i dont understand how we got the formulas and i don't understand why in the first one we ignored the atmospheric pressure please someone explain with details o don't ynderstand this chaoyer at allExample $9-206$

Oil$-$Water Tank

Origin: Textbook

Compute the gage pressure at the bottom of the oil and water tank. The specific gravity of oil is $0\mathrm{.}8.$

Solution

The hydrostatic equation states that

$\frac{p_1}{{}_o}+z_1=\frac{p_2}{{}_o}+z_2$

$\frac{p_2}{{}_w}+z_2=\frac{p_3}{{}_w}+z_3$

The pressure at the interface is then $p_2={}_w(-z_2{)}^{\text{I}}=9\mathrm{.}81(0\mathrm{.}9)$

The pressure at the bottom of the tank is

$p_3=p_2+{}_o(z_2-z_3)=-{}_o{z}_2+{}_w(z_2-z_3)=-0\mathrm{.}8(9\mathrm{.}81)(-0\mathrm{.}9)+9\mathrm{.}81(-0\mathrm{.}9+3)=27\mathrm{.}7$kPa