Force and Pressure

This chapter asks whether solids obey Pascal’s principle and what problems arise in an aeroplane if its hydraulic system is damaged p. 220. Light motor vehicles such as cars use hydraulic brakes, while heavy vehicles such as buses and lorries use air brakes, and both apply Pascal’s principle p. 221.

8.1 Pressure in Fluids

An enclosed system is a physical system where matter cannot enter or leave the system p. 222. In a closed plastic bottle with holes, water from the bottommost hole shoots out the furthest because of the pressure in the water p. 222. When the bottle is compressed, water from each hole shoots further by an equal additional distance p. 222. Pascal’s principle states that pressure exerted on a fluid (liquid or gas) in an enclosed system is transmitted uniformly throughout the fluid and in all directions p. 222. In Activity 8.1, water is pushed out of a round-bottom flask with fine pores by a piston and shoots out in all directions p. 223.

The basic principle in a hydraulic system is the transmission of pressure in all directions based on Pascal’s principle p. 223. A hydraulic system has two pistons of different surface areas, and water or oil is used because they do not have a fixed shape and cannot be compressed p. 223. The pressure exerted by the small piston is the same as the pressure produced at the large piston p. 224. So a 10 N input force on a 2 cm² piston produces a 500 N output force on a 100 cm² piston p. 224.

The hydraulic jack, hydraulic brake and dental chair are three examples of Pascal’s principle in daily life p. 224. In a hydraulic jack, the lever is moved downwards and upwards repeatedly with the release valve closed to push the loaded large piston upwards p. 224. When the lever is moved down, valve A closes and valve B opens, and the liquid transmits its pressure to the large piston p. 225. When the release valve is opened, the loaded large piston pushes the liquid back into the reservoir and returns to its original position p. 225.

In a hydraulic brake, pressing the brake pedal pushes the master cylinder piston, and the brake oil transmits the pressure uniformly through metal pipes to the brake cylinders p. 226. In the disc brake at the front wheel, the brake pad presses onto the steel plate, while in the drum brake at the back wheel, the brake shoe presses on the brake lining p. 226. The frictional force slows down or stops the rotation of the wheels p. 226. The operation of the dental chair is also related to the hydraulic system p. 226.

In a fluid that is not flowing, the fluid pressure is the same at every point p. 227. A Venturi tube is a non-uniform tube with a narrower centre, and when the fluid flows, its velocity is highest at the narrow part p. 227. The narrower the part of the Venturi tube, the lower the pressure in the fluid, which is known as the Venturi effect p. 227. In Activity 8.2, the water levels in tubes X, Y and Z are compared before and after water flows through the Venturi tube p. 228.

Bernoulli’s principle states that a fluid moving at a higher velocity produces a lower pressure in that region p. 228. The lift on an aeroplane wing comes from the aerofoil shape and the angle of attack p. 229. In a Bunsen burner, high velocity gas has low pressure, so air is sucked in p. 229. Helicopters and drones get lift from high velocity airflow and low air pressure above their blades p. 229. Between a moving train and a person near the safety lines, the airflow is fast and the air pressure is low, so a person beyond the safety lines can be pushed towards the train p. 229. Activity 8.4 asks you to design a tool such as a crane that lifts heavy loads using the hydraulic system p. 230.