In this video, we're going to look at how to calculate the pressure in a liquid, and see how it varies with depth. We'll also cover what determines whether an object floats or sinks. Now, pressure in a liquid is a bit of a weird one. If you place an object in some water, then most of the pressure acting on that object will be due to all of the surrounding water molecules.
that are constantly colliding with it. However, a small component will be due to the weight of all the water above the object, which will be felt as a downwards force. As the object moves deeper and deeper though, the amount of pressure due to the weight will increase, as there will be more and more water above the object. Another important factor that determines the pressure is the density of the liquid. because the denser the liquid, the larger its mass per unit of volume, and so the larger its weight will be.
And the last factor is the gravitational field strength, as this is what determines the weight for a given mass. So a bigger gravitational field strength would mean a larger weight. We can see all of this. If we look at the equation for pressure in a liquid, this tells us that the pressure measured in pascals is equal to the height of the column of liquid above the object, which is basically just the depth, times the density of the liquid, times the gravitational field strength.
To see how this works, let's try a question. A person dives from a depth of 20 meters to a depth of 90 meters. Given that the density of water is 1000 kilos per meter cubed, calculate the change in pressure acting on the person.
So this is really two questions in one. We're first going to have to calculate the pressure at the two depths and then find the difference between the two of them. At 20 meters, The pressure would be 20 meters times the density of 1000 times 9.8, which is the gravitational field strength here on earth.
This gives us 196,000 pascals. Meanwhile for 90 meters, we do 90 times 1000 times 9.8, which gives us 882,000 pascals. So the difference in pressure is just 882,000 minus 196,000, so 686,000 pascals.
Alternatively, because the difference in depth was 90 minus 20, so 70 meters, we could have just done 70 times 1,000 times 9.8, and we still have got the same answer of 686. thousand pascals. The next thing we need to look at is why some objects float while others sink, and for this we need to understand upthrust. Let's imagine that we have a box that's submerged in water. Due to the eclations of all the tiny water molecules around the box, the surrounding water will exert forces on the box from all directions. Because the bottom of the box is deeper than the top though, the box will experience a larger upwards force from the bottom than it will a downwards force from the top.
This means that overall there will be a resultant force upwards, which pushes the box up, and it's this upwards force that we refer to as the upthrust. If that was the whole story then everything would float, as all submerged items have upthrust. Importantly though, there's also the object's weight to consider, as that acts downwards, and so pulls the object down.
So really, it's all about whether the upthrust or the weight is larger. If the weight is larger, like we've shown with these arrows, then the object sinks. But if the upthrust is larger, then it floats.
Now luckily for us, Instead of actually calculating the upthrust and weight of the object every time, all we need to know is the density of the object and the density of the liquid that it's in. If the object is more dense, like a rock, then the object would sink. But if it's less dense, like an apple, then it will float. Anyway...
that's everything for this video so hope you found it useful and we'll see you soon