Ch 14: Fluids and Elasticity
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Problem 14
The 30-cm-long left coronary artery is 4.6 mm in diameter. Blood pressure drops by 3.0 mm of mercury over this distance. What are the (a) average blood speed and (b) volume flow rate in L/min through this artery?Problem 14
A 2.0 mL syringe has an inner diameter of 6.0 mm, a needle inner diameter of 0.25 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100 . b. The nurse empties the syringe in 2.0 s. What is the flow speed of the medicine through the needle?Problem 14
The bottom of a steel 'boat' is a 5.0 m x 10 m x 2.0 cm piece of steel (pₛₜₑₑₗ = 7900 kg/m³) . The sides are made of 0.50-cm-thick steel. What minimum height must the sides have for this boat to float in perfectly calm water?
Problem 14
Styrofoam has a density of 150 kg/m³ . What is the maximum mass that can hang without sinking from a 50-cm-diameter Styrofoam sphere in water? Assume the volume of the mass is negligible compared to that of the sphere.Problem 14
In FIGURE CP14.74, a cone of density p₀ and total height l floats in a liquid of density pբ . The height of the cone above the liquid is h. What is the ratio h/l of the exposed height to the total height?
Problem 14
A nuclear power plant draws 3.0 x 10⁶ L/min of cooling water from the ocean. If the water is drawn in through two parallel, 3.0-m-diameter pipes, what is the water speed in each pipe?Problem 14
20°C water flows through a 2.0-m-long, 6.0-mm-diameter pipe. What is the maximum flow rate in L/min for which the flow is laminar?Problem 14
(a) A nonviscous liquid of density p flows at speed v₀ through a horizontal pipe that expands smoothly from diameter d₀ to a larger diameter d₁ . The pressure in the narrower section is p₀. Find an expression for the pressure p₁ in the wider section.Problem 14
A tree loses water to the air by the process of transpiration at the rate of 110 g/h. This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000 vessels, each 100 μm in diameter, what is the upward speed in mm/s of the sap in each vessel? The density of tree sap is 1040 kg/m³.Problem 14
An aquarium of length L , width (front to back) W , and depth D is filled to the top with liquid of density p . (b) Find an expression for the force of the liquid on the front window of the aquarium.Problem 14
Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20 cm. The two liquids do not mix. What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?Problem 14
The average density of the body of a fish is 1080 kg/m³ . To keep from sinking, a fish increases its volume by inflating an internal air bladder, known as a swim bladder, with air. By what percent must the fish increase its volume to be neutrally buoyant in fresh water? The density of air at 20°C is 119 kg/m³.Problem 14
The tank shown in FIGURE CP14.73 is completely filled with a liquid of density p. The right face is not permanently attached to the tank but, instead, is held against a rubber seal by the tension in a spring. To prevent leakage, the spring must both pull with sufficient strength and prevent a torque from pushing the bottom of the right face out. (a) What minimum spring tension is needed?
Problem 14
(b) A pressure gauge reads 50 kPa as water flows at 10.0 m/s through a 16.8-cm-diameter horizontal pipe. What is the reading of a pressure gauge after the pipe has expanded to 20.0 cm in diameter?Problem 14
Water from a vertical pipe emerges as a 10-cm-diameter cylinder and falls straight down 7.5 m into a bucket. The water exits the pipe with a speed of 2.0 m/s. What is the diameter of the column of water as it hits the bucket?
Problem 14
A hurricane wind blows across a 6.0 m x 15.0 m flat roof at a speed of 130 km/h.(b) What is the pressure difference?Problem 14
Air flows through the tube shown in FIGURE P14.62 at a rate of 1200 cm³/s . Assume that air is an ideal fluid. What is the height h of mercury in the right side of the U-tube?
Problem 14
Air flows through the tube shown in FIGURE P14.63. Assume that air is an ideal fluid. (b) What is the volume flow rate?
Problem 14
An unknown liquid flows smoothly through a 6.0-mm-diameter horizontal tube where the pressure gradient is 600 Pa/m. Then the tube diameter gradually shrinks to 3.0 mm. What is the pressure gradient in this narrower portion of the tube?Problem 14
A 55 kg cheerleader uses an oil-filled hydraulic lift to hold four 110 kg football players at a height of 1.0 m. If her piston is 16 cm in diameter, what is the diameter of the football players' piston?Problem 14
A 5.0-m-diameter solid aluminum sphere is launched into space. By how much does its diameter increase? Give your answer in μm.Problem 14
One day when you come into physics lab you find several plastic hemispheres floating like boats in a tank of fresh water. Each lab group is challenged to determine the heaviest rock that can be placed in the bottom of a plastic boat without sinking it. You get one try. Sinking the boat gets you no points, and the maximum number of points goes to the group that can place the heaviest rock without sinking. You begin by measuring one of the hemispheres, finding that it has a mass of 21 g and a diameter of 8.0 cm. What is the mass of the heaviest rock that, in perfectly still water, won't sink the plastic boat?Problem 14
20°C water flows at 1.5 m/s through a 10-m-long, 1.0-mm-diameter horizontal tube and then exits into the air. What is the gauge pressure in kPa at the point where the water enters the tube?Problem 14
A water tank of height h has a small hole at height y. The water is replenished to keep h from changing. The water squirting from the hole has range 𝓍. The range approaches zero as y → 0 because the water squirts right onto the ground. The range also approaches zero as y → h because the horizontal velocity becomes zero. Thus there must be some height y between 0 and h for which the range is a maximum. (a) Find an algebraic expression for the flow speed v with which the water exits the hole at height y.Problem 14
(a) A cylindrical tank of radius 𝑅, filled to the top with a liquid, has a small hole in the side, of radius 𝓇, at distance d below the surface. Find an expression for the volume flow rate through the hole.Problem 14
What is the minimum hose diameter of an ideal vacuum cleaner that could lift a 10 kg (22 lb) dog off the floor?Problem 14
When a second student joins the first, the piston sinks . What is the second student's mass?
Problem 14
The 1.0-m-tall cylinder shown in FIGURE CP14.71 contains air at a pressure of 1 atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?
Hint: Boyle's law, which you learned in chemistry, says p₁V₁ = p₂V₂ for a gas compressed at constant temperature, which we will assume to be the case.
Problem 14
It's possible to use the ideal-gas law to show that the density of the earth's atmosphere decreases exponentially with height. That is, p = p₀ exp (─z/z₀), where z is the height above sea level, p₀ is the density at sea level (you can use the Table 14.1 value), and z₀ is called the scale height of the atmosphere. (b) What is the density of the air in Denver, at an elevation of 1600 m? What percent of sea-level density is this?Problem 14
A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it's been a while since you've checked. You can't find a tire gauge in the car, but you do find the owner's manual and a ruler. Fortunately, you've just finished taking physics, so you tell your friend, 'I don't know, but I can figure it out.' From the owner's manual you find that the car's mass is 1500 kg. It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 15 cm wide and the flattened segment of the tire in contact with the road is 13 cm long. What answer—in psi—will you give your friend?
