CV Calculations for Emergency Shutdown Valve

For any on/off valve, the Cv calculation is not usually necessary. Of what use is it (rhetorical question)?

You would want to know the Cv of valves in order to know the pressure drop across them. This affects the economics of your valve choice - that is, what is acceptable to the process against the cost of the valve.

The Cv and the Gain (delta flow/delta valve travel) and the closing time can be very important factors in determining the suitability of emergency shutdown valves in process systems. For example, will tripping of the Emergency valve shut the system down faster than the anti surge valves on the compressor recycle can open resulting in serious surge of say an axial compressor.

So to answer your question - probably yes, but maybe not.