Question

Calculate the Reynolds number, Re- (2rpv)/ n, 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 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.

Answer 1

1) As the cross section is square, we will use hydraulic diameter

for square, d = 4A/P

so,

d = 4 * 1.5 / 4*1.2247

d = 1.2247 m

so,

NOTE - WHAT ARE THE UNITS OF VISCOSITY IN TABLE ??? IS IS mPa.s (does m here stands for milli..?.)

Reynold's number = 1.204 * 2 * 1.2247 / 0.02217E-3

Reynold's number = 1.33e5

--------------------------------------------------------------------------------------

(2) when v = 27 m/s

Reynold's number = 1.204 * 27 * 1.2247 / 0.02217E-3

Reynold's number = 1.8e6

--------------------------------------------------------------------------------------------

3) for swimmer,

Reynold's number = 1000 * 2.3 * 1.4 / 1.03e-3

Reynold's number = 3.12e6

------------------------------------------------------------------------------------------

4) for whale

Reynold's number = 1000 * 13.9 * 2 * 1.9 / 1.03e-3

Reynold's number = 5.12e7