moving in a wavelike fashion to push against the water.   A large paramecium can have a radius of 0.5 mm. and can move at speeds up to 1mm/s. Calculate the Reynolds number for these "wee beasties"¹

	density (kg/m3)	viscosity (cp=mPa•s)
water 20°C	1000	1.03
air       20°C	1.204	.02217
peanut butter	1090	250,000

Answer 1