Pressure in Fluids
ICSE Class 9 · Physics · Chapter 4
What this chapter covers
- Fluids
- Thrust and pressure
- Pressure exerted by a liquid column
- Factors affecting pressure in a stationary fluid: daily-life consequences
- Transmission of pressure in liquids: Pascal's law
Key points
- Fluids (liquids and gases) can flow and take the shape of their container.
- Thrust is the normal force on a surface (N); pressure is thrust per unit area (Pa = N m-2). 1 Pa = 10 dyne cm-2.
- For the same thrust, a smaller area gives a larger pressure: sharp knives, pointed nails, broad straps and wide sleepers.
- Pressure due to a liquid column: p = hρ g, independent of the shape and base area of the vessel.
- Pressure increases with depth, acts equally in all directions at a point, is equal at the same depth, and is greater in a denser liquid.
- A liquid at rest finds its own level in connected vessels.
- Dams have broad bases, tank walls are thicker at the bottom, and divers wear strong suits, all because pressure grows with depth.
- Pascal's law: pressure applied to an enclosed liquid is transmitted equally and undiminished in all directions.
- F1 / a = F2 / A: a small force on a small piston produces a large force on a large piston.
Questions answered
Define a fluid. Give one example each of a liquid and a gas.
A fluid is a substance that can flow and takes the shape of its container. Water is a liquid; air is a gas.
Distinguish between thrust and pressure, and give their SI units.
Thrust is the normal force on a surface, measured in N; pressure is the thrust per unit area, measured in Pa (N m-2).
Why are the straps of a school bag made broad?
A broad strap spreads the weight over a larger area of the shoulder, reducing the pressure.
Express 1 Pa in dyne cm-2.
1 Pa = 105 dyne ÷ 104 cm2 = 10 dyne cm-2.
Derive the expression for the pressure at a depth h in a liquid of density ρ.
A column of area A and height h has weight Ahρ g; dividing by A gives p = hρ g.
Name three factors on which the pressure in a liquid depends, and one on which it does not.
It depends on the depth, the density of the liquid and g; it does not depend on the shape of the vessel or the area of its base.
Why is a dam made broader at the bottom?
Water pressure increases with depth, so the thrust on the dam is greatest near its base, and a broad base is needed to withstand it.
Why must a deep-sea diver wear a special suit?
The water pressure at great depth is very large; the suit withstands it and protects the diver's body.
Past board exam questions
ICSE 2019 sample paper · 2 marks
A body is completely immersed in a fluid. State two factors on which the upthrust acting on the body depends.
Show answer
1. The volume of the body immersed in the fluid (here the whole volume of the body).
2. The density of the fluid.
(Also the acceleration due to gravity: upthrust = V ρ g.)
ICSE 2019 sample paper · 2 marks
Name and state the principle on which the hydraulic brakes of a car work.
Show answer
Pascal's law: the pressure exerted anywhere in an enclosed liquid is transmitted equally and undiminished in all directions throughout the liquid.
ICSE 2019 sample paper · 3 marks
The area of pistons in hydraulic machine are 6 cm² and 576 cm². What force on the smaller piston will support a load of 1152 N on the larger piston? State the assumption made in the above calculation.
Show answer
By Pascal's law the pressure on both pistons is equal:
(F1)/(A1) = (F2)/(A2) ⇒ F1 = 1152 × (6)/(576) = 12 N.
Assumption: there is no friction (and no leakage) in the machine, the liquid is incompressible, and the pressure is transmitted undiminished (the pistons are at the same level and their weights are neglected).
ICSE 2019 sample paper · 3 marks
(i) Why does a piece of steel sink in water but float on mercury? (ii) If a bowl is formed from the same steel piece then it can float in water. Why?
Show answer
(i) The density of steel (about 7.8 g cm⁻³) is greater than that of water (1 g cm⁻³), so the upthrust of water on the piece is less than its weight and it sinks. The density of mercury (13.6 g cm⁻³) is greater than that of steel, so the piece floats on mercury when it is partly immersed and the upthrust equals its weight.
(ii) When made into a bowl, the steel encloses air, so its average density (mass ÷ total volume) becomes less than that of water. It displaces a much larger volume of water, so the upthrust becomes equal to its weight before it is fully immersed and the bowl floats.
ICSE 2019 sample paper · 4 marks
A metal piece weighs 200 gf in air and 150 gf when completely immersed in water. (i) Calculate the relative density of the metal piece. (ii) How much will it weigh in a liquid of density 0.8 gcm⁻³?
Show answer
(i) Loss of weight in water = 200 − 150 = 50 gf.
R.D. = weight in air ÷ loss of weight in water = 200 ÷ 50 = 4.
(ii) Volume of the piece = 50 cm³ (it displaces 50 g of water). Upthrust in the liquid = 50 × 0.8 = 40 gf.
Weight in the liquid = 200 − 40 = 160 gf.