In one observation, the column in a mercury barometer has a measured height $h$ of $740.35 \mathrm{~mm}$. The temperature is $-5.0^{\circ} \mathrm{C}$, at which temperature the density of mercury $\rho$ is $1.3608 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$. The free-fall acceleration $g$ at the site of the barometer is $9.7835 \mathrm{~m} / \mathrm{s}^2$. What is the atmospheric pressure at that site in pascals and in torr?

In analyzing certain geological features, it is often appropriate to assume that the pressure at some horizontal level of compensation, deep inside Earth, is the same over a large region and is equal to the pressure due to the gravitational force on the overlying material. Thus, the pressure on the level of compensation is given by the fluid pressure formula. This model requires, for one thing, that mountains have roots of continental rock extending into the denser mantle (as shown in figure). Consider a mountain of height $H=6.0 \mathrm{~km}$ on a continent of thickness $T=32 \mathrm{~km}$. The continental rock has a density of $2.9 \mathrm{~g} / \mathrm{cm}^3$, and beneath this rock the mantle has a density of $3.3 \mathrm{~g} / \mathrm{cm}^3$. Calculate the depth $D$ of the root. (Hint: Set the pressure at points $a$ and $b$ equal; the depth $y$ of the level of compensation will cancel out.)

We fully submerge an irregular 3 kilogram lump of material in a certain fluid. The fluid that would have been in the space now occupied by the lump has a mass of 2 kilogram. When we release the lump, does it move upward, move downward, or remain in place?

When a pilot takes a tight turn at high speed in a modern fighter airplane, the blood pressure at the brain level decreases, blood no longer perfuses the brain, and the blood in the brain drains. If the heart maintains the (hydrostatic) gauge pressure in the aorta at 120 torr (or mm Hg) when the pilot undergoes a horizontal centripetal acceleration of 4 g, what is the blood pressure (in torr) at the brain, 30 cm radially inward from the heart? The perfusion in the brain is small enough that the vision switches to black and white and narrows to “tunnel vision” and the pilot can undergo g-LOC (“g-induced loss of consciousness”). Blood density is 1.06 × 10³ kg/m³.

The shown in the given figure is filled with water and is open at the top. If d=5.0 m, what is the force due to the water on face B^??

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density 1.30 × 10³ kg/m³. The area of each base is 4.00 cm², but in one vessel the liquid height is 0.854 m and in the other it is 1.560 m. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

The L-shaped tank shown in given figure is filled with water and is open at the top. If d=5.0 m, what is the force due to the water on face A.

A large aquarium of height 5.00 m is filled with fresh water to a depth of 2.00 m. One wall of the aquarium consists of thick plastic 8.00 m wide. By how much does the total force on that wall increase if the aquarium is next filled to a depth of 4.00 m?

As shown in the figure, an open tube of length L=1.8m and cross-sectional area A=4.6$\mathrm{cm}$^2$is fixed to the top of a cylindrical barrel of diameter$D=1.2 $\mathrm{~m} and height$H=1.8 $$ \mathrm{m}$. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel. Why is that ratio not equal to 1.0? (You need not consider the atmospheric pressure.) $$

A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of 1.08 g/cm³. To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water?

When a person snorkels, the lungs are connected directly to the atmosphere through the snorkel tube and thus are at atmospheric pressure. In atmospheres, what is the difference $\Delta P$ between this internal air pressure and the water pressure against the body if the length of the snorkel tube is $4\text{~ m}$ (probably lethal situation)? In the latter, the pressure difference causes blood vessels on the walls of the lungs to rupture, releasing blood into the lungs. An elephant can safely snorkel through its trunk while swimming with its lungs $4.0\text{~ m}$ below the water surface because the membrane around its lungs contains connective tissue that holds and protects the blood vessels, preventing rupturing.

When a person snorkels, the lungs are connected directly to the atmosphere through the snorkel tube and thus are at atmospheric pressure. In atmospheres, what is the difference $\Delta P$ between this internal air pressure and the water pressure against the body if the length of the snorkel tube is $20\text{~ cm}$ (standard situation) ?

Crew members attempt to escape from a damaged submarine 100 m below the surface. What force must be applied to a pop-out hatch, which is 1.2 m by 0.60 m, to push it out at that depth? Assume that the density of the ocean water is 1024 kg/m³ and the internal air pressure is at 1.00 atm.

What gauge pressure must a machine produce in order to suck mud of density 1800 kg/m³ up a tube by a height of 1.5 m?