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Lesson 2 - Pressure in a liquid at rest

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Paste specification here

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  • Start
    • Formula recall questions
  • Main
    • Bottle with holes at different depths demo
    • Derive equation for pressure on a liquid and complete questions.
    • Explain liquid flow
    • Liquid density measurement
    • Explanation of manometer operation
    • Practice questions
  • Plenary
    • Video - 5 minutes long

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Demo - Change of pressure with depth

Safety

  • Use of laser near water - for obvious reasons take care not to get the laser wet.

Aim

  • Students can see that the pressure in a liquid increases with depth.

Top tips

  • Check the blu tack is well stuck over the holes in the bottle before you start to fill it.
  • Have the bottle in or near a sink!
  • If you are doing the demo with the laser pointer it’s better to darken the room first.

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Method

  • Fill first bottle with blu-tack stuck over the 3 holes in the side.
  • Place the bottle at the edge of the sink.
  • Remove blu tack - starting at the top.
  • Jets of water will spray out further at the bottom of the bottle because the water there is under a higher pressure.
  • Second bottle has lots of holes at the same height to show the pressure is the same at all points around the bottle at the same height.
  • Optional - You can use the laser pointer to show the principle of optical; fibres and total internal reflection - see picture.
  • Let the water fall into your hand so students can see that the laser light bends and travels to the end of the stream of water.

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Lesson 2 - Pressure in a liquid at rest

Recall:

Give the formula for:

  • Pressure
  • Density

Give the units of:

  • Pressure
  • Density
  • Specific heat capacity

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Lesson 2 - Pressure in a Liquid at Rest

Check your answers

Give the formula for:

  • Pressure = F/A
  • Density = m/V

Give the units of:

  • Pressure - Pa
  • Density - kg/m3
  • Specific heat capacity - J/kg°C

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Lesson 2 - Pressure in a Liquid at Rest

Learning objectives:

  • To use the concept of force, mass and volume to explain why the pressure increases with depth in a liquid.
  • To calculate the pressure at a point in a liquid using p = h ρ g.
  • To rearrange the equation p = h ρ g to solve a range of questions involving the pressure in a liquid

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Demo - what does this tell you about how pressure is related to depth?

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Calculating pressure in a fluid

  1. Write down the formula for calculating the mass of water in the cylinder.

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  • How do we need to change this to calculate the weight of the water?

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  • What pressure would the water exert on the bottom of the container?

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Mass = volume x density

So m = Ahρ

W = mg

So W = Ahρg

Pressure = Force/Area

So p = Ahρg

A

p = hρg

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Pressure in fluids

Pressure = depth of fluid x density of fluid x gravitational field strength

p=hρg

What are the units?

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Questions

g = 9.8N/kg, ρfresh water= 1000kg/m3, ρsea water= 1050kg/m3

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  1. What is the increase in pressure on a diver who descends from the surface of a lake to a depth of 10m?

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  • How far under the surface of the sea would the diver need to descend to experience the same pressure?

p = 10 x 1000 x 9.8 = 98,000 Pa = 98kPa

h = p/ρg = 98000/(1050 x 9.8) = 9.5m

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Why do liquids flow?

Imagine we could get water to do this:

  • How would the pressure at A compare to the pressure at B?
  • Imagine a tiny cube of water between A and B what would this pressure difference cause it to do?

A

B

A

B

  • So what must be acting on it?
  • Why doesn’t this happen in solids?

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Why do liquids flow?

  • Pressure at A is higher than B due to more water above it, therefore there is a resultant force acting on the cube of water, making it accelerate to the right.
  • This does not happen in solid because chemical bonds provide enough force to balance out the force caused by the pressure difference. So no resultant force, therefore no acceleration.

A

B

A

B

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Why do liquids flow?

Liquids flow until the pressure along a horizontal line is equal

High

Pressure

Low

Pressure

Equal pressure along a horizontal line

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Measuring density

Why does the pipe need to have a constant cross section?

How does it help us measure density?

Does oil or water have the highest density?

How can you tell?

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How could we use this to work out the air pressure in the balloon?

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Measuring gas pressure

This is a manometer, it is a pressure gauge used to measure the pressure of a gas.

The pressure of the gas from the gas tap changes the levels of water in the U-tube.

The pressure in the gas can be found by measuring the difference in height of the water levels on either side of the U-tube.

The pressure is proportional to the height difference (h) and is calculated using the equation p=hρg

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Manometer

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A = 0.0006m

h = 0.09m

ρ = 1000kg/m3

g = 9.8 N/kg

3a: pfluid = hρg

pfluid = 0.09 x 1000 x 9.8 = 882 Pa

3b: psurface = F/A

Rearrange:

F = p x A

F = 882 x 0.0006 = 0.53N (why 2 s.f?)

What do we know?

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Check your notes:

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Only depth affects pressure

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Logos / symbols

pressure, density, mass