EM 340 Homework set #10
(Due date: Nov. 26)
1. A steel ball of 3mm diameter was dropped into a 0.5m deep container filled with
motor-oil. Assuming that the ball sinking speed is the same from the moment it hits the
oil surface, calculate how long it will take for the ball to sink to the bottom of the
container? Note that the density of Steel is  = 7850 kg/m3 and the properties of oil are
taken from Table 1.1. Also calculate the Reynolds number
Solution: we can use Stokes formula (Eq. 6.77). The force pulling the ball down is its
weight minus the buoyancy:
2
U=
(rSteel - roil )gR2
(6.77)
9m
U=
2
m
(7850 - 919)9.8 × 0.0015 2 = 0.117
9 × 0.29
s
Next the Reynolds number must be calculated to validate the Stokes flow assumption:
Re =
919 × 0.117 × 0.003
= 1.11
0.29
and clearly the assumption was reasonable.
2. A large 1.9 m wide and 0.5 m high plate is carried above a truck perpendicular to the
vehicle motion (like a flat plate normal to the free stream). Calculate the additional power
required to carry the plate at a speed of 72 km/hr. Use air density as 1.22 and estimate the
drag coefficient from tables in the book.
Solution
The drag coeff. From Fig. 8.25 is then ~ 1.2
and the power requirement:
3. The antenna of a car traveling at 90km/hr is resonating (vibrating violently) at a
frequency of 500Hz. Estimate the antenna’s diameter (or which diameter to avoid?).
Solution:
Assume St ~ 0.2 and the diameter is
4. Assuming a person’s drag coefficient is CD~1.2, frontal area is 0.55m2 and air density
is 1.2 kg/m3. Calculate the wind forces on his body when the stormy wind speed reaches
108 km/hr.
Solution
5. A student is rolling down a slope of 5 deg with his skateboard. Neglecting the friction
in the wheels and assuming he weights 70kg, his frontal area is 0.7 m2, and his drag
coefficient is 1.1, calculate his terminal velocity (= 1.2 kg/m3 ).
Solution