A horizontal glass tube is filled with mercury. The tube thas three different cross sections as shwn: with `A_(1)=18cm^(2),A_(2)=8cm^(2)` and `A_(3)=9cm^(2)`. The piston is pushed so as to throw out mercury at a constant speed of v=6m/s at the other end of the tube. Assume that mercuty is an ideal fluid with density `rho_(Hg)=1.36xx10^(4)kg//m^(3)`. Take `g=10m//s^(2)P_("atm")=1.01xx10^(5)Pa`

(i) Find the force needed to push the piston assuming that friction force between the piston and the tube wal is f=40N
(ii) Find the height (h) of mercury column in the attached vertical tube. What happens to this height if the piston is pushed with smaller speed?

Answer

(i)371.2N
(ii) 26cm. Height h will increase