A ball is traveling at a horizonal spee of 7.75 m/s and isspinning about a verti

Question

A ball is traveling at a horizonal spee of 7.75 m/s and isspinning about a vertical axis with angular velocity of 57.7 rad/s.if the radius of the ball is .1 m and the density of air is1.204kg.m^3 find the magnitude of the pressure differential actingto make this ball curve in flight. (assume the ball carries a layerof air on its surface at rest with the spinning surface- i.e.spinning around with the surface) The problems I am having with this problem is, understanding what the "magnitude of the pressure differential" is. v=7.75 r=.1 =57.7 air= 1.204 The equation i think i should use is (4/3)(4r3 air v) any help is appreciated A ball is traveling at a horizonal spee of 7.75 m/s and isspinning about a vertical axis with angular velocity of 57.7 rad/s.if the radius of the ball is .1 m and the density of air is1.204kg.m^3 find the magnitude of the pressure differential actingto make this ball curve in flight. (assume the ball carries a layerof air on its surface at rest with the spinning surface- i.e.spinning around with the surface) The problems I am having with this problem is, understanding what the "magnitude of the pressure differential" is. v=7.75 r=.1 =57.7 air= 1.204 The equation i think i should use is (4/3)(4r3 air v) any help is appreciated

Explanation / Answer

According to Bernoulli's equation
P1 + (1/2)v1^2 + gh1 = P2 + (1/2)v2^2 +gh2 h1 = h2 = 0 or P1 - P2 = (1/2)v2^2 -(1/2)v1^2          = 1000 kg/m^3 v1 = 7.75 m/s v2 = r * w = .1 * 57.7 = 5.77m/s          

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