Concept explainers
As described in Prob. 1.22, in addition to the downward force of gravity (weight) and drag, an object falling through a fluid is also subject to a buoyancy force that is proportional to the displaced volume. For example, for a sphere with diameter
(a) Derive a
(b) Rewrite the differential equation from (a) for the special case of a sphere.
(c) Use the equation developed in (b) to compute the terminal velocity (i.e., for the steady-state case). Use the following parameter values for a sphere falling through water: sphere diameter
(d) Use Euler's method with a step size of
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