Atmospheric Pressure and Archimedes' Principle

Lessons

Senior 3 · Physics

Atmospheric Pressure and Archimedes' Principle

5 lessons

Lesson 3 of 5

Applications of Atmospheric Pressure

25 min

Who lifts the juice?

When you drink juice through a straw, it feels as if you are pulling the juice up. You are not: your mouth cannot pull on a liquid. What you do is lower the air pressure inside your mouth and the straw. The atmosphere, still pressing on the surface of the juice in the glass with about 84 kPa in Kigali, then pushes the juice up the straw into the low-pressure space. The same idea, "lower the pressure on one side and let the atmosphere push", explains a whole family of everyday devices.

Straw, syringe, sucker and vacuum cleaner

Device	What you do	What the atmosphere does
Drinking straw	Expand your lungs and cheeks, lowering the pressure in your mouth and straw	Pushes on the drink's surface and forces the drink up the straw
Syringe (filling)	Pull the plunger back, so the space in the barrel grows and its pressure falls	Pushes the liquid through the needle into the barrel
Rubber sucker	Press it flat on a smooth surface, squeezing most of the air out from under it	Presses on the outside of the sucker and holds it against the surface
Vacuum cleaner	A fan inside blows air out of the back, lowering the pressure inside	Air outside rushes in through the nozzle, carrying dust into the bag or filter

In each case the fluid moves, or the object is held, from the region of higher pressure towards the region of lower pressure.

Worked example 1: how long can a straw be?

A strong pupil can lower the pressure in his mouth by about 10 kPa below atmospheric (an illustrative value). How high can he raise water up a straw? Could anyone drink through a straw 10 m long in Kigali?

h = \frac{\Delta p}{\rho\,g} = \frac{10\,000}{1000 \times 9.8} \approx 1.0\ \text{m}

So about 1 m. Even with a perfect vacuum in the mouth, the atmosphere in Kigali could push water up only $\frac{84\,000}{1000 \times 9.8} \approx 8.6\ \text{m}$ , so a 10 m straw could never work there.

Worked example 2: the holding force of a sucker

A rubber sucker of radius 3.0 cm is pressed onto a tile in Kigali (84 kPa). The pressure of the air left under it is 30 kPa. Find the force holding it on.

A = \pi r^{2} = \pi \times 0.030^{2} \approx 2.83 \times 10^{-3}\ \mathrm{m^2}

F = (p_0 - p)\,A = (84\,000 - 30\,000) \times 2.83 \times 10^{-3} \approx 150\ \text{N}

Enough to hold a load of about 15 kg, as long as no air leaks in. On a rough surface air creeps in under the rim, the pressure difference disappears, and the sucker falls off.

Definition

Siphon: a tube, filled with liquid, that carries the liquid from a container up over its rim and down to an outlet lower than the liquid surface, with no pump.

Lift pump (suction pump): a pump that raises water by lowering the pressure above the water in a pipe, so that atmospheric pressure on the water outside pushes it up.

The siphon

Fill the tube with water, close both ends, put one end below the surface in the tank and the other in the lower bucket, and open them. The water keeps flowing, up over the rim and down, until the tank's surface falls to the level of the outlet or the inlet comes out of the water.

Why it works. Consider the top of the bend. On the tank side, the atmosphere pushes the water up with a pressure $p_{0}$ , reduced by the weight of the short column: the pressure there is $p_0 - h_1\rho g$ . On the outlet side, the column is taller, so the pressure at the top of the bend from that side is only $p_0 - h_2\rho g$ . Since $h_{2} > h_{1}$ , the push from the tank side is greater, and the water moves towards the outlet.

Two conditions follow: the outlet must be lower than the liquid surface in the tank, and the top of the bend must be less than $\frac{p_0}{\rho g}$ above that surface (8.6 m for water in Kigali), or the water column breaks.

Warning

Never start a fuel siphon by mouth. Petrol, diesel and paraffin sucked into the mouth can be breathed into the lungs, causing a dangerous pneumonia, and they are poisonous to swallow. Use a siphon hose with a squeeze bulb or hand pump, outdoors, away from any flame.

The lift pump

A lift pump has a barrel with a piston that moves up and down, and two one-way flap valves: one in the piston and one at the bottom of the barrel, above the pipe that reaches down into the well.

Upstroke: the piston rises. Its valve is closed, so it lifts the water above it out through the spout. Below it, the space grows and the pressure falls; atmospheric pressure on the water in the well pushes water up the pipe, through the open bottom valve, into the barrel.
Downstroke: the piston falls. The bottom valve is pushed shut, so the water in the barrel cannot go back down; it forces the piston valve open and passes through to the space above the piston.
The next upstroke lifts this water out of the spout, while more water is pushed up from the well.

