A glass Utube with a uniform diameter of 0.850 cm is used to determine the densi

Question

A glass Utube with a uniform diameter of 0.850 cm is used to determine the density

of an oil. A 24.5 cm column of water balances a 27.2 cm column of the oil so that interfaces A and B of the mercury with the other liquids are at

the same height. The density of water is 1000 kg/m^3

(a) Calculate the density of the oil.

(b) Calculate the absolute pressure at B, the interface between the water and the

mercury.

A new tube, identical to the Utube except for a cone shape on the left is filled with the same volume of mercury that was in the Utube. The mercury is at the same height on both sides of the new tube as it was in the Utube, as shown by the dashed line. The same volumes of oil and water that were in the Utube are now poured into the new tube, on the left and right respectively.

(c) Indicate the new position of B relative to A.

____ Above A ____ Below A ____ At the same height as A

Justify your answer.

(d) A small piece of wood with density less than that of the oil is placed so that it floats in

the left side of the tube. Indicate whether the pressure at the bottom of the tube

increases, decreases, or remains the same.

____ Increases ____ Decreases ____ Remains the same

Explanation / Answer

a) rho_oil*g*h1 = rho_water*g*h2

rho_oil = rho_water*h2/h1

= 1000*24.5/27.2

= 900.74 kg/m^3

b) P = Po*rho_water*g*h2

= 1.013*10^5 + 1000*9.8*0.245

= 103701 N/m^2

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