Applied Hydraulics #$1\mathrm{.}5\mathrm{.}2$

Mercury $($Specific Gravity $=13\mathrm{.}6)$ is used in a glass tube to measure pressure. If the surface tension is $0\mathrm{.}57$ N$/$m and the contact angle ranges from $40$ degrees to $50$ degrees, determine the minimum diameter of the tube so that the measurement error in the manometer does not exceed $1\mathrm{.}0$ mm$.$