After pouring some water into the U-tube of (Figure 1), you pour a volume V_1 of

Question

After pouring some water into the U-tube of (Figure 1), you pour a volume V_1 of oil of mass density P_1 = 800 kg/m^3 into the left side of the tube and a volume V2 of oil of mass density P2 =700 kg/m^3 into the right side. Once the two oils have been added, the levels on the left and right sides are the same, and the water level on the right side is a height h_2=15 mm higher than the water level on the left side. What is the height h_1 of the oil on the left side? Express your answer with the appropriate units.

Explanation / Answer

given

rho1 = 800 kg/m^3

rho2 = 700 kg/m^3

h1 = 15 mm = 0.015 m

we know, rho_water = 1000 kg/m^3

Pressure at the bottom line in two sides of the tube is same

Po + P_left = Po + P_right (here Po is atmopshric pressure)

rho1*g*h1 = rho2*g*(h1 - h2) + rho_water*g*h2

rho1*h1 = rho2*(h1 - h2) + rho_water*h2

800*h1 = 700*(h1 - 0.015) + 1000*0.015

800*h1 = 700*h1 - 10.5 + 15

h1*(800 - 700) = 15 - 10.5

h1*100 = 4.5

h1 = 4.5/100

= 0.045 m or 4.5 cm or 45 mm

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