Chapter 9I9-1. U=U(x) =c 1 x+c 2 , U=U(r) =c 1 lnr+c 2 , U=U(ρ) =−c 1 /ρ+c 2
I9-2.
Streamlinessinαx+ cosαy=cand velocity field is derivable from potential function
φ=V 0 cosαx−V 0 sinαyI9-3.
Streamlines xy=c
Potential φ=x^2 −y^2I9-4.
Streamlinesy^2 −x^2 =c
Potentialφ= 2xyI9-5. φ=φ(r) = ln(r 0 /r)
I9-6. True
I9-7. Write∇^2 φ=∇·(∇φ) = 0and∇×(∇φ) = 0
I9-8. (c)
Solutions Chapter 9