𝑅? =
𝜌??
𝜇
(4)
In the equation, ρ is the density (either air or
water), V is the free stream velocity, D is the
diameter, and μ is the dynamic viscosity. The
table below shows the calculated Reynold
’s
number values for air versus water.
Air
Water
Density (slugs/ft^3)
0.0024
1.94
Free Stream
Velocity (ft/s)
29.64
2.933
Diameter (ft)
0.0417
0.0417
Dynamic Viscosity
(lb-s/ft^2)
4.14E-
07
2.09E-05
Reynold's Number,
Re
7088
11349
Table 2. Reynold’s Number (Air vs.
Water)
The Reynold’s number for air isn’t
too far off from that of water. From that, we
can assume that both types of flows are
similar. The equation below is then used to
solve for the drag force caused by water flow
around the cylinder.
𝐹
𝐷
𝑤
=
1
2
?
𝐷
𝜌?
2
? (5)
In the equation above, F
D
/w represents the
drag force per unit length. The variable C
D
=
0.5322, ρ = 1.94 slugs/ft
3
, V = 2.933 ft/s, and
D = 0.0417 ft. Thus, F
D
/w = 0.1815 lbs/ft.