Answer:
1) Height of oil in right limb = 67.31 cm
2) Height of water in the right limb = 16.83 cm
Explanation:
The U-tube manometer is shown in the attached figure
Foe equilibrium The pressure at the bottom of the U tube should be same
Let the height of the water in the left limb of the manometer be [tex]h_L[/tex]
Thus the pressure at the bottom is found using the equation of pressure statics as
[tex]P_{bottom}=P_{atm}+\rho _{water}\times g\times h_{L}.............(i)[/tex]
Similarly for the liquid in the right limb the pressure at the bottom is the sum of the oil column and the water column
Thus we can write
[tex]P_{bottom}=P_{atm}+\rho _{water}\times g\times h_{}+\rho _{oil}\times g\times 4h_{}...........(ii)[/tex]
Equating the equations 'i' and 'ii' we get
[tex]P_{atm}+\rho _{water}\times g\times h_{L}=P_{atm}+\rho _{water}\times g\times h_{}+\rho _{oil}\times g\times 4h_{}\\\\\rho _{water}\times g\times 0.7=\rho _{oil}\times 4h\times g+\rho _{water}\times h\times g\\\\\therefore h_{}=\frac{0.7\times \rho _{water}}{4\times \rho _{oil}+\rho _{water}}\\\\h_{}=\frac{0.7\times 1000}{4\times 790+1000}=16.83cm[/tex]
Thus the height of oil is [tex]4\times 16.83=67.31cm[/tex] andthe height of water in the right limb is 16.83 cm.
