... and some modern steam vessels use steam turbines. Their speed is at least partially limited by the need to prevent turbine blades from flying off. But, in addition, trying to turn the turbines faster takes a lot more steam. So you also have limits due to the boilers' steam producing capacity.
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Steam turbines caught on during WWI, I think the Nevada was the first battleship to have them, her sister Oklahoma had traditional compound engines for a side by side comparison. Everything after had turbines but a few classes had electric motors to actually move the ship (late WWI era)
USS Iowa following Operation Hailstone:
Cdr (Rear Admiral, posthumously) Moriya Setsuji's (former CO of SUZUKAZE) destroyer NOWAKI flees the onslaught. Both American battleships - the fastest in the world - give chase at 32.5 knots. At 35,000 yards, NEW JERSEY and IOWA open fire and straddle NOWAKI with their first salvos. NOWAKI flees into the sun's glare, so at 38,000 yards both battleships fire under radar control. At 22 miles, these are the longest range shots ever fired by American battleships against an enemy vessel. At 39,000 yards, Admiral Spruance orders Cease Fire. NOWAKI escapes and eventually makes her way back to Yokosuka.
That had to be scary on the Nowaki who had a top speed of 35kts... so she was barely outpacing two battleships firing from beyond the horizon.
Allegedly the captain of the Iowa called for more steam, the engineer reported back he had plenty of steam but nowhere to put it as the throttles were wide open.
And the Rodney bypassed her governors during the Bismark chase and actually beat her test speed while carrying parts for a refit in the US while chasing Bismarck.
So there is some wiggle room especially for short periods of time.
USS Iowa during a high speed run in the 1980's, it is hitting the hulls max speed so the stern is getting sucked down as it tries to force its way faster with more brute force.
http://www.navsource.org/archives/01/0161049.jpg