Pressure & Pressure Differences in Fluids Flashcards

All 32 cards in this deck

What is a fluid?

A substance that can flow — a liquid or a gas.

Why does atmospheric pressure decrease with height above the Earth's surface?

There are fewer air molecules above you, so less weight of air pushing down; the air is also less dense higher up.

What causes the total pressure at a point in a liquid such as the sea?

The pressure due to the liquid above that point plus atmospheric pressure pushing down on the surface.

True or false? The atmosphere has the same density at all heights.

False. The atmosphere is densest near the Earth's surface and gets less dense with height.

True or false? At sea level a diver at the water surface experiences zero pressure.

False. Atmospheric pressure still acts on them, about $100\,000$ Pa.

In which direction does the pressure in a fluid act on a surface?

It produces a force acting normal (at right angles) to the surface.

What is the equation linking pressure, force and area?

$\text{pressure} = \dfrac{\text{force normal to surface}}{\text{area of that surface}}$, i.e. $P = \dfrac{F}{A}$

What are the units of pressure, force and area in $P = F \div A$?

Pressure in pascals (Pa), force in newtons (N), area in metres squared (m$^2$).

What are the steps to calculate pressure from a force and an area given in cm²?

e.g. a force of $60$ N normal to an area of $200$ cm²

1. Convert the area to m$^2$ by dividing by $10\,000$: $200 \div 10\,000 = 0.02$ m$^2$
2. Divide force by area: $P = 60 \div 0.02$
3. Pressure $= 3000$ Pa

Why does a sharp blade cut more easily than a blunt one for the same force?

Its smaller contact area gives a much greater pressure, since $P = F \div A$.

In a hydraulic system, why is the output force on the wide piston larger than the input force on the narrow piston?

The pressure in the oil is the same throughout, and the wide piston has a larger area, so $F = P \times A$ is greater.

True or false? Snowshoes stop a walker sinking into snow because they reduce the walker's weight.

False. They increase the contact area, which reduces the pressure on the snow; the weight is unchanged.

How does the pressure in a liquid change as you go deeper?

It increases with depth, because there is a greater weight of liquid above pushing down.

How does the density of a liquid affect the pressure at a given depth?

A denser liquid gives a greater pressure, because the column of liquid above has more mass and so more weight.

True or false? At the same depth in a liquid, the pressure is the same in all directions.

True. The pressure at a point acts equally in all directions, giving a force normal to any surface there.

True or false? The pressure at the bottom of a container of water depends on the width of the container.

False. It depends only on the depth, the density of the liquid and $g$ (plus atmospheric pressure).

Why are dam walls built thicker at the bottom than at the top?

Water pressure increases with depth, so the force on the wall is greatest at the bottom.

What is the equation for the pressure due to a column of liquid?

$P = h \times \rho \times g$ — pressure = height (depth) of column $\times$ density $\times$ gravitational field strength.

State the units of each quantity in $P = h \rho g$.

$P$ in Pa, $h$ in m, $\rho$ in kg/m$^3$, $g$ in N/kg.

What are the steps to calculate the pressure due to a column of liquid?

e.g. water of density $1000$ kg/m$^3$ at a depth of $3$ m, $g = 10$ N/kg

1. Select $P = h\rho g$
2. Substitute: $P = 3 \times 1000 \times 10$
3. Pressure $= 30\,000$ Pa

What are the steps to find the depth $h$ from a pressure due to a liquid?

e.g. $P = 20\,000$ Pa in water, $\rho = 1000$ kg/m$^3$, $g = 10$ N/kg

1. Write $P = h\rho g$ and substitute: $20\,000 = h \times 1000 \times 10$
2. Rearrange: $h = \dfrac{20\,000}{1000 \times 10}$
3. $h = 2$ m

What are the steps to find the difference in pressure between two depths in a liquid?

e.g. between $2$ m and $5$ m deep in water ($\rho = 1000$ kg/m$^3$, $g = 10$ N/kg)

1. Find the difference in depth: $5 - 2 = 3$ m
2. Use $\Delta P = \Delta h \times \rho \times g = 3 \times 1000 \times 10$
3. Difference in pressure $= 30\,000$ Pa

True or false? In $P = h\rho g$, $h$ is the total height of the container.

False. $h$ is the depth of the point below the surface of the liquid.

Does $P = h\rho g$ give the total pressure at a depth in an open tank?

No — it gives only the pressure due to the liquid; add atmospheric pressure for the total.

What is upthrust?

The upward force that a fluid exerts on an object immersed in it.

Why does a fluid exert an upthrust on a submerged object?

The pressure at the bottom of the object is greater than at the top, so the upward force on the bottom is greater than the downward force on the top.

What is the upthrust on an object equal to?

The weight of the fluid displaced by the object.

What condition on upthrust and weight makes an object float?

It floats if the upthrust can equal its weight; it sinks if its weight is greater than the maximum upthrust.

How do densities tell you whether an object will float in a liquid?

It floats if its density is less than the density of the liquid, and sinks if its density is greater.

True or false? Objects in air experience no upthrust.

False. Air is a fluid, so it gives an upthrust — it is just very small because air has a low density.

What happens to the upthrust on an object as it is lowered further into water, while still only partly immersed?

The upthrust increases, because more water is displaced.

True or false? Once an object is completely submerged, lowering it deeper into the same liquid increases the upthrust on it.

False. The volume of liquid displaced no longer changes, so the upthrust stays the same.