Question

Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation ? Explain.

Answer 1

Using Bernoulli's theorem : $P+\rho gh+\frac{1}{2}\rho v^2=$ constant

where $P$ is the absolute pressure at a point, $\rho$ 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 $P_1+\rho g{h}_1+\frac{1}{2}\rho v_1^2=$ $P_2+\rho g{h}_2+\frac{1}{2}\rho v_2^2$

Subtracting atmospheric pressure from both sides.

We get $P_1-P_o+\rho g{h}_1+\frac{1}{2}\rho v_1^2=$ $P_2-P_o+\rho g{h}_2+\frac{1}{2}\rho v_2^2$

Gauge pressure $P_i^{\prime }=P_i-P_o$ $(i=1,2)$

$⟹$ $P_1^{\prime }+\rho g{h}_1+\frac{1}{2}\rho v_1^2=$ $P_2^{\prime }+\rho g{h}_2+\frac{1}{2}\rho v_2^2$

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.