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A hydrometer is an instrument used to determine liquid density. A simple one is sketched in Figure P14.16. The bulb of a syringe is squeezed and released to let the atmosphere lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. The rod, of length L and average density ρ0, floats partially immersed in the liquid of density ρ. A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by
Figure P14.16 Problems 16 and 17
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Physics for Scientists and Engineers with Modern Physics
- A tank with a flat bottom of area A and vertical sides is filled to a depth h with water. The pressure is P0 at the top surface. (a) What is the absolute pressure at the bottom of the tank? (b) Suppose an object of mass M and density less than the density of water is placed into the tank and floats. No water overflows. What is the resulting increase in pressure at the bottom of the tank?arrow_forwardA rectangular block of Styrofoam 25.0 cm in length, 15.0 cm in width, and 12.0 cm in height is placed in a large tub of water. Assume the density of Styrofoam is 3.00 102 kg/m3. a. What volume of the block is submerged? b. A copper block is now placed atop the Styrofoam block so that the top of the Styrofoam block is level with the surface of the water. What is the mass of the copper block?arrow_forwardA hollow copper (Cu = 8.92 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?arrow_forward
- (a) A water hose 2.00 cm in diameter is used to fill a 20.0-L bucket. If it takes 1.00 min to fill the bucket, what is the speed v at which water moves through the hose? (Note: 1 L = 1 000 cm3.) (b) The hose has a nozzle 1.00 cm in diameter. Find the speed of the water at the nozzle.arrow_forwardA 10.0-kg block of metal measuring 12.0 cm by 10.0 cm by 10.0 cm is suspended from a scale and immersed in water as shown in Figure P15.24b. The 12.0-cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. (a) What are the magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water? (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.arrow_forwardA manometer is shown in Figure P15.36. Rank the pressures at the five locations indicated from highest to lowest. Indicate equal pressures, if any. FIGURE P15.36arrow_forward
- A uniform wooden board of length L and mass M is hinged at the top of a vertical wall of a container partially filled with a certain liquid (Fig. P15.81). (If there were no liquid in the container, the board would hang straight down.) Three-fifths of the length of the board is submerged in the liquid when the board is in equilibrium. Find the ratio of the densities of the liquid and the board.arrow_forwardFigure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists of a Venturi tube through which the fluid moves and a manometer used to measure the pressure difference between regions 1 and 2. The fluid of density tube moves from left to right in the Venturi tube. Its speed in region 1 is v1, and its speed in region 2 is v2. The necks cross-sectional area is A2, and the cross-sectional area of the rest of the tube is A1. The manometer contains a fluid of density mano. a. Do you expect the fluid to be higher on the left side or the right side of the manometer? b. The speed v2 of the fluid in the neck comes from measuring the difference between the heights (yR yL) of the fluid on the two sides of manometer. Derive an expression for v2 in terms of (yR yL), A1, A2, tube, and mano. FIGURE P15.52arrow_forwardFigure P15.47 shows a stream of water in steady flow from a kitchen faucet. At the faucet, the diameter of the stream is 0.960 cm. The stream fills a 125-cm3 container in 16.3 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. Figure P15.47arrow_forward
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