Pressure in fluids

An object moving through a fluid experiences a drag force due to the viscosity of the fluid.

Some liquid chocolate is poured into a mould. Within the chocolate a bubble of air is formed. The bubble has negligible weight and moves upwards at a constant speed, as shown.

Calculate the constant speed at which the air bubble moves upwards in the liquid chocolate.

radius of air bubble = 6.8 10^–3m density of liquid chocolate = 925 kg m^–3 viscosity of liquid chocolate = 52.6 Pa s

The viscosity of a gas increases with temperature.

It is suggested that the relationship between viscosity η and temperature T is of the form

where A and B are constants.

Explain why a graph of log η against logT would give a straight line.

The table shows data for the viscosity of hydrogen gas over a range

Plot a graph of log η against logT. You should use the columns provided to show any processed data.

Determine values for A and B. You are not required to state the units of A.

Helium is available in small metal canisters. The helium can be used to fill party balloons.

A full canister contains helium gas at a temperature of 18.5C and a pressure of 1.65×10⁷Pa. The canister is approximately spherical, with a radius of 4.3610^–2m.

Calculate the mass of helium gas in the full canister.

mass of 6.02×10²³ atoms of helium = 4.00×10^–3kg

Student X and Student Y discuss the weight of the canister and its contents after a number of balloons have been filled.

Student X suggests that the weight will have increased, because the upthrust exerted on the canister by the helium will be reduced.

Student Y suggests that the weight will have decreased, because helium has been released from the canister.

Assess which student’s suggestion is correct.

A sphere of radius r is made from material of density ρ_M. The sphere is fully immersed in a liquid of density ρ_L. Which of the following expressions gives the upthrust on the sphere?

A raindrop is falling through the air with an increasing velocity. The forces on the raindrop are weight W, upthrust U and viscous drag F.

Which of the following shows the relationship between these forces?

A student investigated the terminal velocity of steel spheres falling through oil.

The student obtained the following results.

radius of steel sphere = 1.50 mm volume of steel sphere = 1.41 10⁻⁸m³ mass of steel sphere = 1.10 10⁻⁴kg maximum speed of sphere = 0.849 m s⁻¹

The student had the following table.

Identify which type of oil the student used.

The values in the table are for oil at 26 °C.

Explain the effect of carrying out the investigation with oil at a lower temperature.

A student is investigating a ‘Cartesian diver’.

The diver is made from a plastic pipette. When placed in a plastic bottle full of water the diver rises to the top and touches the lid.

Show that the downward force of the lid on the diver is about 0.02 N.

volume of diver = 8.010^–6m³

mass of diver = 0.0059 kg

density of water = 1.010³kg m^–3

When the pressure is increased by squeezing the bottle, water is forced into the diver increasing its weight. The diver sinks, then remains at rest in the position shown.

The volume of air in the empty pipette in part (a) was 8.010^–6m³.

Show that the volume now occupied by the air is about 610^–6m³.

The pressure of the air in the empty pipette in part (a) was 1.0110⁵Pa.

Calculate the pressure of the air in part (b).