Problems

$1)$ Prove that the pressuce is the same in all directions at a point

in a static fluid for the three$-$dimensional case.

$2)$ Estimate the absolute and relative pressure at point $A.$

${}_w=9806\frac{N}{m^3}$;$,S{G}_{\text{m}\text{e}\text{r}\text{c}\text{u}\text{r}\text{y}}=13\mathrm{.}6$;$,P_{\text{a}\text{t}\text{m}}=101\mathrm{.}34kN{m}^2$

$3)$ For the U$-$tube monometer, estimate $x$ if the pressure of gas is equal to $39\mathrm{.}24k\frac{N}{m^2}.{}_{\text{o}\text{i}\text{l}}=7\mathrm{.}85k\frac{N}{m^3}$;${}_w=9\mathrm{.}806k\frac{N}{m}3$;$S{G}_{\text{m}\text{e}\text{r}\text{c}\text{u}\text{r}\text{y}}=13\mathrm{.}6$;

$P_{\text{a}\text{t}\text{m}}=101\mathrm{.}34k\frac{N}{m^2}$