Worked example 3: the limit of a lift pump

Find the greatest depth from which a lift pump could raise water (a) at sea level (101 kPa); (b) in Kigali (84 kPa).

\text{(a) } h = \frac{101\,000}{1000 \times 9.8} \approx 10.3\ \text{m} \qquad \text{(b) } h = \frac{84\,000}{1000 \times 9.8} \approx 8.6\ \text{m}

These are theoretical limits for a perfect vacuum above the water; leaking valves and air dissolved in the water mean that a real lift pump works only from a shallower depth. For deeper boreholes, the pump's cylinder is placed down in the water, so that the piston pushes the water up from below instead of relying on the atmosphere.

Tip

Always say who does the pushing. In every one of these devices, something lowers the pressure on one side, and the atmosphere does the work of pushing the liquid or holding the object. The atmosphere can push water up by at most $\frac{p_0}{\rho g}$ : about 10 m at sea level and 8.6 m in Kigali.

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Practice

Explain how you drink through a straw. Why would it not work on the Moon, which has no atmosphere?
Explain how a syringe is filled with medicine from a small bottle.
A sucker has a radius of 2.0 cm. The air pressure under it is 20 kPa and atmospheric pressure is 84 kPa. Find the force holding it on.
Explain why a rubber sucker holds well on glass but not on a rough plastered wall.
State the two conditions needed for a siphon to work.
Farmers sometimes use a siphon to take water from a channel over a bank into a field. Explain why the outlet must be lower than the water surface in the channel.
Describe the actions of the two valves of a lift pump on the upstroke and on the downstroke.
A well is 11 m deep to the water surface. A villager in Kigali says a lift pump fixed at the top will raise water "if we pump hard enough". Evaluate this claim, and suggest what should be used instead.

Show answersHide answers

You lower the pressure in your mouth and the straw; the greater atmospheric pressure on the drink's surface pushes it up the straw. On the Moon nothing presses on the drink's surface, so nothing pushes it up.
Push the plunger in, put the needle in the liquid and pull the plunger back. The space in the barrel grows and its pressure falls, so the pressure in the bottle (atmospheric or greater) pushes the liquid into the syringe.
$F = (84\,000 - 20\,000) \times \pi \times 0.020^{2} \approx 64\,000 \times 1.26 \times 10^{-3} \approx 80\ \text{N}$ .
On smooth glass the rim seals and no air can get under the sucker, so the low pressure beneath it lasts. On a rough wall air leaks in through the gaps, the pressure under the sucker rises to atmospheric, and nothing holds it.
The tube must be full of liquid, and the outlet must be lower than the surface of the liquid in the upper container (with the bend not more than about $\frac{p_0}{\rho g}$ above that surface).
Water flows only if the push on the channel side of the bend ( $p_0 - h_1\rho g$ ) is greater than on the outlet side ( $p_0 - h_2\rho g$ ), which needs $h_{2} > h_{1}$ : the outlet lower than the channel's surface. If the outlet were higher, the water would flow back into the channel.
Upstroke: piston valve closed (lifts the water above the piston out of the spout); bottom valve open (atmospheric pressure pushes water up into the barrel). Downstroke: bottom valve closed (water cannot return to the well); piston valve open (water passes to the space above the piston).
The claim is wrong. Even with a perfect vacuum, atmospheric pressure in Kigali can push water up only about 8.6 m, and a real pump manages less. Pumping harder cannot change the push of the atmosphere. Use a deep-well pump whose cylinder is placed down in the water, or an electric submersible pump.

Key points

Straws, syringes, suckers and vacuum cleaners work by lowering the pressure on one side; the atmosphere does the pushing.
A siphon needs a tube full of liquid and an outlet below the liquid surface; flow is driven by the difference between $p_0 - h_1\rho g$ and $p_0 - h_2\rho g$ .
A lift pump uses two one-way valves; atmospheric pressure pushes water up the pipe.
The atmosphere can raise water at most $\frac{p_0}{\rho g}$ : about 10.3 m at sea level, 8.6 m in Kigali.

Sources and credits

11.6: Gauge Pressure, Absolute Pressure, and Pressure Measurement, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Consulted for the physics; no text was copied.

Written by Ganzaa: the lesson text, the lift-pump and siphon diagrams, the table, worked examples and practice exercises.

1Who lifts the juice?

2Straw, syringe, sucker and vacuum cleaner

3The siphon

4The lift pump

Who lifts the juice?

Straw, syringe, sucker and vacuum cleaner

The siphon

The lift pump