Figure (a) below shows a U-shaped tube containing an amount of mercury. The left arm of the tube has cross-sectional area A1 of 11.0 cm2, and the right arm has a cross-sectional area A2 of 4.90 cm2. In both arms, the mercury is at the same level, as shown. In figure (b) below, 300 g of water is poured into the right arm of the tube and sits atop the mercury, all of it within the right arm. The mercury level in the right arm has been displaced downward, and the mercury level in the left arm has been displaced upward from its original level by a distance h. The density of mercury is 13.6 g/cm3, and the density of water is 1.00 g/cm3. Figure (a) shows a U-shaped tube filled with mercury. Both arms of the U-shaped tube are vertical. The left arm with cross-sectional area A1 is wider than the right arm with cross-sectional area A2. The height of the mercury is the same in both arms. Figure (b) shows the same U-shaped tube, but now most of the right arm is filled with water. The height of the column of water in the right arm is much greater than the height of the column of mercury in the left arm. The height of the mercury in the left arm is greater than the height of the mercury in the arms in Figure (a), and the difference in height is labeled h. (a) What is the length (in cm) of the column of water in the right arm of the U-shaped tube? cm (b) What distance h (in cm) does the mercury rise in the left arm? cm

On another planet that you are exploring, a large tank is open to the atmosphere and contains ethanol. A horizontal pipe of cross-sectional area 7.0×10−4m27.0×10−4m2 has one end inserted into the tank just above the bottom of the tank. The other end of the pipe is open to the atmosphere. The viscosity of the ethanol can be neglected. You measure the volume flow rate of the ethanol from the tank as a function of the depth hh of the ethanol in the tank. If you graph the volume flow rate squared as a function of hh, your data lie close to a straight line that has slope 2.09×10−5m5/s22.09×10−5m5/s2.   What is the value of gg, the acceleration of a free-falling object at the surface of the planet? Express your answer with the appropriate units.

In the hydraulic system shown in the figure (see below) the piston on the left has a diameter of 5.2 cm and a mass of 2.0kg. The piston on the right has a diameter of 15 cm and a mass of 3.6 kg. If the density of the fluid is 700 kg/m^3, what is the height difference h between the two pistons?

Maria is filling a bucket of water from a faucet. After she turns it on, she sees that the cross-sectional area of the water stream right below the faucet is about the size of a quarter, or 4.62 × 10^−4 m2 . The stream constricts to about the size of a dime, or 2.52 × 10^−4 m2 , after falling 2.50 cm. If the bucket Maria is filling has a volume of 10.0 L, how long will it take to fill the bucket?

The figure below shows a horizontal pipe with a varying cross section. A liquid with a density of 1.65 g/cm³ flows from left to right in the pipe, from larger to smaller cross section. The left side's cross-sectional area is 10.0 cm², and while in this side, the speed of the liquid is 2.72 m/s, and the pressure is 1.20 × 105 Pa. The right side's cross sectional-area is 4.00 cm². (a) What is the speed (in m/s) of the liquid in the right side (the smaller section)? (Enter your answer to at least three significant figures.) m/s (b) What is the pressure (in Pa) of the liquid in the right side (the smaller section)? Pa