u can derive bernoulli's equa. by,..
if KE is half mvsquare chng in KE during displacement dy would be d(half mv square)=mv*dv(diffrentiation)

by applying work energy theorem....

mv*dv=Adl*dP ; whre Adl is the vol. of fluid element...

by doing dis..............

equa.. will be
p+row*g*y+halfrow*vsquare=constant