Practice & Test Mechanical Properties of Fluids

A U-tube with both ends open to the atmosphere contains two immiscible liquids. One liquid is water of density $1000 \text{ kg/m}^3$ and the other liquid is oil of unknown density. The water column in the right arm is 10 cm high, and the oil column in the left arm is 12.5 cm high. The interface between the two liquids is at the same level in both arms. What is the density of the oil?

A U-tube closed at one end is filled with three immiscible liquids having densities $\rho, 3\rho$ and $8\rho$ as shown in the following figure. The pressure at point C inside the tube is (Figure: the left arm of the U-tube is open to the atmosphere, pressure $p_0$. Reading down the left arm: a column of height $h$ of the liquid of density $\rho$, then a column of height $2h$ of density $3\rho$, then the liquid of density $8\rho$, which fills the bend and rises up the right arm. A horizontal dashed line joins A on the left arm to B on the right arm at the level of the $3\rho$/$8\rho$ interface, a height $h/4$ above the bottom of the straight portion of the tube. The right arm is closed at the top; the point C lies in the closed space immediately above the top of the $8\rho$ column, whose surface is a height $2h/3$ above the bottom of the straight portion of the tube.)

A hydraulic lift is used to lift a car of mass 3000 kg. The cross-sectional area of the lift on which the car is supported is $5 \times 10^{-2}\ m^{2}$. What is the pressure on the smaller piston, if both the pistons are at the same horizontal level? Take g = 10 m/s$^{2}$.