A nurse administers medication in a saline solution to a patient by infusion into a vien in patient's arm. The density of the solution is `1.0xx10^3(kg)/(m^3)` and the gauge pressure in the vien is `2.4xx10^3Pa`. How high above the insertion point must the container be hung so that there is sufficient pressure to force the fluid into the patient?

Explanation

The container must be hung high enough so that the gauge pressure due to liquid in the tube and the contain is at least as great as the gauge pressure inside the vein i.e.,
`P_(liquid)=rhogh=2.4xx10^3Pa`
i.e, `h=(2.4xx10^3Pa)/(rhog)`
Thus , `h=(2.4xx10^3Pa)/((1.0xx10^3(kg)/(m^3))(9.8(m)/(s^2)))`
`=0.24m=24cm`
To actually establish a flow through the needle the container would need to be higher than 24 cm.