Capacitor rated voltage always should be at least twice as working voltage by default if we whant quality of product and reliability.
This capacitor rated at 16V will do the job, at 10V its on edge, and you risk life and health of 4700uF capacitor.
I will use 25V not lower. :wink:
Also load/consumer will suffer if that output filter capacitor goes down.
Among other things LM317 IC needs filtering capacitors to make factory guaranteed voltage according to datasheet.
I dont think that you need 4700uF for this circuit LM317 can provide up to 1,5A in best way, and about 1000uF per 1A is needed. 2200uF will be enough for this circuit.
Before add one more 100nF (0,1uF) if LM317 is far from first filter capacitor.
Also one more, and one big thing input voltage for LM317 should be at least 3V higher then output voltage, LM317 is not LDO voltage regulator. If you dont respect that you will get on output some unregulated and unwanted voltage.