Video: Fluid Pressure

A scuba diver dives to a depth of 1.25 m below the surface of the sea. The sea water has a density of 1025 kg/m³. What pressure does the water exert on the diver, to the nearest pascal?

02:51

Video Transcript

A scuba diver dives to a depth of 1.25 metres below the surface of the sea. The seawater has a density of 1025 kilograms per metres cubed. What pressure does the water exert on the diver to the nearest pascal?

Okay, so in this question, we’re talking about the sea. So let’s say this is the surface of the sea. And specifically, we’re talking about a scuba diver who’s dived to a depth of 1.25 metres below the surface. Now we’ve also been told that the seawater has a density of 1025 kilograms per metre cubed. What we’ve been asked to do is to find out the amount of pressure exerted by the water onto the diver to the nearest pascal.

To do this, we can use the equation used to find the pressure exerted by a liquid onto an object immersed in that liquid. The equation in question is that the pressure exerted by the liquid on the object is equal to the density of the liquid multiplied by the gravitational field strength of the planet that they’re on, in this case Earth, multiplied by the depth of that object below the surface of the liquid.

Now since we’ve been asked to find out the pressure, we don’t need to rearrange this equation. All we need to do is to sub in the values. So the pressure exerted on the diver by the water is equal to the density of the liquid first of all — the liquid in this case is the water, and we’ve been told this density is 1025 kilograms per metres cubed — multiplied by the gravitational field strength of Earth, which we can recall is a constant 9.8 metres per second squared. So we plug that into our equation. And we also need to multiply it by the depth of the diver below the surface of the water. That’s 1.25 metres.

Now before we evaluate the right-hand side of the equation, we also need to remember that we’re working in standard units. For example, the standard unit of density is kilograms per metres cubed. So we’ve got this in standard units. The standard units of gravitational field strength is metres per second squared. So we’ve also got this in standard units. And the standard units of depth or length is metres. So yet again, we’ve got this in standard units.

What this means is that if all the quantities on the right-hand side are in their standard units, then the quantities on the left-hand side, specifically the pressure, will also be in standard units, which in this case for pressure is pascals. So when we evaluate the right-hand side, we’ll find the answer in pascals. And actually doing this gives us a value of 12556.25 pascals.

However, this is not our final answer. Remember, we’ve been asked to give our answer to the nearest pascal. So we need to round. Specifically, we need to round this value here. So we look at the next one, this two, to see what happens to the six. Now the value after the decimal point, this two, is less than five. Therefore, our six is not going to round up. It’s gonna stay the same. And hence, we found our final answer. The pressure exerted by the water on the diver to the nearest pascal is 12556 pascals.

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