Tests on a sphere are conducted in a wind tunnel at an air speed of U 0 The velocity of flow toward the sphere along the longitudinal axis is found to be u U 0 (1 r 3 0 x 3 ), where r 0 is the radius of the sphere and x the distance from its center Determine the acceleration of an air particle on t...

Tests on a sphere are conducted in a wind tunnel at an air speed of U 0

Question:

Tests on a sphere are conducted in a wind tunnel at an air speed of U₀. The velocity of flow toward the sphere along the longitudinal axis is found to be u = –U₀ (1 – r³₀/x³), where r₀ is the radius of the sphere and x the distance from its center. Determine the acceleration of an air particle on the x-axis upstream of the sphere in terms of x, r₀, and U₀.