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How is pressure distributed in a liquid?


Oh, no! Jenny’s got a flat tyre. She’ll need to lift the car to change the tyre. How can she lift something as heavy as a car? On her own, Jenny isn't strong enough — she can't produce enough force — to lift a car.

But luckily, she’s got a jack, which she can use to lift the car easily. The jack uses a liquid to multiply forces. It uses a hydraulic system. Let’s see how it works! First, we need to remember three things about liquids and pressure.

One, liquids cannot be squeezed to take up less space. Fill up a syringe with water. Cover the opening with your finger and try to press the syringe’s plunger. You can feel the pressure build up in the syringe, but the plunger doesn’t move. The plunger only moves when you remove your finger from the opening and the water can flow out.

The volume of a liquid doesn’t change under pressure — we say that liquids are incompressible. Two, force applied from one side creates equal pressure everywhere, inside a liquid. When you press the plunger of a full syringe, pressure spreads evenly through the liquid and onto the walls of the syringe. Pressure in liquids is transmitted equally in all directions. Three, pressure is equal to force divided by the area to which the force is applied.

Now — how do these properties play a role in Jenny's hydraulic car jack? The jack has two cylinders connected to each other. Each cylinder is filled with liquid and contains a metal part that can slide up and down: a piston. One of the cylinders is much smaller than the other one. When Jenny presses the lever on the jack, the piston inside the smaller cylinder presses the liquid in it.

The liquid cannot be compressed, so it moves to the other cylinder, and pushes the larger piston upwards. The pressure also spreads evenly throughout the liquid. So, because the two cylinders are connected, the pressure in the bigger cylinder has to be equal to the one in the smaller cylinder. However, the cylinders and pistons have different surface areas, so the force acting on each piston differs. How much does it differ?

Let’s use the pressure formula to see! The force Jenny applies to the smaller piston is 200 newtons. The area of the small piston is 0.1 m2 [square meters]. The pressure she created is 200 newtons divided by 0.1 m2 [square meters] – 2000 pascals. The area of the bigger piston is 0.8 m2 [square meters].

The pressure exerted on the big piston is 2000 pascals. So, the force exerted on the area of the big piston is 2000 pascals times 0.8 m2 [square meters], which equals 1600 newtons. On her side, Jenny applied a force of 200 newtons, which became 1600 newtons on the other side. The force has been multiplied! Every time Jenny pushes the lever, she increases the pressure in the liquid, which in turn increases the force of the bigger piston that slowly lifts the car!

Hydraulic systems like the one in the car jack, have many applications: from machines such as cranes and excavators, to car brakes and ferris wheels. And it’s not even that much effort, the liquid does all the hard work for me!