Please show all work and explain along the way if possible! 1. The largest and t
ID: 3897063 • Letter: P
Question
Please show all work and explain along the way if possible!
1. The largest and the smallest balls used in the experiment are with diameter 9.52 mm, and 2.38 mm respectively. For a glycerin with viscosity 1.5 Pa.s, what is the time necessary for each ball to reach a velocity 99% of the terminal velocity? Density of the ball material is 1.42 g/cm^3. Round the result to three decimal places.
2. What is the Reynold's number for the fastest falling ball in the experiment. Use the same data as in problem 1, glycerin density of 1.30 g/cm^3, and acceleration of gravity 9.81 m/s^2.
GIVEN:
Re = (p x v x L) / n
F = Fw - Fb - Fv
F = 4/3(pi)r^3(ps - pf)(g) - 6(pi)nrv
Vterm = Kr^2
K = (2g / 9)(ps - pf / n)
n = 2g(ps - pf) / 9K
Vterm = Kr^alpha
Log(Vterm) = log(k) + alphaLog(r)
v(t) / Vterm = 1 - e^ (-t / x)
x = 2(ps)(r^2) / 9n
g = 9.81 m/s^2
n = 1.5 Pa.s
ps = 1.42 g/cm^3
pf = 1.30 g/cm^3
large r = 4.76 mm
small r = 1.17 mm
v(t) / Vterm = .99
Explanation / Answer
as per stokes law
v = g * D^2 *(d p
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