As was stated earlier, closure rate is determined by the penstock/scroll case allowable pressure. Too fast and water hammer can cause a failure.
As for opening rate, this is a function of the torque available and the inertia of the machine. If you could open the gates instantaneously the unit would still ramp up to speed almost linearly due to the inertial constraints. The problem comes in as you approach sync speed. Now you have to control overshoot. Wicket gate opening rates are generally established so the system is over damped to prevent overshoot.
Realize, the limiting factor in unit control generally isn't gate speed it's the characteristic time of the unit as a whole due to inertia. There's also fluid dynamic limitations, close or open the gates too quickly and you'll probably notice more cavitation damage at your wicket gates, stay vanes, and turbine blades/buckets.
Tom Moritz
Mechanical Engineer
US Bureau of Reclamation