
Assuming there is no atmospheric pressure on piston, P1=πR2F and P2=P0.
Applying Bernoulli's equation at point 1 and 2,
p1+ρgh1+21ρv12=p2+ρgh2+21ρv22
⇒(πR2F)+ρg(h1−h2)=P0+21ρv22
⇒v2=πR2ρ2F−ρ2P0+2g(h1−h2)
v2=3.14×12×10002×(5×105)−10002×1.01×105+2×10×10
≈17.8ms−1