Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain
Using Bernoulli's theorem : P+ρgh+21ρv2= constant where P is the absolute pressure at a point, ρ is the density of the fluid, h is the height of that point above a reference point and v is the velocity of fluid at that point. Thus P1+ρgh1+21ρv12= P2+ρgh2+21ρv22 Subtracting atmospheric pressure from both sides. We get P1−Po+ρgh1+21ρv12= P2−Po+ρgh2+21ρv22 Gauge pressure Pi′=Pi−Po (i=1,2) ⟹ P1′+ρgh1+21ρv12= P2′+ρgh2+21ρv22 Thus the Bernoulli's equation remains in the same form. Hence, it does not matter if one uses gauge instead of absolute pressure in applying Bernoulli's equation.
