Both　the　heat　transfer　and　the　flow　resistance　are　important　for　the　design　of　heat　transfer　enhancement　techniques.　The　field　synergy　principle　of　velocity　and　temperature　has　been　widely　used　in　the　optimization　of　convective　heat　transfer　processes,　but　the　field　synergy　principle　for　flow　resistance　is　still　lacking.　In　this　work,　a　field　synergy　principle　between　velocity　and　pressure　is　derived　for　the　flow　resistance.　The　derivation　of　the　principle　is　based　on　the　divergence　theorem.　The　differential　equations　are　used　to　clarify　the　physical　meaning　of　the　principle.　The　analysis　demonstrates　that　the　negative　of　the　integral　of　the　product　of　velocity　and　total　pressure　gradient　equals　the　pumping　power　of　the　flow.　Therefore,　the　principle　states　that　the　better　the　synergy　of　velocity　and　total　pressure　fields,　which　means　smaller　intersection　angle　between　velocity　and　total　pressure　gradient,　the　lower　the　pumping　power　consumed.　The　static　pressure　can　also　be　used　in　the　principle　when　the　change　of　the　flow　rate　of　dynamic　pressure　is　insignificant.　Numerical　examples　are　used　to　validate　the　principle.　This　study　indicates　that　the　synergy　among　velocity,　temperature,　and　pressure　fields　is　important　for　the　design　of　high-efficiency　heat　transfer　enhancement　techniques.