Which instrument is commonly used to measure relative humidity?

During blood transfusion the needle is inserted in a vein where the gauge pressure is $2000 \mathrm{Pa}$. At what height must the blood container be placed so that blood may just enter the vein? ( Take the density of blood to be $1.06 {\mathrm{Kgm}}^{-1}$)

Torricelli’s barometer used mercury. Pascal duplicated it using French wine of density$984 {\mathrm{kgm}}^{-3}$. Determine the height of the wine column for normal atmospheric pressure.

It is known that density $\mathrm{\rho }$ of air decreases with height $y$ as $\mathrm{\rho }=\mathrm{\rho }₀{\mathrm{e}}^{-\mathrm{y}/\mathrm{y}₀}$. Where ${\rho }_0= 1.25 \mathrm{kg} {\mathrm{m}}^{-3}$ is the density at sea level, and ${\mathrm{y}}_0$ is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of $g$ remains constant.

Explain why

The blood pressure in humans is greater at the feet than at the brain

A vertical off-shore structure is built to withstand a maximum stress of ${10}^{9 }\mathrm{Pa}$. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly $3 \mathrm{km}$, and ignore ocean currents.
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A U-tube contains water and methylated spirit separated by mercury. The colunms in the two arms are in level with $10 \mathrm{cm}$ of water in one arm and $12.5 \mathrm{cm}$ of spirit in the other. If $15.0 \mathrm{cm}$ of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms? (Specific gravity of mercury $= 13.6$, Specific gravity of spirit is $0.8$)

A U-tube contains water and methylated spirit separated by mercury. The colunms in the two arms are in level with $10.0 \mathrm{cm}$of water in one arm and $12.5 \mathrm{cm}$ of spirit in the other. What is the specific gravity of spirit?

A tank with a square base of area$1.0 {\mathrm{m}}^2$ is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area $20 {\mathrm{cm}}^2$. The tank is filled with water in one compartment, and an acid (of relative density $1.7$) in the other, both to a height of $4.0 \mathrm{m}$. Compute the force necessary to keep the door close.

Explain why,

Atmospheric pressure at the height of about $6 \mathrm{km}$ decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than$100 \mathrm{km}$.