Simulates, via Monte Carlo
(limited time), the height attained by a random volume, V,
of incoherent material in a conical hopper with semi-included angle¹
θ, in order to find the distribution of the height,
possibly to avoid spills. (For [V] = dm³, it is of course
[H] = dm.)
The volume is considered
either Gaussian, with σ = δ,
or (symmetrical) triangular in μ ± a,
with a = δ.
In the Figure, is shown a hopper (fr. trémie,
pt tremonha²). Without loss of generality,
an unlimited height is admitted for the (complete) cone.
Plots the density function (pdf), f(h), and
the probability function (cdf), F(h),
for the height, and computes its mean and standard-deviation.
(Vol. of cone.xlsx)
Other suggested data:
triangular, (μ, δ) = (1, 0.67);
Gaussian, (μ, δ) = (1, 0.17).
¹ Or "half-wall angle" ([Nguyen et al.,
1979])
² From Latin trimodia, a measure of
three bushels (fr boisseau, pt alqueire: 12.75 L) |
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