5.5 Pressure & Pressure Differences in Fluids

Figure 1 shows a cylindrical container which has a base of diameter of 0.15 m and is filled with water to a depth of 0.35 m.

Figure 1

The mass of the water is 6.2 kg.

Calculate the weight of the water in the container.

Calculate the pressure due to the liquid on the base of the container. State the unit.

The water-filled cylinder is placed on a laboratory bench.

Suggest why the total pressure on the bench is higher than the value calculated in part (b).

Higher Only

A bead of hollow glass is dropped into the water and comes to rest floating 12 cm above the base of the cylinder as shown in Figure 2.

Calculate the total pressure on the bead.

Atmospheric pressure at sea level = 1.01 × 10⁵ Pa

Density of water = 1000 kg/m³

Higher Only

Figure 1 shows a hollow metal cylinder containing air, floating in the sea. The density of the metal used to make the cylinder is greater than the density of seawater.

Figure 1

Explain why the cylinder floats.

The cylinder has a length of 1.8 m. It floats with 1.2 m submerged in the sea. The bottom of the cylinder has a cross-sectional area of cross-section of 0.80 m².

 
The density of seawater is 1020 kg/m³. Calculate the force exerted on the bottom of the cylinder due to the depth of the seawater.  

force = ....................................................... N

Deduce the weight of the cylinder. Explain your answer.

Pressure difference in water can be demonstrated using the apparatus shown in Figure 2. The apparatus is hollow and has three short tubes at different depths. When the tube is completely filled with water, water comes out of all the tubes. 

Figure 2

Complete Figure 2 by drawing the paths of water you would expect to see from the other two tubes. Explain why you have drawn this pattern.

The Dead Sea contains some of the most saline (salty) water on Earth, with a density (on the surface) of around 1250 kg/m³.

State the relationship between the pressure of a liquid, gravitational field strength, density of the liquid and depth.

Calculate the pressure exerted by the water at a depth of 20m.

The gravitational field strength is 10 N/kg.

Show your working and include a unit with your answer.

A pressure gauge sinks to the bottom of the Dead Sea.

On the bottom it gives a reading of 5 000 000 Pa.

Use the above reading to estimate the depth of the Dead Sea.

Show your working and include a unit with your answer.

In actual fact, the actual depth of the Dead Sea is less than the figure calculated from the above pressure.

What does this imply about the average density of the water compared to the figure given at the start of this question?

Table 2 below gives some data showing how atmospheric pressure varies with altitude above sea level.

Table 2

Explain why atmospheric pressure decreases when the altitude increases.

Plot a graph of atmospheric pressure (y-axis) again altitude (x-axis).

Include an appropriate line of best fit.

Commercial aircraft typically fly at altitudes of around 10 km.

Use your graph to estimate the atmospheric pressure at this height.

Atmospheric pressure  =  _____________ kPa

The pressure inside an aircraft is usually kept at around 80 kPa.

The doors to the aircraft have an area of around 2.0 m².

Calculate the resultant force acting on the door at an altitude of 10 km.

Figure 3 shows two of the forces acting on a submerged balloon, which is travelling upwards through water at a constant velocity.

Figure 3

One of the forces acting on the balloon is missing from the diagram.

Add a further labelled arrow to the diagram to show the relative size and direction of this force.

Explain, in terms of pressure, why the water exerts upthrust on the balloon.