A closed vessel is filled with water. The area of the lower base of the vessel $S_{1}=100 m^{2}$, the area of the upper base $S_{2}=200 \: m^{2}$ the height of the vessel $h=50 m$. The water pressure force on the upper base $F_{2}=100 \: N$. find the pressure force on the lower base of the vessel if the density of water $\rho_{0} =1000 \: kg/m^{3}$, the acceleration of free fall $g=10 \: m/s^{2}$
Decision:
Water pressure on the top base $p_{2}= \frac{F_{2}}{S_{2}}$, on the bottom base $p_{1} = p_{2} + \rho gh = \frac{F_{2}}{S_{2}} + \rho gh$. Pressure force on the bottom base:
$F_{1}=p_{1}S_{1}=F_{2} \frac{S_{1}}{S_{2}}+ \rho ghS_{1}=100 N$.
Decision:
Water pressure on the top base $p_{2}= \frac{F_{2}}{S_{2}}$, on the bottom base $p_{1} = p_{2} + \rho gh = \frac{F_{2}}{S_{2}} + \rho gh$. Pressure force on the bottom base:
$F_{1}=p_{1}S_{1}=F_{2} \frac{S_{1}}{S_{2}}+ \rho ghS_{1}=100 N$.