Hydrostatic Pressure and Its Applications

Flashcards testing knowledge on hydrostatic pressure, gas and atmospheric pressure, hydraulic systems, and floatation based on the provided physics lecture notes.

How is pressure defined in physics, and what is its formula?

Pressure is defined as the force acting on a unit area. Its formula is $\text{Pressure} = \frac{\text{Perpendicular force applied } (F)}{\text{area } (A)}$ .

What is the SI unit of pressure, and after which scientist is it named?

The unit of pressure is Newtons per square meter ($\text{N}\text{m}^{-2}$), which is named the Pascal ($\text{Pa}$) after the French scientist Blaise Pascal ($1\text{ N}\text{m}^{-2} = 1\text{ Pa}$).

Is pressure a scalar or a vector quantity?

Pressure is a scalar quantity because it has only magnitude.

What pressure is exerted by a $400\text{ N}$ box placed on a table with a bottom area of $0.2\text{ m}^2$ ?

The pressure exerted is $2000\text{ Pa}$, calculated as $\text{Pressure} = \frac{400\text{ N}}{0.2\text{ m}^2} = 2000\text{ Pa}$ .

What force is exerted on the ground by a pile of soil distributed over an area of $8\text{ m}^2$ exerting a pressure of $150\text{ Pa}$?

The force exerted is $1200\text{ N}$, calculated as $\text{Force} = \text{Pressure} \times \text{area} = 150\text{ N}\text{m}^{-2} \times 8\text{ m}^2 = 1200\text{ N}$.

What simple experiment demonstrates that water pressure acts in every direction?

Filling a polythene bag with holes with water and holding it shows water exiting through every hole on all sides, demonstrating that liquid pressure acts in every direction.

What does the equal horizontal distance traveled by water streams exiting holes at the same level near the bottom of a bottle demonstrate?

It demonstrates that the pressure at the same level of a liquid is the same.

How does hydrostatic pressure vary with the height or depth of a liquid column?

The pressure in a liquid increases with the depth or vertical height of the liquid column.

Does liquid pressure depend on the shape or the amount of liquid in a container?

No, liquid pressure depends only on the vertical height of the liquid column and does not depend on the shape of the liquid column or the amount of liquid.

What formula is used to calculate the liquid pressure at a point situated at a depth in a liquid?

The formula is $P = h\rho g$, where $h$ is the height of the liquid column, $\rho$ is the density of the liquid, and $g$ is the gravitational acceleration.

What is the pressure at a depth of $1.5\text{ m}$ at the bottom of a lake, given a water density of $1000\text{ kg}\text{ m}^{-3}$ and $g = 10\text{ m}\text{ s}^{-2}$?

The pressure is $15\text{ }000\text{ Pa}$, calculated as $P = 1.5\text{ m} \times 1000\text{ kg}\text{ m}^{-3} \times 10\text{ m}\text{ s}^{-2} = 15\text{ }000\text{ Pa}$.

What pressure is exerted by sea water at a depth of $10\text{ m}$ if the sea water density is $1050\text{ kg}\text{ m}^{-3}$ and $g = 10\text{ m}\text{ s}^{-2}$?

The pressure is $105\text{ }000\text{ Pa}$, calculated as $P = 10\text{ m} \times 1050\text{ kg}\text{ m}^{-3} \times 10\text{ m}\text{ s}^{-2} = 105\text{ }000\text{ Pa}$.

Why can pressure exerted at one point in a liquid be transmitted to another point in the liquid?

Because liquids do not get compressed by forces exerted on them.

In a hydraulic press, if a force of $20\text{ N}$ is applied on piston A of area $10\text{ cm}^2$, what force is exerted on piston B of area $200\text{ cm}^2$?

The transmitted pressure is $2\text{ N}\text{ cm}^{-2}$ ($20\text{ }000\text{ N}\text{ m}^{-2}$), generating a total force of $400\text{ N}$ on piston B ($2\text{ N}\text{ cm}^{-2} \times 200\text{ cm}^2 = 400\text{ N}$).

Why is the small piston replaced by a compressor in actual hoists used in vehicle service stations?

Because lifting a vehicle using a small piston requires moving it over a large distance, which is difficult, so a compressor pumps oil directly into the cylinder instead.

In a vehicle brake system, why is the force applied on the brake pads greater than the force applied on the brake pedal by the driver?

Because the cross-sectional area of the slave cylinder near the wheel is larger than that of the master cylinder.

What are the two ways in which pressure can be produced by a gas?

1. By the weight of a column of gas (producing atmospheric pressure). 2. When a compressed gas attempts to expand.

What is atmospheric pressure, and who first measured it?

Atmospheric pressure is the pressure existing at any point in the atmosphere due to the weight of the air column above that point. It was first measured by the Italian scientist Torricelli.

What is the height of the mercury column inside a mercury barometer that balances atmospheric pressure at sea level?

The height of the mercury column is about $76\text{ cm}$ (or $76\text{ cm Hg}$).

What exists in the empty space above the mercury column in a mercury barometer?

A vacuum exists in that space because no air can enter.

What is the atmospheric pressure at the top of Mount Everest?

The atmospheric pressure at the top of Everest is about $25\text{ cm Hg}$.

How does an aneroid barometer function without containing a liquid?

It contains a cavity with thin metallic walls from which air has been evacuated. Variations in external atmospheric pressure change the shape of the cavity walls, which rotates an attached indicator along a scale.

How does drinking through a straw depend on atmospheric pressure?

Sucking air reduces the pressure inside the straw. The higher atmospheric pressure acting on the liquid surface outside pushes the liquid up into the straw.

What is the atmospheric pressure at sea level in Pascals, given a mercury column height of $76\text{ cm}$, mercury density of $13600\text{ kg}\text{ m}^{-3}$, and $g = 10\text{ m}\text{ s}^{-2}$?

The pressure is $103\text{ }360\text{ Pa}$, calculated as $P = \frac{76}{100}\text{ m} \times 13600\text{ kg}\text{ m}^{-3} \times 10\text{ m}\text{ s}^{-2} = 103\text{ }360\text{ Pa}$.

What height of a water column can be balanced by an atmospheric pressure of $103\text{ }360\text{ Pa}$ given a water density of $1000\text{ kg}\text{ m}^{-3}$ and $g = 10\text{ m}\text{ s}^{-2}$?

The height is $10.3360\text{ m}$, calculated as $h = \frac{103360}{1000 \times 10} = 10.3360\text{ m}$.

What is upthrust?

Upthrust is the upward force exerted by a fluid on an object that is immersed or floating in that fluid.

What occurs when the upthrust acting on an object fully immersed in a fluid is less than the weight of the object?

The object sinks in the fluid.

What occurs when the upthrust acting on an object fully immersed in a fluid is equal to the weight of the object?

The object floats in the fluid while being fully submerged in it.

What occurs when the upthrust acting on an object fully immersed in a fluid is greater than the weight of the object?

The object floats while partially submerged so that the upthrust acting on it equals the weight of the object.

What is a hydrometer, and according to which principle is it constructed?

A hydrometer is a glass instrument used to measure the density of liquids and solutions, constructed in accordance with Archimedes' principle.

Why does a hydrometer immerse deeper in a low-density liquid than in a high-density liquid?

Because a low-density liquid requires a larger volume of liquid to be displaced to produce the required upthrust to balance the hydrometer's weight.