In the hydraulic system shown in the figureFigure 1 the pist

In the hydraulic system shown in the figure(Figure 1). the piston on the left has a diameter of 4.5 cm and a mass of 1.9 kg. The piston on the right has a diameter of 12 cut and a mass of 3.1 kg. If the density of the fluid is 700 kg/m^3 what is the height difference h between the two pistons? Express your answer using hwo significant figures.

Solution

Set the pressures equal P_L = P_R

m_L g / A_L = m_R g / A_R + p g h

h = 1/p [m_L / A_L - m_R / A_R] = 1/p [m_L / pi/4 D_L²- m_R / pi/4 D_R²]

h = [ 4 / pi * p ] * [m_L / D_L² -  m_R / D_R²]

= [ 4 / pi * 700 ] * [1.9 / 0.045² - 3.1 / 0.12²]

= 1.32 m