# HW4 - this distance in the time it takes to travel from the mound to the plate A baseball is obviously spherical but for the purposes of this

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MAE 150A, Winter 2009 J. D. Eldredge Homework 4 (5 problems), due Friday, February 6 1. Problem 11.50, Wilcox (2nd edition: 11.46) 2. Problem 11.52, Wilcox (2nd edition: 11.48) 3. Problem 11.51, Wilcox (2nd edition: 11.52) 4. Use Matlab to plot the streamline pattern for uniform ﬂow U past a circular cylinder of radius R and circulation Γ. Since ψ is constant on streamlines, a contour plot of ψ will produce a streamline pattern (without the arrows). The contour function in Matlab can help with this (type help contour ). I’ve attached an example of what one might look like. Construct a plot for three diﬀerent values of the parameter Γ / ( U R ), which correspond to (respectively): two stagnation points on cylinder surface, one stagnation point on surface, and no stagnation points on surface. 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 Streamlines for Γ = 1/2 Γ c x/R y/R 5. A baseball pitcher wants to throw a curveball that ‘breaks’ 1 m (i.e. it moves horizontally by
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Unformatted text preview: this distance in the time it takes to travel from the mound to the plate). A baseball is obviously spherical, but for the purposes of this problem we will take it to be cylindrical (with axis oriented vertically), with a mass per unit depth of 2 kg/m and a diameter of 7 cm. Suppose that the pitch is thrown with a velocity of 80 mph. The distance from the mound to homeplate is 60 ft 6 in, and the density of air is 1.2 kg/m 3 . Using potential ﬂow theory (and thus ignoring drag forces), estimate the rotation rate (in rev/min) that the pitch must be thrown with in order to achieve the desired break. (Note: for rigid body rotation, the vorticity is equal to twice the rotation rate. Relate circulation to this.)...
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## This note was uploaded on 10/09/2009 for the course MAE 150A taught by Professor Eldridge during the Spring '09 term at UCLA.

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