Exam 12: Fluid Mechanics

Bernoulli's principle: Water flows in the horizontal pipe shown in the figure. At A the diameter is 5.00 cm and at B the diameter is 4.00 cm The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. The manometer reading h is 4.40 cm. We can treat water as an ideal fluid having a density of 1000 kg/m³. What volume of water is flowing through the pipe per second?

Viscosity: Glycerin, with a viscosity of 1.50 N ∙ s/m², is flowing with an average speed of 1.20 m/s through a tube that has a radius of 5.00 mm and is 25.0 cm long. What is the drop in pressure between the ends of the tube?

Pressure: One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. A square window in an outside wall of the house measures 2.02 m on each side. What net force (directed outwards) is exerted on this window? (1 atm = 1.01 × 10⁵ Pa.)

Pressure in a fluid: In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is 510 kg/ .

Viscosity: Suppose that the build-up of fatty tissue on the wall of an artery decreased the radius by 10%. By what percent would the arterial pressure difference produced by the heart have to be increased to maintain a constant blood flow?

Bernoulli's principle: You are driving a late model convertible car at the 65 mph speed limit with its soft flexible roof closed up and the windows closed. You observe that the roof

Density: What is the radius of a sphere that has a density of 5000 kg/m³ and a mass of 6.00 kg?

Buoyancy: A cup of water containing an ice cube at 0°C is filled to the brim. The tip of the ice cube sticks out of the surface. As the ice melts, you observe that

Density: A sphere is constructed of two concentric parts. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m³. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The material in the outer shell has a density 9000 kg/m³. (a) What is the mass of the sphere? (b) What is the average density of this sphere?

Buoyancy: A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m³?

Pressure in a fluid: On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 10⁵ N/m². At a depth 5.00 m below the surface, the absolute pressure is 8.00 × 10⁵ N/m². The density of liquid nitrogen is 808 kg/m³. (a) What is the atmospheric pressure on planet X? (b) What is the acceleration due to gravity on planet X?

Buoyancy: A 7.8-kg solid sphere, made of metal whose density is 2500 kg/ , is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³), what is the tension in the cord?

Bernoulli's principle: A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m³, and the density of the paint is 1200 kg/m³. We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate?

Pascal's principle: A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem, you can neglect the weight of the pistons.)

Buoyancy: A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What net force does the water exert on the lower face of the cylinder?

Buoyancy: A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What is the weight of the cylinder?

Flow rate: An incompressible fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

Pascal's principle: A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil with a density of 800 kg/m³ and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem, you can neglect the weight of the pistons.)

Buoyancy: A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

Buoyancy: A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.