Find the acceleration of a fluid particle for the following velocity profiles: (a) (v_{x}=Aleft(1-y^{2} ight) ; v_{y}=0

Find the acceleration of a fluid particle for the following velocity profiles:

(a) \(v_{x}=A\left(1-y^{2}\right) ; v_{y}=0 ; v_{z}=0\)

(b) \(v_{x}=A x ; v_{y}=-A y ; v_{z}=0\)

(c) \(v_{r}=0 ; v_{\theta}=A r ; v_{z}=0\)

(d) \(v_{r}=0 ; v_{\theta}=A / r ; v_{z}=0\)

(e) \(v_{r}=0 ; v_{\theta}=0 ; v_{z}=f(r)\)