$1-113$ Intravenous infusions are usually driven by gravity by hanging the fluid bottle at sufficient height to counteract the blood pressure in the vein and to force the fluid into the body. The higher the bottle is raised, the higher the flow rate of the fluid will be$.($a$)$ If it is observed that the fluid and the blood pressures balance each other when the bottle is $80cm$ above the arm level, determine the gage pressure of the blood. $($b$)$ If the gage pressure of the fluid at the arm level needs to be $15$ kPa for sufficient flow rate, determine how high the bottle must be placed. Take the density of the fluid to be $1020k\frac{g}{m^3}.$