Chapter 14: Fluids and Elasticity

A 6.0 m * 12.0 m swimming pool slopes linearly from a 1.0 m depth at one end to a 3.0 m depth at the other. What is the mass of water in the pool?

Postural hypotension is the occurrence of low systolic blood pressure when a person stands up too quickly from a reclining position. A brain blood pressure lower than $90mm$of $Hg$can cause fainting or lightheadedness. In a healthy adult, the automatic constriction and expansion of blood vessels keep the brain blood pressure constant while posture is changing, but disease or aging can weaken this response. If the blood pressure in your brain is $118mm$of $Hg$while lying down, what would it be when you stand up if this automatic response failed? Assume your brain is $40cm$from your heart and the density of blood is$1060kg/m^3$.

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$1500kg$. It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are $15cm$ wide and the flattened segment of the tire in contact with the road is $13cm$ long. What answer-in psi-will you give your friend?

A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is $10.0cm$deep. How far upward from its initial position does the mercury in the right arm rise?

Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Although most tiltmeters today are electronic, the traditional tiltmeter, used for decades, consisted of two or more water-filled metal cans placed some distance apart and connected by a hose. FIGURE $P14.45$shows two such cans, each having a window to measure the water height. Suppose the cans are placed so that the water level in both is initially at the $5.0cm$mark. A week later, the water level in can $2$is at the $6.5cm$mark.

A. Did can $2$move up or down relative to can $1$? By what distance?

B. Where is the water level now in can $1$?

Glycerin is poured into an open U-shaped tube until the height in both sides is $20cm$. Ethyl alcohol is then poured into one arm until the height of the alcohol column is $20cm$. 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?

An aquarium of length $L$, width (front to back) $W$, and depth $D$is filled to the top with liquid of density

a. Find an expression for the force of the liquid on the bottom of the aquarium.

b. Find an expression for the force of the liquid on the front window of the aquarium.

c. Evaluate the forces for a$100cm$-long, $35\text{-cm-wide,}40-\mathrm{cm}$deep aquarium filled with water.

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, $\rho ={\rho }_0\exp \left(-z/z_0\right)$, where $Z$is the height above sea level, ${\rho }_0$is the density at sea level (you can use the Table $14.1$value), and ${\mathrm{z}}_0$is called the scale height of the atmosphere.

a. Determine the value of ${\mathrm{z}}_0$.

Hint: What is the weight of a column of air?

b. What is the density of the air in Denver, at an elevation of $1600m$? What percent of sea-level density is this?

The average density of the body of a fish is $1080\mathrm{kg}/{\mathrm{m}}^3$. 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 ${20}^{\circ }\mathrm{C}\text{is}1.19\mathrm{kg}/{\mathrm{m}}^3$.

A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?