Bernoulli Fountain

A piston is pressed with a force $\vec{\bf F}$ on a hydraulic cylinder containing water ($\rho = 10^3$ kg/m$^3$). The cross sectional area of the cylinder is $A = 100$ cm$^2$. The water therein is forced into a pipe with a cross sectional area of $a = 1$ cm$^2$ that rises vertically a height $H = 50$ meters. Both the end of the pipe (at the top) and the back of the piston (at the bottom) are open to atmospheric pressure.

a) What does $F$ have to be to make the water spurt from the pipe with a speed of 10 meters/sec at the top?

b) What is the pressure (in atmospheres, where 1 atm = 10$^5$ Pascals) inside the cylinder at the bottom at that time?